consensus of output coupled linear multi agent systems under fast switching network averaging approach this study addresses the problem of consensus of multi agent systems consisting of a set of identical mimo lti systems under a time varying network that has a well defined average with uniform convergence to the average the information delivered through the communication network is the output of each system first it is shown that consensus is reached asymptotically by using a group of compensators if the network switches sufficiently fast and the compensators are designed such that the multi agent system asymptotically achieves consensus for the average of the network further we find a relation between the two agreements one obtained from considering the switching network and the other obtained from replacing the network with its average then for a class of minimum phase systems we remove the fast switching condition by redesigning the compensators finally the formation stabilization of unicycle type mobile robots is dealt with as an application of the problem and it is demonstrated via a computer simulation

observer based finite time coordinated tracking for general linear multi agent systems in this paper four observer based distributed controllers are proposed for general linear multi agent systems to achieve finite time coordinated tracking under different situations specifically for the cases of undirected communication graphs and directed communication graphs among the followers both the situations of relative state measurement and relative output measurement among neighboring agents are considered under both kinds of communication topologies when relative state information of the neighbors is available distributed observer based controllers are designed which achieve exact coordinated tracking in finite time when only relative output information is available another finite time observer is introduced for each follower to estimate the relative state information together with the distributed controllers designed for the state feedback case finite time exact coordinated tracking can still be achieved in this situation numerical simulations are provided to illustrate the effectiveness of the proposed controllers

quantized consensus by the admm probabilistic versus deterministic quantizers this paper develops efficient algorithms for distributed average consensus with quantized communication using the alternating direction method of multipliers admm we first study the effects of probabilistic and deterministic quantizations on a distributed admm algorithm with probabilistic quantization this algorithm yields linear convergence to the desired average in the mean sense with a bounded variance when deterministic quantization is employed the distributed admm converges to a consensus within 3 lceil log 1 delta omega rceil iterations where delta 0 depends on the network topology and omega is a polynomial fraction depending on the quantization resolution the agents data and the network topology a tight upper bound on the consensus error is also obtained which depends only on the quantization resolution and the average degree of the graph this bound is much preferred in large scale networks over existing algorithms whose consensus errors are increasing in the range of agents data the quantization resolution and the number of agents we finally propose our algorithm which combines both probabilistic and deterministic quantizations simulations show that the consensus error of our algorithm is typically less than one quantization resolution for all connected networks where agents data can be of arbitrary magnitudes

properties of the composite quadratic lyapunov functions a composite quadratic lyapunov function introduced recently was shown to be very useful in the study of set invariance properties for linear systems with input and state constraints and for systems with a class of convex concave nonlinearities in this note more properties about this function are revealed in particular we study the continuity of the optimal parameter involved in this function this continuity is crucial in the construction of a continuous feedback law which makes the convex hull of a group of ellipsoids invariant

principles of uncertainty what are they why do we need them the meaning and utility of three principles of uncertainty is discussed these principles which are referred to as a principle of minimum uncertainty a principle of maximum uncertainty and a principle of uncertainty invariance depend on the theory in which uncertainty is conceptualized due to a connection between uncertainty and information the principles may also be conceived as principles of information to make the principles operational in a particular uncertainty theory we need to measure the amount of relevant uncertainty and associated information in each problem situation describable within the theory well justified measures of uncertainty have thus far been established only in some uncertainty theories these theories their uncertainty measures and the associated uncertainty principles are overviewed in the paper

unified cooperative control of multiple agents on a sphere for different spherical patterns in this technical note we consider the cooperative control of multiple agents on a sphere provide the appropriate attraction repulsion interactions between agents with introduction of the state dependent repulsive coefficients and design the unified control laws for agents to achieve three fundamental spherical configurations or patterns rendezvous uniform deployment and formation using both the first and second order models we present the analysis of the stability scaling and geometric patterns of the models on the sphere under different attraction repulsion parameters with illustration of the geometrical patterns and the geometrical isomerism by simulations the closed loop dynamics of agents are invariant with respect to group rotation actions on the sphere

second order leader following consensus of nonlinear multi agent systems via pinning control abstract without assuming that the interaction diagraph is strongly connected or contains a directed spanning tree this paper studies the second order leader following consensus problem of nonlinear multi agent systems with general network topologies based on graph theory matrix theory and lasalle s invariance principle a pinning control algorithm is proposed to achieve leader following consensus in a network of agents with nonlinear second order dynamics furthermore a pinning consensus protocol is developed for coupled double integrators with a constant reference velocity in particular this paper addresses what kind of agents and how many agents should be pinned and establishes some sufficient conditions to guarantee that all agents asymptotically follow the virtual leader numerical simulations are given to verify the theoretical analysis

