almost equitable partitions and new necessary conditions for network controllability abstract in this paper we consider the controllability problem for multi agent networked control systems the main results of the paper are new graph theoretic necessary conditions for controllability involving almost equitable graph vertex partitions we generalize the known results on the role of graph symmetries and uncontrollability to weighted digraphs with multiple leaders and we also consider the broadcasted control scenario our results show that the internal structure of communities in a graph can induce obstructions to controllability that cannot be characterized by symmetry arguments alone and that in some cases depend on the number theoretic properties of the communities we show via examples that our results can be used to account for a large portion of uncontrollable inducing leader selections that could not have otherwise been accounted for using symmetry results

global leader following consensus of a group of general linear systems using bounded controls this paper studies the global leader following consensus problem for a multi agent system with bounded controls the follower agents and the leader agent are all described by a general linear system both a bounded state feedback control law and a bounded output feedback control law are constructed for each follower agent in the group the feedback law for each input of an agent uses a multi hop relay protocol in which the agent obtains the information of other agents through multi hop paths in the communication network the number of hops each agent uses to obtain its information about other agents for an input is less than or equal to the sum of the number of eigenvalues at the origin and the number of pairs of non zero imaginary eigenvalues of the sub system corresponding to the input and the feedback gains are constructed from the adjacency matrix of the communication network it is shown that global leader following consensus is achieved under these feedback control laws when the communication topology among follower agents is a strongly connected and detailed balanced directed graph and the leader is a neighbor of at least one follower

consensus in networks of multiagents with cooperation and competition via stochastically switching topologies in this brief we provide some theoretical analysis of the consensus for networks of agents via stochastically switching topologies we consider both discrete time case and continuous time case the main contribution of this brief is that the underlying graph topology is more general in both cases than those appeared in previous papers the weight matrix of the coupling graph is not assumed to be nonnegative or metzler that is in the model discussed here the off diagonal entries of the weight matrix of the coupling graph may be negative this means that sometimes the coupling may not benefit but may prevent the consensus of the coupled agents in the continuous time case the switching time intervals also take a more general form of random variables than those appeared in previous works we focus our study on such networks and give sufficient conditions that ensure almost sure consensus in both discrete time case and continuous time case as applications we give several corollaries under more specific assumptions i e the switching can be some independent and identically distributed i i d random variable series or a markov chain numerical examples are also provided in both discrete time and continuous time cases to demonstrate the validity of our theoretical results

controllability of the multi agent system modeled by the threshold graph with one repeated degree abstract the controllability issue of multi agent systems modeled by a special class of graphs is studied suppose the modeling graph is simple connected and driven by only one controller the author shows that the system is controllable if the graph has exactly two vertices with the same degree and either one of these two vertices is selected to receive the control input this result is extended to the case of the threshold graph that has only one repeated degree specifically it is shown that if the threshold graph has only one repeated degree and its multiplicity is m then m 1 is the minimum number of the controllers required to make the system controllable in addition the necessary and sufficient condition that characterizes the binary control vectors to ensure the controllability of the system is derived

upper and lower bounds for controllable subspaces of networks of diffusively coupled agents this technical note studies the controllability of diffusively coupled networks where some agents called leaders are under the influence of external control inputs first we consider networks where agents have general linear dynamics then we turn our attention to infer network controllability from its underlying graph topology to do this we consider networks with agents having single integrator dynamics for such networks we provide lower and upper bounds for the controllable subspaces in terms of the distance partitions and the maximal almost equitable partitions respectively we also provide an algorithm for computing the maximal almost equitable partition for a given graph and a set of leaders

coordination and geometric optimization via distributed dynamical systems this paper discusses dynamical systems for disk covering and sphere packing problems we present facility location functions from geometric optimization and characterize their differentiable properties we design and analyze a collection of distributed control laws that are related to nonsmooth gradient systems the resulting dynamical systems promise to be of use in coordination problems for networked robots in this setting the distributed control laws correspond to local interactions between the robots the technical approach relies on concepts from computational geometry nonsmooth analysis and the dynamical system approach to algorithms

finite time stabilisation of cyclic formations using bearing only measurements this paper studies decentralised formation control of multiple vehicles in the plane when each vehicle can only measure the local bearings of their neighbours by using bearing only sensors since the inter vehicle distance cannot be measured the target formation involves no distance constraints more specifically the target formation considered in this paper is an angle constrained cyclic formation where each vehicle has exactly two neighbours and the angle at each vehicle subtended by its two neighbours is pre specified to stabilise the target formation we propose a discontinuous control law that only requires the sign information of the angle errors due to the discontinuity of the proposed control law the stability of the closed loop system is analysed by employing a locally lipschitz lyapunov function and nonsmooth analysis tools we prove that the target formation is locally finite time stable with collision avoidance guaranteed

nonuniform line coverage from noisy scalar measurements we study the problem of distributed coverage control in a network of mobile agents arranged on a line the goal is to design distributed dynamics for the agents to achieve optimal coverage positions with respect to a scalar density field that measures the relative importance of each point on the line unlike previous work which implicitly assumed the agents know this density field we only assume that each agent can access noisy samples of the field at points close to its current location we provide a simple randomized protocol wherein every agent samples the scalar field at three nearby points at each step and which guarantees convergence to the optimal positions we further analyze the convergence time of this protocol and show that under suitable assumptions the squared distance to the optimal coverage configuration decays as o 1 t with the number of iterations t where the constant scales polynomially with the number of agents n we illustrate these results with simulations

brief paper notes on averaging over acyclic digraphs and discrete coverage control in this paper we study averaging algorithms and coverage control laws in a unified light first we characterize the convergence properties of averaging algorithms over acyclic digraphs with fixed and controlled switching topology second we introduce and study novel discrete coverage control laws which are useful in practical implementations of coverage strategies we characterize the close relationship of the novel discrete control laws with continuous coverage control laws and with averaging algorithms over a class of acyclic digraphs that we term discrete voronoi graphs these results provide a unified framework to model a vast class of distributed optimization problems

dynamical systems that sort lists diagonalize matrices and solve linear programming problems abstract we establish a number of properties associated with the dynamical system h h h n where h and n are symmetric n by n matrices and a b ab ba the most important of these come from the fact that this equation is equivalent to a certain gradient flow on the space of orthogonal matrices we are especially interested in the role of this equation as an analog computer for example we show how to map the data associated with a linear programming problem into h 0 and n in such a way as to have h h h n evolve to a solution of the linear programming problem this result can be applied to find systems which solve a variety of genetic combinatorial optimization problems and it even provides an algorithm for diagonalizing symmetric matrices

leader following consensus of fractional order multi agent systems via adaptive pinning control in this paper the leader following consensus problem of fractional order multi agent systems is considered via adaptive pinning control the dynamics of leader and all followers with linear and nonlinear functions are investigated respectively we assume that the node should be pinned if its in degree is less than its out degree in the paper under this assumption and based on the stability theory of fractional order differential systems some leader following consensus criteria are derived which are easily obtained by matrix inequalities the control of each agent using local information is designed and detailed analysis of the leader following consensus is presented the design technique is based on algebraic graph theory and the riccati inequality several simulation examples are presented to demonstrate the effectiveness of the proposed method

controllability of discrete time multi agent systems with directed topology and input delay this paper investigates the controllability of first order and second order discrete time multi agent systems with directed topology and input delay the problem is studied in the leader follower framework where a number of agents are selected to be leaders and serve as control inputs to all other agents sufficient and necessary conditions are derived for the controllability of first order discrete time multi agent systems with sampling period and feedback gain satisfying certain conditions it is proved under three different protocols that the controllability of second order discrete time multi agent systems is equivalent to that of a pair of submatrices of laplacian matrix in addition the controllability of both first order and second order discrete time multi agent systems with input delay is shown through some transformations to be equivalent to that of the transformed non delayed systems finally some simulation examples are given to illustrate the theoretical results

controllability and observability of network of networks via cartesian products the paper presents a system theoretic analysis framework for a network of networks formed from smaller factor networks via graph cartesian products we provide a compositional framework for extending the controllability and observability of the factor networks to that of the composite network of networks we then delve into the effectiveness of designing control and estimation algorithms for the composite network via its symmetry and gramian structure an example demonstrating the usefulness of our results in the context of social networks with a cartesian product structure is then presented

application of the boundary element method to transient heat conduction an advanced boundary element method bem is presented for the transient heat conduction analysis of engineering components the numerical implementation necessarily includes higher order conforming elements self adaptive integration and a multiregion capability planar three dimensional and axisymmetric analyses are all addressed with a consistent time domain convolution approach which completely eliminates the need for volume discretization for most practical analyses the resulting general purpose algorithm establishes bem as an attractive alternative to the more familiar finite difference and finite element methods for this class of problems several detailed numerical examples are included to emphasize the accuracy stability and generality of the present bem furthermore a new efficient treatment is introduced for bodies with embedded holes this development provides a powerful analytical tool for transient solutions of components such as casting moulds and turbine blades which are cumbersome to model when employing the conventional domain based methods

on the reachability and observability of path and cycle graphs in this technical note we investigate the reachability and observability properties of a network system running a laplacian based average consensus algorithm when the communication graph is a path or a cycle specifically we provide necessary and sufficient conditions based on simple rules from number theory to characterize all and only the nodes from which the network system is reachable respectively observable interesting immediate corollaries of our results are i a path graph is reachable observable from any single node if and only if the number of nodes of the graph is a power of two n 2i i n and ii a cycle is reachable observable from any pair of nodes if and only if n is a prime number for any set of control observation nodes we provide a closed form expression for the unreachable unobservable eigenvalues and for the eigenvectors of the unreachable unobservable subsystem

a decomposition approach to distributed control of spatially invariant systems this note considers the decentralized control of spatially invariant systems i e systems of homogeneous interacting components the main idea is for individual components to model interactions with neighbors as disturbances that satisfy certain magnitude bounds while simultaneously self imposing symmetric magnitude bounds these magnitude bounds can be interpreted as negotiated levels of interaction among components it turns out that this approach is equivalent to constructing a feedback that is robustly stabilizing with structured uncertainties

graph controllability classes for the laplacian leader follower dynamics in this paper we consider the problem of obtaining graph theoretic characterizations of controllability for the laplacian based leader follower dynamics our developments rely on the notion of graph controllability classes namely the classes of essentially controllable completely uncontrollable and conditionally controllable graphs in addition to the topology of the underlying graph the controllability classes rely on the specification of the control vectors our particular focus is on the set of binary control vectors the choice of binary control vectors is naturally adapted to the laplacian dynamics as it captures the case when the controller is unable to distinguish between the followers and moreover controllability properties are invariant under binary complements we prove that the class of essentially controllable graphs is a strict subset of the class of asymmetric graphs and provide numerical results that suggests that the ratio of essentially controllable graphs to asymmetric graphs increases as the number of vertices increases although graph symmetries play an important role in graph theoretic characterizations of controllability we provide an explicit class of asymmetric graphs that are completely uncontrollable namely the class of block graphs of steiner triple systems we prove that for graphs on four and five vertices a repeated laplacian eigenvalue is a necessary condition for complete uncontrollability but however show through explicit examples that for eight and nine vertices a repeated eigenvalue is not necessary for complete uncontrollability for the case of conditional controllability we give an easily checkable necessary condition that identifies a class of binary control vectors that result in a two dimensional controllable subspace several constructive examples demonstrate our results

profit intensity and cases of non compliance with the law of demand supply abstract we consider properties of the measurement intensity of a random variable for which the probability density function represented by the corresponding wigner function attains negative values on a part of the domain we consider a simple economic interpretation of this problem this model is used to present the applicability of the method to the analysis of the negative probability on markets where there are anomalies in the law of supply and demand e g giffen s goods it turns out that the new conditions to optimize the intensity require a new strategy we propose a strategy so called a rebours strategy based on the fixed point method and explore its effectiveness

lyapunov stability theory of nonsmooth systems this paper develops nonsmooth lyapunov stability theory and lasalle s invariance principle for a class of nonsmooth lipschitz continuous lyapunov functions and absolutely continuous state trajectories computable tests based on filipov s differential inclusion and clarke s generalized gradient are derived the primary use of these results is in analyzing the stability of equilibria of differential equations with discontinuous right hand side such as in nonsmooth dynamic systems or variable structure control

from global finite time linear computations to local edge based interaction rules a network of locally interacting agents can be thought of as performing a distributed computation but not all computations can be faithfully distributed this technical note investigates which global linear transformations can be computed in finite time using local rules with time varying weights i e rules which rely solely on information from adjacent nodes in a network the main result states that a linear transformation is computable in finite time using local rules if and only if the transformation has positive determinant an optimal control problem is solved for finding the local interaction rules and simulations are performed to elucidate how optimal solutions can be obtained