information semantics of possibilistic uncertainty abstract all major theories of uncertainty permit defining numerical uncertainty measures formulae can originate by axiomatic approach or by modifying either shannon or related entropy model the latter has a very natural semantics as the complexity of transmission of specific information about the uncertainty assignment such interpretation has been lacking in the possibility model based on fuzzy set theory this paper presents such information semantics for this theory it is accomplished by demonstrating that possibilistic uncertainty can be viewed as the expected value of information identifying the acceptability of choices from the fuzzy domain

homogeneous networks of non introspective agents under external disturbances h almost synchronization this paper addresses the problem of h almost synchronization for homogeneous networks of general linear agents subject to external disturbances and under directional communication links agents are presumed to be non introspective i e agents are not aware of their own states or outputs and the only available information for each agent is a network measurement that is a linear combination of relative outputs under a certain set of conditions a family of dynamic protocols is developed such that the impact of disturbances on the synchronization error dynamics expressed in terms of the h norm of the corresponding closed loop transfer function is reduced to any arbitrarily small value

distributed consensus of second order multi agent systems with heterogeneous unknown inertias and control gains under a directed graph in this paper we study the consensus problem for second order multi agent systems with heterogeneous unknown inertias and control gains under a general directed graph unlike the existing consensus algorithms for second order multi agent systems in which all agents are assumed to have common unit inertias or share common control gains we allow the inertias and the control gains to be heterogeneous and time varying for each agent we propose fully distributed consensus algorithms over a general directed graph when there exist respectively absolute velocity damping and relative velocity damping novel integral type lyapunov functions are proposed to study the consensus convergence moreover the adaptive sigma modification schemes for the gain adaptation are proposed which renders smaller control gains and thus requires smaller amplitude on the control input without sacrificing consensus convergence furthermore we show that one proposed algorithm also works for consensus of agents with intrinsic lipschitz nonlinear dynamics the control gains are varying and updated by distributed adaptive laws as a result the proposed algorithms require no global information and thus can be implemented in a fully distributed manner

geometric analysis of the formation problem for autonomous robots in the formation control problem for autonomous robots a distributed control law steers the robots to the desired target formation a local stability result of the target formation can be derived by methods of linearization and center manifold theory or via a lyapunov based approach besides the target formation the closed loop dynamics of the robots feature various other undesired invariant sets such as nonrigid formations this note addresses a global stability analysis of the closed loop formation control dynamics we pursue a differential geometric approach and derive purely algebraic conditions for local stability of invariant embedded submanifolds these theoretical results are then applied to the well known example of a cyclic triangular formation and result in instability of all invariant sets other than the target formation

coverage optimization and spatial load balancing by robotic sensor networks this technical note studies robotic sensor networks performing static coverage optimization with area constraints given a density function describing the probability of events happening and a performance function measuring the cost to service a location the objective is to position sensors in the environment so as to minimize the expected servicing cost moreover because of load balancing considerations the area of the region assigned to each robot is constrained to be a pre specified amount we characterize the optimal configurations as center generalized voronoi configurations the generalized voronoi partition depends on a set of weights one per robot assigned to the network we design a jacobi iterative algorithm to find the weight assignment whose corresponding generalized voronoi partition satisfies the area constraints this algorithm is distributed over the generalized delaunay graph we also design the move to center and compute weight strategy to steer the robotic network towards the set of center generalized voronoi configurations while monotonically optimizing coverage

coordinated motion design on lie groups the present paper proposes a unified geometric framework for coordinated motion on lie groups it first gives a general problem formulation and analyzes ensuing conditions for coordinated motion then it introduces a precise method to design control laws in fully actuated and underactuated settings with simple integrator dynamics it thereby shows that coordination can be studied in a systematic way once the lie group geometry of the configuration space is well characterized applying the proposed general methodology to particular examples allows to retrieve control laws that have been proposed in the literature on intuitive grounds a link with brockett s double bracket flows is also made the concepts are illustrated on so 3 se 2 and se 3

measures of discord in the dempster shafer theory abstract this paper is a companion of a previous paper in which a new measure of uncertainty called a measure of discord was introduced while the previous paper focuses on intuitive justification of this new measure and identification of deficiencies of some previously considered measures this paper is oriented toward a mathematical consideration of the measure of discord also discussed in the paper is a total measure of uncertainty in the dempster shafer theory defined as the sum of discord and nonspecificity