steady state thermoelastic analysis of 3d solids with fiber inclusions by boundary element method in this work a boundary element based analysis methodology for the steady state uncoupled thermoelastic analysis of fiber reinforced three dimensional solids is presented for efficient analysis and modeling the cylindrical shaped fibers are idealized by a system of curvilinear line elements with a prescribed diameter the variations in the displacement traction temperature and flux fields in the circumferential direction are represented in terms of a trigonometric shape function together with a linear or quadratic variation in the longitudinal direction this facilitates semi analytical integration around the fiber which reduces the computational task significantly the numerical accuracy of the proposed method of analysis is verified and some examples of thermoelastic analysis of fiber reinforced solids are presented

learning coverage control of mobile sensing agents in one dimensional stochastic environments this technical note presents learning coverage control of mobile sensing agents without a priori statistical information regarding random signal locations in a one dimensional space in particular the proposed algorithm controls the usage probability of each agent in a network while simultaneously satisfying an overall network formation topology the proposed control algorithm is rather direct not involving any identification of an unknown probability density function associated to random signal locations our approach builds on diffeomorphic function learning with kernels the almost sure convergence properties of the proposed control algorithm are analyzed using the ode approach numerical simulations for different scenarios demonstrate the effectiveness of the proposed approach

quadratic stabilisability of multi agent systems under switching topologies this paper addresses the stabilisability of multi agent systems mass under switching topologies necessary and or sufficient conditions are presented in terms of graph topology these conditions explicitly reveal how the intrinsic dynamics of the agents the communication topology and the external control input affect stabilisability jointly with the appropriate selection of some agents to which the external inputs are applied and the suitable design of neighbour interaction rules via a switching topology an mas is proved to be stabilisable even if so is not for each of uncertain subsystem in addition a method is proposed to constructively design a switching rule for mass with norm bounded time varying uncertainties the switching rules designed via this method do not rely on uncertainties and the switched mas is quadratically stabilisable via decentralised external self feedback for all uncertainties with respect to applications of the stabilisability results the formation control and the cooper

laplacian controllability classes for threshold graphs abstract let g be a graph on n vertices with laplacian matrix l and let b be a binary vector of length n the pair l b is controllable if the smallest l invariant subspace containing b is of dimension n the graph g is called essentially controllable if l b is controllable for every b ker l completely uncontrollable if l b is uncontrollable for every b and conditionally controllable if it is neither essentially controllable nor completely uncontrollable in this paper we completely characterize the graph controllability classes for threshold graphs we first observe that the class of threshold graphs contains no essentially controllable graph we prove that a threshold graph is completely uncontrollable if and only if its laplacian matrix has a repeated eigenvalue in the process we fully characterize the set of conditionally controllable threshold graphs

subjective modelling of supply and demand the minimum of fisher information solution abstract two of the present authors have put forward a projective geometry based model of rational trading that implies a model for subjective demand supply profiles if one considers closing of a position as a random process we would like to present the analysis of a subjectivity in such trading models in our model the trader gets the maximal profit intensity when the probability of transaction is 0 5853 we also present a comparison with the model based on the maximum of entropy principle to the best of our knowledge this is one of the first analyses that show a concrete situation in which trader profit optimal value is in the class of price negotiating algorithms strategies resulting in non monotonic demand supply curves of the rest of the world a collective opponent our model suggests that there might be a new class of rational trader strategies that almost neglects the supply demand profile of the market this class emerges when one tries to minimize the information that strategies reveal

semistability finite time stability differential inclusions and discontinuous dynamical systems having a continuum of equilibria this paper focuses on semistability and finite time semistability for discontinuous dynamical systems having a continuum of equilibria semistability is the property whereby the solutions of a dynamical system converge to lyapunov stable equilibrium points determined by the system initial conditions in this paper we extend the theory of semistability to discontinuous autonomous dynamical systems in particular lyapunov based tests for semistability and finite time semistability for autonomous differential inclusions are established

stochastic stability of continuous time consensus protocols a unified approach to studying convergence and stochastic stability of continuous time consensus protocols cps is presented in this work our method applies to networks with directed information flow both cooperative and noncooperative interactions networks under weak stochastic forcing and those whose topology and strength of connections may vary in time the graph theoretic interpretation of the analytical results is emphasized we show how the spectral properties such as algebraic connectivity and total effective resistance as well as the geometric properties such as the dimension and the structure of the cycle subspace of the underlying graph shape stability of the corresponding cps in addition we explore certain implications of spectral graph theory to cp design in particular we point out that expanders sparse highly connected graphs generate cps whose performance remains uniformly high when the size of the network grows unboundedly similarly we highlight the benefits of using random

boundary element methods for three dimensional thermoplasticity abstract a new boundary element formulation is presented for quasistatic thermoplasticity the governing integral equations utilize kernel functions based upon the fundamental solutions of uncoupled thermoelasticity thereby eliminating volume discretization except in regions where plasticity occurs as a result the boundary element approach becomes an attractive alternative to finite element methods particularly for problems involving localized plastic effects in addition the present work introduces a temperature dependent strain hardening material model and includes the body heat sources due to inelastic dissipation the entire three dimensional formulation has been implemented in a general purpose boundary element code details of this numerical implementation are provided along with results of several illustrative examples

controllability of multiagent networks with antagonistic interactions this paper addresses the controllability of a class of antagonistic multiagent networks with both positive and negative edges all the agents of the multiagent network run a consensus algorithm using a signed laplacian based on the generalized equitable partition we propose a graph theoretic characterization of an upper bound on the controllable subspace then we provide a necessary condition for the controllability of the system and give an algorithm to compute the partition furthermore we prove that for a structurally balanced network the controllability is equivalent to that of the corresponding all positive network if the leaders are chosen from the same vertex set several examples are given to illustrate these results

boundary element methods in three dimensional thermoelasticity abstract a boundary element method is developed for the solution of time dependent problems in three dimensional thermoelasticity the time domain boundary only formulation represents the first of its kind for quasistatic analysis which by definition considers transient heat conduction but ignores the effects of inertia by eliminating the need for volume discretization the method becomes an attractive alternative to finite element analysis for this class of problems additionally because an exact green s function is used in the interior steep thermal gradients can be captured much more readily than with standard domain based methods the presentation includes details of the fundamental solution a derivation of the boundary integral equations and an overview of a general purpose numerical implementation this implementation permits the solution of large multiregion problems with arbitrary geometry and boundary conditions several examples are included to validate the proposed method as well as to highlight its usefulness

controllability and observability of grid graphs via reduction and symmetries in this paper we investigate the controllability and observability properties of a family of linear dynamical systems whose structure is induced by the laplacian of a grid graph this analysis is motivated by several applications in network control and estimation quantum computation and discretization of partial differential equations specifically we characterize the structure of the grid eigenvectors by means of suitable decompositions of the graph for each eigenvalue based on its multiplicity and on suitable symmetries of the corresponding eigenvectors we provide necessary and sufficient conditions to characterize all and only the nodes from which the induced dynamical system is controllable observable we discuss the proposed criteria and show through suitable examples how such criteria reduce the complexity of the controllability respectively observability analysis of the grid

advanced boundary element analysis of two and three dimensional problems of elasto plasticity an advanced formulation of the boundary element method has been developed for inelastic analysis based on an initial stress approach the iterative solution algorithm makes use of an accelerated initial stress approach in which the past history of initial stresses are used to obtain an initial estimate for the current increment in the present analysis the geometry and functions are represented by higher order quadratic shape functions to model complex geometries and rapid functional variations accurately the methods of numerical integration of the kernels particularly the singular type are substantially improved by devising suitable automatic sub segmentation routines that incorporate the recent developments in mapping procedures the formulations have been implemented for two dimensional plane stress plane strain and three dimensional elasto plasticity problems

network topology and communication data rate for consensusability of discrete time multi agent systems this paper investigates the joint effect of agent dynamic network topology and communication data rate on consensusability of linear discrete time multi agent systems neglecting the finite communication data rate constraint and under undirected graphs a necessary and sufficient condition for consensusability under a common control protocol is given which explicitly reveals how the intrinsic entropy rate of the agent dynamic and the communication graph jointly affect consensusability the result is established by solving a discrete time simultaneous stabilization problem a lower bound of the optimal convergence rate to consensus which is shown to be tight for some special cases is provided as well moreover a necessary and sufficient condition for formationability of multi agent systems is obtained as a special case the discrete time second order consensus is discussed where an optimal control gain is designed to achieve the fastest convergence the effects of undirected graphs on consensability formationability and optimal convergence rate are exactly quantified by the ratio of the second smallest to the largest eigenvalues of the graph laplacian matrix an extension to directed graphs is also made the consensus problem under a finite communication data rate is finally investigated

finite time distributed consensus via binary control protocols this paper investigates the finite time distributed consensus problem for multi agent systems using a binary consensus protocol and the pinning control scheme compared with other consensus algorithms which need the complete state or output information of neighbors the proposed algorithm only requires sign information of the relative state measurements that is the differences between a node s state and that of its neighbors this corresponds to only requiring a single bit quantization error relative to each neighbor this signum protocol is realistic in terms of observed behavior in animal groups where relative motion is determined not by full time signal measurements but by coarse estimates of relative heading differences between neighbors the signum protocol does not require explicit measurement of time signals from neighbors and hence has the potential to significantly reduce the requirements for both computation and sensing analysis of discontinuous dynamical systems is used including the filippov solutions and set valued lie derivative based on the second order information on the evolution of lyapunov functions the conditions that guarantee the finite time consensus for the systems are identified numerical examples are given to illustrate the theoretical results

nonsmooth coordination and geometric optimization via distributed dynamical systems emerging applications for networked and cooperative robots motivate the study of motion coordination for groups of agents for example it is envisioned that groups of agents will perform a variety of useful tasks including surveillance exploration and environmental monitoring this paper deals with basic interactions among mobile agents such as move away from the closest other agent or move toward the furthest vertex of your own voronoi polygon these simple interactions amount to distributed dynamical systems because their implementation requires only minimal information about neighboring agents we characterize the close relationship between these distributed dynamical systems and the disk covering and sphere packing cost functions from geometric optimization our main results are as follows i we characterize the smoothness properties of these geometric cost functions ii we show that the interaction laws are variations of the nonsmooth gradient of the cost functions and iii we establish various asymptotic convergence properties of the laws the technical approach relies on concepts from computational geometry nonsmooth analysis and nonsmooth stability theory

finite time convergent gradient flows with applications to network consensus this paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function extending recent results on nonsmooth stability analysis we characterize their asymptotic convergence properties and identify conditions that guarantee finite time convergence we discuss the application of the results to consensus problems in multi agent systems and show how the proposed nonsmooth gradient flows achieve consensus in finite time

coordinated path following in the presence of communication losses and time delays this paper addresses the problem of steering a group of vehicles along given spatial paths while holding a desired time varying geometrical formation pattern the solution to this problem henceforth referred to as the coordinated path following cpf problem unfolds in two basic steps first a path following pf control law is designed to drive each vehicle to its assigned path with a nominal speed profile that may be path dependent this is done by making each vehicle approach a virtual target that moves along the path according to a conveniently defined dynamic law in the second step the speeds of the virtual targets also called coordination states are adjusted about their nominal values so as to synchronize their positions and achieve indirectly vehicle coordination in the problem formulation it is explicitly considered that each vehicle transmits its coordination state to a subset of the other vehicles only as determined by the communications topology adopted it is shown that the system that is obtained by putting together the pf and coordination subsystems can be naturally viewed as either the feedback or the cascade connection of the latter two using this fact and recent results from nonlinear systems and graph theory conditions are derived under which the pf and the coordination errors are driven to a neighborhood of zero in the presence of communication losses and time delays two different situations are considered the first captures the case where the communication graph is alternately connected and disconnected brief connectivity losses the second reflects an operational scenario where the union of the communication graphs over uniform intervals of time remains connected uniformly connected in mean to better root the paper in a nontrivial design example a cpf algorithm is derived for multiple underactuated autonomous underwater vehicles auvs simulation results are presented and discussed

a class of uncontrollable diffusively coupled multiagent systems with multichain topologies we construct systematically a class of uncontrollable diffusively coupled multiagent systems with a single leader and multichain topologies for studying the controllability of diffusively coupled multiagent systems such identified uncontrollable systems serve as counterexamples that prove the need to modify the existing sufficient condition using graph partitioning characterization the uncontrollability of the constructed multichain structures can be preserved when the structures are further augmented to get better connected the paper also provides an algorithm to obtain the minimal leader invariant relaxed equitable partition for the graph associated with any diffusively coupled multiagent system guided by a single leader

protocols design and uncontrollable topologies construction for multi agent networks this note investigates the controllability issues of multi agent systems where each node contains generic linear dynamics first a neighbor based control protocol is proposed under which it is shown that the controllability of a multi agent system is solely decided by its communication topology structure we then further consider the effects of communication topology on the controllability from a graph theory point of view by explicitly constructing topologies the construction exhibits a partition of the designed graph with identified leaders under which the system is shown to be uncontrollable