synchronization and dynamic consensus of heterogeneous networked systems we present an analysis framework for the study of synchronization of heterogeneous nonlinear systems interconnected over networks described by directed graphs heterogeneous systems may have totally different dynamical models albeit of the same dimension or may possess equal models with different lumped parameters we show that their behavior when network interconnected is fully characterized in terms of two properties whose study may be recasted in terms of the stability analysis of two corresponding interconnected dynamical systems that evolve in orthogonal spaces on one hand we have the so called emergent dynamics and on the other the synchronization error dynamics based on this premise we introduce the concept of dynamic consensus and we present results on robust stability which assess the conditions for practical asymptotic synchronization of networked systems and characterize their collective behavior to illustrate our main theoretical findings we broach a brief case study on mutual synchronization of heterogeneous chaotic oscillators

intrinsic reduced attitude formation with ring inter agent graph this paper investigates the reduced attitude formation control problem for a group of rigid body agents using feedback based on relative attitude information under both undirected and directed cyc

ergodic properties of diffusion type quantum dynamical semigroups we develop a framework for investigation of asymptotic behavior of quantum markov semigroups on c algebras associated with noncommutative elliptic generators an exponential rate of convergence toward the projection onto the fixed point subalgebra has been established and in a particular case of the semigroup selecting rotationally invariant states of a three dimensional quantum system the time factor of such a convergence has been estimated

agreeing asynchronously this paper formulates and solves a version of the widely studied vicsek consensus problem in which each member of a group of n 1 agents independently updates its heading at times determined by its own clock it is not assumed that the agents clocks are synchronized or that the ldquoeventrdquo times between which any one agent updates its heading are evenly spaced nor is it assumed that heading updates must occur instantaneously using the concept of ldquoanalytic synchronizationrdquo together with several key results concerned with properties of ldquocompositionsrdquo of directed graphs it is shown that the conditions under which a consensus is achieved are essentially the same as those applicable in the synchronous case provided the notion of an agent s neighbor between its event times is appropriately defined however in sharp contrast with the synchronous case where for analysis an n dimensional state space model is adequate for the asynchronous version of the problem a 2n dimensional state space model is required it is explained how to analyze this model despite the fact that unlike the synchronous case the stochastic matrices involved do not have all positive diagonal entries

cooperative optimal control for lipschitz nonlinear systems over generally directed topologies abstract this paper studies the cooperative optimal control for multi agent systems mass with lipschitz nonlinearities over general digraphs the leader following consensus model consisting of multiple followers and one leader is constructed distributed optimal control protocols using the linear quadratic regulator approach are designed under the proposed protocols the performance index of the mas is optimized by solving the algebraic riccati equation are the weighting matrices of performance index rely on the lipschitz nonlinearities leading to optimal performance simulation studies are finally reported to illustrate the effectiveness of presented protocols

exponential synchronization of the high dimensional kuramoto model with identical oscillators under digraphs abstract for the kuramoto model and its variations it is difficult to analyze the exponential synchronization under the general digraphs due to the lack of symmetry in this paper for the high dimensional kuramoto model of identical oscillators a matrix riccati differential equation mrde is proposed to describe the error dynamics based on the mrde the exponential synchronization is proved by constructing a total error function for the case of digraphs admitting directed spanning trees

the consensus for discrete time linear multi agent systems under directed switching networks the existing results on the leaderless and leader following consensus problems for discrete time linear multi agent systems subject to jointly connected switching networks are limited to undirected networks this note will first study the stability property for a class of discrete time linear switched systems this stability result will then be applied to the two consensus problems for discrete time linear multi agent systems subject to directed jointly connected switching networks it is shown that in some interesting cases the two problems are solvable by the distributed state feedback control law even if the switching networks are directed and every time disconnected

on constructing lyapunov functions for multi agent systems lyapunov equations that depend on communication graph topologies provide building blocks of lyapunov functions which play an important role in controller design and stability analysis of multi agent systems however construction of such a lyapunov equation in some published works has a flaw or requires unnecessarily strong graph conditions this paper presents several choices of lyapunov equations over various graph topologies

sufficient conditions for conservativity of minimal quantum dynamical semigroups abstract the conservativity of a minimal quantum dynamical semigroup is proved whenever there exists a generalized subharmonic operator bounded from below by the dissipative part of the infinitesimal generator we discuss applications of this criteria in mathematical physics and quantum probability