edge agreement graph theoretic performance bounds and passivity analysis this work explores the properties of the edge variant of the graph laplacian in the context of the edge agreement problem we show that the edge laplacian and its corresponding agreement protocol provides a useful perspective on the well known node agreement or the consensus algorithm specifically the dynamics induced by the edge laplacian facilitates a better understanding of the role of certain subgraphs e g cycles and spanning trees in the original agreement problem using the edge laplacian we proceed to examine graph theoretic characterizations of the h2 and h performance for the agreement protocol these results are subsequently applied in the contexts of optimal sensor placement for consensus based applications finally the edge laplacian is employed to provide new insights into the nonlinear extension of linear agreement to agents with passive dynamics

necessary and sufficient graphical conditions for formation control of unicycles the feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control the directed graph defined by the information flow plays a key role it is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node a similar result is given for formation stabilization to a line and to more general geometric arrangements

parameter estimation by fixed point of function of information processing intensity abstract we present a new method of estimating the dispersion of a distribution which is based on the surprising property of a function that measures information processing intensity it turns out that this function has a maximum at its fixed point fixed point equation is used to estimate the parameter of the distribution that is of interest to us the main result consists in showing that only part of available experimental data is relevant for the parameters estimation process we illustrate the estimation method by using the example of an exponential distribution

development of bem for thermoplasticity abstract a boundary element method bem for general thermoplastic analysis is presented a thermally sensitive two surface material model is used to simulate constitutive behavior the nonlinear system of equations arising from an initial stress approach is solved using a new newton raphson solution algorithm the stress tensors are collapsed into a scalar variable using certain characteristic tensors arising out of the constitutive equations this leads to a simpler system requiring much less computation the solution algorithm is iterative in nature and checks for convergence at the end of each increment the resulting robust analysis tool is then utilized in solving several practical applications to illustrate the growing importance of bem as an alternative to the finite element method

development of a boundary element method for time dependent planar thermoelasticity abstract a new boundary element method is developed for two dimensional quasistatic thermoelasticity this time domain formulation involves only surface quantities consequently volume discretization is completely eliminated and the method becomes a viable alternative to the usual finite element approaches after presenting a brief overview of the governing equations boundary integral equations for coupled quasistatic thermoelasticity are derived by starting with existing fundamental solutions along with an appropriate reciprocal theorem details of a general purpose numerical implementation are then discussed next boundary element methods for the two more practical theories uncoupled quasistatic and steady state thermoelasticity are developed directly from limiting forms of the coupled formulation several numerical examples are provided to illustrate the validity and attractiveness of the boundary element approach for this entire class of problems

brief paper decentralized coordination of autonomous swarms using parallel gibbs sampling in this paper we present analysis of a discrete time decentralized stochastic coordination algorithm for a group of mobile nodes called an autonomous swarm on a finite spatial lattice all nodes take their moves by sampling in parallel their locally perceived gibbs distributions corresponding to a pairwise nearest neighbor potential the algorithm has no explicit requirements on the connectedness of the underlying information graph which varies with the swarm configuration it is established that with an appropriate annealing schedule the algorithm results in swarm configurations converging to the global minimizers of a modified potential energy function the extent of discrepancy between the modified and original potential energy functions is determined by the maximum node travel between time steps and when such distance is small the ultimate swarm configurations are close to the global minimizers of the original potential energy simulation results are further presented to illustrate the capability of the sampling algorithm in approximate global optimization for swarms

on the control and estimation over relative sensing networks in this note we consider certain structural aspects of estimation and control over relative sensing networks rsns in this venue using tools from basic algebraic graph theory namely the incidence matrix and cut and cycle spaces of a connect graph we examine transformations among relative sensing topologies for a networked system these transformations are parameterized for noise free as well as noisy networks and their utility in the context of network centric robust control and control reconfigurations is explored

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

zero forcing sets and controllability of dynamical systems defined on graphs in this technical note controllability of systems defined on graphs is discussed we consider the problem of controllability of the network for a family of matrices carrying the structure of an underlying directed graph a one to one correspondence between the set of leaders rendering the network controllable and zero forcing sets is established to illustrate the proposed results special cases including path cycle and complete graphs are discussed moreover as shown for graphs with a tree structure the proposed results of the present technical note together with the existing results on the zero forcing sets lead to a minimal leader selection scheme in particular cases

observability through a matrix weighted graph observability of an array of identical linear time invariant systems with incommensurable output matrices is studied where an array is called observable when identically zero relative outputs imply synchronized solutions for the individual systems it is shown that the observability of an array is equivalent to the connectivity of its interconnection graph whose edges are assigned matrix weights moreover to better understand the relative behavior of distant units pairwise observability that concerns with the synchronization of a certain pair of individual systems in the array is studied this milder version of observability is shown to be closely related to certain connectivity properties of the interconnection graph as well pairwise observability is also analyzed using the circuit theoretic tool effective conductance the observability of a certain pair of units is proved to be equivalent to the nonsingularity of the matrix valued effective conductance between the associated pair of nodes of a resistive network with matrix valued parameters whose node admittance matrix is the laplacian of the array s interconnection graph

nodes selection strategy in cooperative tracking problem in this paper a new optimization problem is addressed for node selection that has application potentials in input output switches for sensors in control system design and leader determination in social networks the purpose of the addressed problem is to develop a strategy for selecting a subset of nodes as controlled nodes in order to minimize certain objective function consisting of the convergence speed and the energy of control action over a finite time horizon for networks with fixed controlled nodes an upper bound of the objective function is obtained which is shown to be convex and independent of the time horizon for networks with switched controlled nodes a greedy algorithm is proposed to reduce the computation complexity resulting from the length of the time horizon where the nodes selection is carried out over divided small time intervals the cost gap is also analyzed between the strategy of optimizing over the whole time horizon and the strategy of optimizing over the small intervals finally the proposed nodes selection strategy is validated through simulations and two regions are found in which the number of optimal controlled nodes is determined

constructing a controllable graph under edge constraints abstract this paper is concerned with the problem of constructing a controllable graph subject to some practical edge constraints specifically suppose the total amount of vertices and the upper bounds on the graph diameter or on the vertex degree are given we consider the problem of exploring a class of feasible graphs that satisfy the constraints using the hybrid of a path graph and an antiregular graph we propose a simple and systematic method to generate a class of controllable graphs whose diameters or degrees cover the full possible ranges the method to select the control vector to ensure the controllability of the combined graph is also proposed numerical examples are provided to demonstrate our results

brief paper the zermelo voronoi diagram a dynamic partition problem we consider a voronoi like partition problem in the plane for a given finite set of generators each element in this partition is uniquely associated with a particular generator in the following sense an agent that resides within a set of the partition at a given time will arrive at the generator associated with this set faster than any other agent that resides anywhere outside this set at the same instant of time the agent s motion is affected by the presence of a temporally varying drift which is induced by local winds currents as a result the minimum time to a destination is not equivalent to the minimum distance traveled this simple fact has important ramifications over the partitioning problem it is shown that this problem can be interpreted as a dynamic voronoi diagram problem where the generators are not fixed but rather they are moving targets to be reached in minimum time the problem is solved by first reducing it to a standard voronoi diagram by means of a time varying coordinate transformation we then extend the approach to solve the dual problem where the generators are the initial locations of a given set of agents distributed over the plane such that each element in the partition consists of the terminal positions that can be reached by the corresponding agent faster than any other agent

asymptotic properties of consensus type algorithms for networked systems with regime switching topologies this paper is concerned with asymptotic properties of consensus type algorithms for networked systems whose topologies switch randomly the regime switching process is modeled as a discrete time markov chain with a finite state space the consensus control is achieved by using stochastic approximation methods in the setup the regime switching process the markov chain contains a rate parameter e 0 in the transition probability matrix that characterizes how frequently the topology switches on the other hand the consensus control algorithm uses a stepsize m that defines how fast the network states are updated depending on their relative values three distinct scenarios emerge under suitable conditions we show that when 0 e o m a continuous time interpolation of the iterates converges weakly to a system of randomly switching ordinary differential equations modulated by a continuous time markov chain in this case a scaled sequence of tracking errors converges to a system of switching diffusion when 0 email protected email protected the network topology is almost non switching during consensus control transient intervals and hence the limit dynamic system is simply an autonomous differential equation when email protected email protected the markov chain acts as a fast varying noise and only its averaged network matrices are relevant resulting in a limit differential equation that is an average with respect to the stationary measure of the markov chain simulation results are presented to demonstrate these findings

optimal partitioning for spatiotemporal coverage in a drift field abstract we consider the problem of partitioning an area in the plane populated by a team of aerial marine vehicles into a finite collection of non overlapping sets the sets of this partition are in an one to one correspondence with the vehicles under the following rule each point in the given set of the partition can be reached by the corresponding vehicle in this set faster than any other vehicle in the presence of a spatiotemporal drift field consequently a voronoi like partition results which encodes the proximity relations between the vehicles and arbitrary points in the plane with respect to the minimum time to go the construction of this voronoi like partition is based on its interpretation as the intersection of a forest of the cost minimum time to go surfaces emanating from each generator with their common lower envelope the characterization of each cost surface is achieved by means of an efficient expansion scheme of the level sets of the minimum time to go function which utilizes in turn the structure of the optimal synthesis of the minimum time problem without resorting to exhaustive numerical techniques e g fast marching methods we examine the topological characteristics of the partition by using control system theoretic concepts and tools the theoretical developments are illustrated with a number of numerical examples

2d and 3d transient heat conduction analysis by bem via particular integrals abstract particular integral formulations are presented for 2d and 3d transient potential flow heat conduction analysis the results of the analysis are compared with an alternative formulation developed using the volume integral conversion approach although the mathematical foundation of the two methods are different both formulations are shown to produce almost identical results for the particular integral formulation the steady state heat conduction equation is used as the complementary solution and two global shape functions gsfs are considered to approximate the transient term of the heat conduction equation the numerical results for three example problems are given and compared with their analytical solutions

the merchandising mathematician model profit intensities abstract a simple model of a buying selling cycle is proposed it is based on a notion of a profit intensity supply and demand curves and geometrical interpretation are discussed in this context

zero forcing number constrained matchings and strong structural controllability abstract the zero forcing number is a graph invariant introduced to study the minimum rank of the graph in 2008 aazami proved the np hardness of computing the zero forcing number of a simple undirected graph we complete this np hardness result by showing that the non equivalent problem of computing the zero forcing number of a directed graph allowing loops is also np hard the rest of the paper is devoted to the strong controllability of a networked system this kind of controllability takes into account only the structure of the interconnection graph but not the interconnection strengths along the edges we provide a necessary and sufficient condition in terms of zero forcing sets for the strong controllability of a system whose underlying graph is a directed graph allowing loops moreover we explain how our result differs from a recent related result discovered by monshizadeh et al finally we show how to solve the problem of finding efficiently a minimum size input set for the strong controllability of a self damped system with a tree structure

theorems on partitioned matrices revisited and their applications to graph spectra some old results about spectra of partitioned matrices due to goddard and schneider or haynsworth are re proved a new result is given for the spectrum of a block stochastic matrix with the property that each off diagonal block has equal entries and each diagonal block has equal diagonal entries and equal off diagonal entries the result is applied to the study of the spectra of the usual graph matrices by partitioning the vertex set of the graph according to the neighborhood equivalence relation the concept of a reduced graph matrix is introduced the question of when n 2 is the second largest signless laplacian eigenvalue of a connected graph of order n is treated a recent conjecture posed by tam fan and zhou on graphs that maximize the signless laplacian spectral radius over all not necessarily connected graphs with given numbers of vertices and edges is refuted the laplacian spectrum of a degree maximal graph is reconsidered

asymptotic optimality of multicenter voronoi configurations for random field estimation this technical note deals with multi agent networks performing estimation tasks consider a network of mobile agents with sensors that can take measurements of a spatial stochastic process using the kriging statistical technique a field estimate may be calculated over the environment with an associated error variance at each point we study a single snapshot scenario in which the spatial process mean is known and each agent can only take one measurement we consider two optimization problems with respect to the measurement locations using as objective functions the maximum error variance and the extended prediction variance as the correlation between distinct locations vanishes we show that circumcenter and incenter voronoi configurations become network configurations that optimize the maximum error variance and the extended prediction variance respectively we also present distributed coordination algorithms that steer the network towards these configurations

controllability of multi agent systems with directed and weighted signed networks abstract this paper studies the controllability of multi agent systems with signed networks which are represented by directed weighted signed graphs the adjacency weights of network depict the property of interactions positive weight means cooperative interaction while negative weight antagonistic interaction first by using switching equivalent transformation the controllability of three kinds of signed networks is studied structurally balanced anti balanced and strictly unbalanced it is shown that the controllability of the structurally balanced network is equivalent to that of the associated underlying network then a graph theoretic necessary condition for controllability is given by virtue of almost equitable partition of directed weighted signed networks furthermore some necessary and sufficient conditions are given for the controllability of generic linear multi agent systems in addition several examples are presented to illustrate the theoretical results