distributed impulsive group consensus in second order multi agent systems under directed topology this paper investigates the impulsive group consensus problems of second order multi agent systems under directed network topology with acyclic partition two distributed impulsive sampled data protocols are presented to realise group consensus for both cases with leaders and leaderless and then some simple yet generic criteria on convergence for such algorithms are established it is shown that for the case with leaderless a feature of the present protocols is to give an explicit expression of group consensus states in terms of the initial values of the agents which allows us to develop a simple approach yielding the desired group or cluster consensus while for the case of virtual leaders a pinning like tracking technique is effectively designed to regulate all the agents access to the virtual leaders respectively for the purpose of practical control strategy finally simulation results are presented to illustrate the effectiveness of the theoretical analysis

randomized optimal consensus of multi agent systems in this paper we formulate and solve a randomized optimal consensus problem for multi agent systems with stochastically time varying interconnection topology the considered multi agent system with a simple randomized iterating rule achieves an almost sure consensus meanwhile solving the optimization problem min z r email protected i 1 nf i z in which the optimal solution set of objective function f i can only be observed by agent i itself at each time step simply determined by a bernoulli trial each agent independently and randomly chooses either taking an average among its neighbor set or projecting onto the optimal solution set of its own optimization component both directed and bidirectional communication graphs are studied connectivity conditions are proposed to guarantee an optimal consensus almost surely with proper convexity and intersection assumptions the convergence analysis is carried out using convex analysis we compare the randomized algorithm with the deterministic one via a numerical example the results illustrate that a group of autonomous agents can reach an optimal opinion by each node simply making a randomized trade off between following its neighbors or sticking to its own opinion at each time step

consensus in time delayed multi agent systems with quantized dwell times abstract this paper investigates the effects of quantized dwell times in solving consensus problems in time delayed multi agent systems with the asynchronous property of unpredictable quantization jumps in inter agent communications the quantized dwell times can be introduced on purpose or be inherent from quantizing devices they beneficially avoid undesirable fast chattering of quantizers outputs and mathematical difficulties in convergence analysis the main result shows that the largest eigenvalue of the interaction graph laplacian well characterizes the dependence of maximum allowable time delay on quantized dwell times and quantizer parameters under the assumption of heterogeneous time varying transmission delays simulations are presented to show the effectiveness of the main result

adaptive task space synchronisation of networked robotic agents without task space velocity measurements in this paper we investigate the problem of task space synchronisation of multiple robotic agents in the presence of uncertain kinematics and dynamics our control objective is to realise synchronisation without the measurements of task space velocity the communication topology is assumed to be directed graphs containing a spanning tree a decentralised task space observer with kinematic parameter updating is proposed to avoid the reliance of task space velocity based on the observer we propose the distributed adaptive synchronisation controller for two cases 1 the leaderless consensus case and 2 the leader follower case where all the followers track the convex hull spanned by the virtual leaders and for each follower it is required that there exists at least one leader that has a directed path to the follower the asymptotic synchronisation is proved with lyapunov analysis and input output stability analysis tools simulations with multiple robotic agents are performed to show the effectivenes

finite time consensus for multi agent systems with globally bounded convergence time under directed communication graphs abstractin this paper we study the finite time consensus problems with globally bounded convergence time also known as fixed time consensus problems for multi agent systems subject to directed communication graphs two new distributed control strategies are proposed such that leaderless and leader follower consensus are achieved with convergence time independent on the initial conditions of the agents fixed time formation generation and formation tracking problems are also solved as the generalizations simulation examples are provided to demonstrate the performance of the new controllers

quantized consensus on first order integrator networks abstract this paper studies the quantized average consensus problem of first order integrator agents with connected undirected communication graphs because quantized data is inherently associated with discrete time measurements a sampled data based average consensus protocol is proposed in which each agent uses the quantized states of its neighbors measured synchronously at sampling times to update its own state it is proved that for a connected network the distance between the individual state and the average of initial states becomes smaller than the quantization step size in finite time provided the sampling size is smaller than a constant depending on the degree of the communication topology when the sampling size tends to zero an asynchronous protocol is investigated in which the limitation of the switching frequency of quantizers is considered it is shown that for a connected network the given protocol drives the state of each agent into a neighborhood of the average of initial states provided the dwell time of quantizers is small enough