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper

centroidal voronoi tessellations applications and algorithms a centroidal voronoi tessellation is a voronoi tessellation whose generating points are the centroids centers of mass of the corresponding voronoi regions we give some applications of such tessellations to problems in image compression quadrature finite difference methods distribution of resources cellular biology statistics and the territorial behavior of animals we discuss methods for computing these tessellations provide some analyses concerning both the tessellations and the methods for their determination and finally present the results of some numerical experiments

on the equivalence between dissipativity and optimality of discontinuous nonlinear regulators for filippov dynamical systems in this paper we derive guaranteed gain sector and disk margins for nonlinear optimal and inverse optimal discontinuous feedback regulators that minimize a nonlinear nonquadratic performance functional for filippov dynamical systems specifically we consider dynamical systems with lebesgue measurable and locally essentially bounded vector fields characterized by differential inclusions involving filippov set valued maps in addition we extend classical dissipativity theory to address the problem of dissipative discontinuous dynamical systems these results are then used to derive extended kalman yakubovich popov conditions for characterizing necessary and sufficient conditions for dissipativity of discontinuous systems using clarke gradients and locally lipschitz continuous storage functions furthermore using the newly developed dissipativity notions we develop a return difference inequality to provide connections between dissipativity and optimality of nonlinear discontinuous controllers for filippov dynamical systems specifically using the extended kalman yakubovich popov conditions we show that our discontinuous feedback control law satisfies a return difference inequality if and only if the controller is dissipative with respect to a quadratic supply rate

on the controllability properties of circulant networks this paper examines the controllability of a group of first order agents adopting a weighted consensus type coordination protocol over a circulant network specifically it is shown that a circulant network with laplacian eigenvalues of maximum algebraic multiplicity q is controllable from q nodes our approach leverages on the cauchy binet formula which in conjunction with the popov belevitch hautus test leads to new insights on structural aspects of network controllability

controllability of multi agent systems with periodically switching topologies and switching leaders abstractthis paper considers controllability of multi agent systems with periodically switching topologies and switching leaders the concept of m periodic controllability is proposed and a criterion for m periodic controllability is established the effect of the duration of subsystems on controllability is analysed by utilising a property of analytic functions in addition the influence of switching periods on controllability is investigated and an algorithm is proposed to search for the fewest periods to ensure controllability a necessary condition for m periodic controllability is obtained from the perspective of eigenvectors of the subsystems laplacian matrices for a system with switching leaders it is proved that switching leader controllability is equivalent to multiple leader controllability furthermore both the switching order and the tenure of agents being leaders have no effect on the controllability some examples are provided to illustrate the theoretical results

controllability of heterogeneous multi agent systems under directed and weighted topology abstractthis paper considers the controllability problem for both continuous and discrete time linear heterogeneous multi agent systems with directed and weighted communication topology first two kinds of neighbour based control protocols based on the distributed protocol of first order and second order multi agent systems are proposed under which it is shown that a heterogeneous multi agent system is controllable if the underlying communication topology is controllable then under special leader selection the result shows that the controllability of a heterogeneous multi agent system is solely decided by its communication topology graph furthermore some necessary and or sufficient conditions are derived for controllability of communication topology from algebraic and graphical perspectives finally simulation examples are presented to demonstrate the effectiveness of the theoretical results

adaptive information collection by robotic sensor networks for spatial estimation this work deals with trajectory optimization for a robotic sensor network sampling a spatio temporal random field we examine the optimal sampling problem of minimizing the maximum predictive variance of the estimator over the space of network trajectories this is a high dimensional multi modal nonsmooth optimization problem known to be np hard even for static fields and discrete design spaces under an asymptotic regime of near independence between distinct sample locations we show that the solutions to a novel generalized disk covering problem are solutions to the optimal sampling problem this result effectively transforms the search for the optimal trajectories into a geometric optimization problem constrained versions of the latter are also of interest as they can accommodate trajectories that satisfy a maximum velocity restriction on the robots we characterize the solution for the unconstrained and constrained versions of the geometric optimization problem as generalized multicircumcenter trajectories and provide algorithms which enable the network to find them in a distributed fashion several simulations illustrate our results

on the reduced signless laplacian spectrum of a degree maximal graph abstract for a simple graph g the signless laplacian of g is the matrix a g d g where a g is the adjacency matrix and d g is the diagonal matrix of vertex degrees of g the reduced signless laplacian of g is the matrix g b g where b g is the reduced adjacency matrix of g and g is the diagonal matrix whose diagonal entries are the common degrees for vertices belonging to the same neighborhood equivalence class of g a graph is said to be degree maximal if it is connected and its degree sequence is not majorized by the degree sequence of any other connected graph for a maximal graph we obtain a formula for the characteristic polynomial of its reduced signless laplacian and use the formula to derive a localization result for its reduced signless laplacian eigenvalues and to compare the signless laplacian spectral radii of two well known maximal graphs we also obtain a necessary condition for a maximal graph to have maximal signless laplacian spectral radius among all connected graphs with given numbers of vertices and edges

finite time semistability and consensus for nonlinear dynamical networks this paper focuses on semistability and finite time stability analysis and synthesis of systems having a continuum of equilibria semistability is the property whereby the solutions of a dynamical system converge to lyapunov stable equilibrium points determined by the system initial conditions in this paper we merge the theories of semistability and finite time stability to develop a rigorous framework for finite time semistability in particular finite time semistability for a continuum of equilibria of continuous autonomous systems is established continuity of the settling time function as well as lyapunov and converse lyapunov theorems for semistability are also developed in addition necessary and sufficient conditions for finite time semistability of homogeneous systems are addressed by exploiting the fact that a homogeneous system is finite time semistable if and only if it is semistable and has a negative degree of homogeneity unlike previous work on homogeneous systems our results involve homogeneity with respect to semistable dynamics and require us to adopt a geometric description of homogeneity finally we use these results to develop a general framework for designing semistable protocols in dynamical networks for achieving coordination tasks in finite time

performance and design of cycles in consensus networks abstract this work explores the role of cycles in consensus seeking networks for analysis and synthesis purposes cycles are critical for many reasons including improving the convergence rate of the system resilience to link failures and the overall performance of the system the focus of this work examines how cycles impact the h 2 performance of consensus networks a first contribution shows that the addition of cycles always improves the performance of the system we provide an analytic characterization of how the addition of edges improves the performance and show that it is related to the inverse of the cycle lengths and the number of shared edges between independent cycles these results are then used to consider the design of consensus networks in this direction we present an l 1 relaxation method that leads to a convex program for adding a fixed number of edges to a consensus networks we also demonstrate how this relaxation can be used to embed additional performance criteria such as maximization of the algebraic connectivity of the graph

symmetry invariance of multiagent formations in self pursuit structure in the interconnection topology among individuals of a multiagent system plays a fundamental role in the system s steady state and transient behaviors this paper explores how certain interconnection topologies influence symmetry in a multiagent system s trajectories it is shown how circulant connectivity preserves rotation and in particular instances dihedral group symmetries in a formation of locally interacting planar integrators moreover it is revealed to what extent circulant connectivity is also necessary in order that symmetric formations remain symmetric under the multiagent system s dynamics

inelastic transient dynamic analysis of three dimensional problems by bem a direct boundary element formulation and its numerical implementation for inelastic transient dynamic analysis of three dimensional solids is presented the formulation is based on an initial stress approach and is the first ever of its kind in the field of the boundary element method this formulation employs the navier cauchy equation of motion graffi s dynamic reciprocal theorem stokes fundamental solution and the divergence theorem together with kinematical and constitutive equations to obtain the pertinent integral equations of the problem in the time domain within the context of small displacement theory of elastoplasticity the boundary integral equations are cast in an incremental form in which elastoplastic relations of the incremental type are used for the material description these equations are then solved using a time stepping algorithm in conjunction with an iterative solution scheme to satisfy the constitutive relations higher order shape functions are used to approximate the field quantities in space as well as in time finally the applicability of this methodology is demonstrated by presenting a few example problems

degree maximal graphs are laplacian integral abstract an integer sequence d d 1 d 2 d n is graphic if there is a graph whose degree sequence is d a graph g is maximal if its degree sequence is majorized by no other graphic sequence the laplacian matrix of g is l g d g a g where d g is the diagonal matrix of vertex degrees and a g is the 0 1 adjacency matrix the article contains an explicit algorithmic construction of all maximal graphs from which it follows e g that apart from 0 the laplacian spectrum of a maximal graph is the conjugate of its degree sequence

nonuniform coverage and cartograms in this paper we investigate nonuniform coverage of a planar region by a network of autonomous mobile agents we derive centralized nonuniform coverage control laws from uniform coverage algorithms using cartograms transformations that map nonuniform metrics to a near euclidean metric we also investigate time varying coverage metrics and the design of control algorithms to cover regions with slowly varying nonuniform metrics our results are applicable to the design of mobile sensor networks notably when the coverage metric varies as data is collected such as in the case of an information metric the results apply also to the study of animal groups foraging for food that is nonuniformly distributed and possibly changing

two and three dimensional transient heat conduction and thermoelastic analyses by bem via efficient time convolution abstract efficient re integration based convolution algorithms are presented for a large class of problems involving transient two and three dimensional heat conduction and uncoupled thermoelastic analyses based on the earlier works of dargush and banerjee g f dargush p k banerjee application of boundary element method to transient heat conduction int j numer methods engrg 31 1991 1231 1248 g f dargush p k banerjee development of a boundary element method for time dependent planar thermoelasticity int j solids struct 25 1989 999 1021 the main motivation behind the current development is the fact that the storage based convolution approach used in earlier developments was not found to be very suitable for solving large scale practical problems because of substantial computer disk space requirement and the inability to handle time dependent boundary conditions in this paper a re integration based full convolution as well as an efficient and simplified re integration based fast convolution algorithms are presented in which all of the time convolution steps have been calculated by preserving the energy balance as expressed in the convolution while assuming equivalent values of variables to represent the total effect the accuracy and efficiency of the developed algorithms are demonstrated via numerical examples

cluster consensus in discrete time networks of multiagents with inter cluster nonidentical inputs in this paper cluster consensus of multiagent systems is studied via inter cluster nonidentical inputs here we consider general graph topologies which might be time varying the cluster consensus is defined by two aspects intracluster synchronization the state at which differences between each pair of agents in the same cluster converge to zero and inter cluster separation the state at which agents in different clusters are separated for intra cluster synchronization the concepts and theories of consensus including the spanning trees scramblingness infinite stochastic matrix product and hajnal inequality are extended as a result it is proved that if the graph has cluster spanning trees and all vertices self linked then the static linear system can realize intra cluster synchronization for the time varying coupling cases it is proved that if there exists t 0 such that the union graph across any t length time interval has cluster spanning trees and all graphs has all vertices self linked then the time varying linear system can also realize intra cluster synchronization under the assumption of common inter cluster influence a sort of inter cluster nonidentical inputs are utilized to realize inter cluster separation such that each agent in the same cluster receives the same inputs and agents in different clusters have different inputs in addition the boundedness of the infinite sum of the inputs can guarantee the boundedness of the trajectory as an application we employ a modified non bayesian social learning model to illustrate the effectiveness of our results

two and three dimensional transient thermoelastic analysis by bem via particular integrals abstract particular integral formulations are presented for two and three dimensional transient uncoupled thermoelastic analysis these formulations differ from previous particular integral formulations in that the equation of uncoupled thermoelasticity including the heat conduction equation is fully satisfied to obtain particular integrals the equation of the steady state thermoelasticity is now used as the complementary solution and two global shape functions are considered to approximate the transient term of the heat conduction equation so that two sets of particular integrals could be derived the numerical results for both sets of particular integrals are given for three example problems and compared with their analytical solutions

controllability improvement for multi agent systems leader selection and weight adjustment abstractfor an uncontrollable system adding leaders and adjusting edge weights are two methods to improve controllability in this paper the controllability of multi agent systems under directed topologies is studied especially on the leader selection problem and the weight adjustment problem for a multi agent system necessary and sufficient algebraic conditions for controllability with fewest leaders are proposed to improve controllability by adjusting edge weights the system is supposed to be structurally controllable which holds if and only if the communication topology contains a spanning tree it is also proved that the number of the fewest edges needed to be assigned on new weights equals the rank deficiency of controllability matrix in addition a leader selection algorithm and a weight adjustment algorithm are presented simulation examples are provided to illustrate the theoretical results

distributed control design for spatially interconnected systems this paper deals with analysis synthesis and implementation of distributed controllers designed for spatially interconnected systems we develop a state space framework for posing problems of this type and focus on systems whose model is spatially discrete in this paper analysis and synthesis results are developed for this class of systems using the l sub 2 induced norm as the performance criterion the results are stated in terms of linear matrix inequalities and are thus readily amenable to computation a special implementation of the resulting controllers is presented which is particularly attractive for distributed operation of the controller several examples are provided to further illustrate the application of the results

containment control of single integrator network with limited communication data rate this technical note investigates distributed containment control for a single integrator continuous time multi agent system with a limited communication data rate network topology is a directed communication graph the containment control with quantized communication for each follower is designed using only its neighbour s quantized information so that all followers move into the convex hull spanned by the leaders necessary and sufficient criteria which guarantee achievement of containment consensus are given if the communication data rates are unfixed or fixed under a given bound on communication data rate an algorithm is established to achieve the containment consensus finally all the theoretical results are illustrated by numerical simulations