distributed adaptive consensus for multiple mechanical systems with switching topologies and time varying delay abstract this paper studies the adaptive consensus problem of networked mechanical systems with time varying delay and jointly connected topologies two different consensus protocols are proposed first we present an adaptive consensus protocol for the connected switching topologies based on graph theory lyapunov stability theory and switching control theory the stability of the proposed algorithm is demonstrated then we investigate the problem under the more general jointly connected topologies and with concurrent time varying communication delay the proposed consensus protocol consists of two parts one is for the connected agents which contains the current states disagreement among them and the other is designed for the isolated agents which contains the states difference between the current and past a distinctive feature of this work is to address the consensus control problem of mechanical systems with unknown parameters time varying delay and switching topologies in a unified theoretical framework numerical simulation is provided to demonstrate the effectiveness of the obtained results

heisenberg evolution of quantum observables represented by unbounded operators this paper deals with open quantum systems in particular we focus on the adjoint quantum master equations with initial conditions given by unbounded operators examples of this type of initial data are the position and momentum operators of quantum oscillators and the occupation number operator in many body particle systems the article establishes the existence and uniqueness of solutions of the operator equations governing the motion of unbounded observables under the born markov approximations to this end we develop the relation between operator evolution equations arising in quantum mechanics and stochastic evolutions equations of schrodinger type furthermore we examine quantum dynamical semigroup properties of the heisenberg evolutions of general classes of observables

h consensus of second order multi agent systems with asymmetric delays abstract this paper is concerned with the problem of consensus in the h sense for second order continuous time multi agent systems with multiple asymmetric time varying delays by using a model transformation approach and matrix theory we establish several conditions in terms of linear matrix inequalities such that consensus of multi agent systems can be achieved in the h sense the feasibility of the consensus conditions is also analyzed as an application we consider the case of intermittent measurement between agents numerical examples are presented to illustrate the theoretical results which can be applied to the case of negative information weights

cooperative output regulation of heterogeneous multi agent systems an h_ infty criterion in this note the cooperative output regulation problem of heterogeneous linear multi agent systems is investigated our approach is based on internal model and dynamic error feedback among the agents under some standard assumptions the problem is solved by an internal model and a stabilizing h controller we showed that the exo signal free system is stabilized if each controlled agent is robust in the sense of h norm to resist the disturbance measured by the second largest eigenvalue of the graph adjacency matrix then the synthesis problem is solved using algebraic riccati equation furthermore we showed that this condition is a generalization of existing results

on exponential synchronization of kuramoto oscillators in this technical note we study the problem of exponential synchronization for one of the most popular models of coupled phase oscillators the kuramoto model we consider the special case of finite oscillators with distinct bounded natural frequencies our first result derives a lower bound on the coupling gain which is necessary for the onset of synchronization this bound improves the one derived by jadbabaie we then calculate a lower bound on the coupling gain that is sufficient to guarantee oscillator synchronization and derive further sufficient conditions to ensure exponential synchronization of the angular frequencies of all oscillators to the mean natural frequency of the group we also characterize the coupling gain that is sufficient for the oscillator phase differences to approach any desired compact set in finite time

brief paper distributed adaptive control for synchronization of unknown nonlinear networked systems this paper is concerned with synchronization of distributed node dynamics to a prescribed target or control node dynamics a design method is presented for adaptive synchronization controllers for distributed systems having non identical unknown nonlinear dynamics and for a target dynamics to be tracked that is also nonlinear and unknown the development is for strongly connected digraph communication structures a lyapunov technique is presented for designing a robust adaptive synchronization control protocol the proper selection of the lyapunov function is the key to ensuring that the resulting control laws thus found are implementable in a distributed fashion lyapunov functions are defined in terms of a local neighborhood tracking synchronization error and the frobenius norm the resulting protocol consists of a linear protocol and a nonlinear control term with adaptive update law at each node singular value analysis is used it is shown that the singular values of certain key matrices are intimately related to structural properties of the graph

randomized gradient free method for multiagent optimization over time varying networks in this brief we consider the multiagent optimization over a network where multiple agents try to minimize a sum of nonsmooth but lipschitz continuous functions subject to a convex state constraint set the underlying network topology is modeled as time varying we propose a randomized derivative free method where in each update the random gradient free oracles are utilized instead of the subgradients sgs in contrast to the existing work we do not require that agents are able to compute the sgs of their objective functions we establish the convergence of the method to an approximate solution of the multiagent optimization problem within the error level depending on the smoothing parameter and the lipschitz constant of each agent s objective function finally a numerical example is provided to demonstrate the effectiveness of the method

pattern recognition as a quest for minimum entropy abstract we shall show that many known algorithms of clustering and pattern recognition can be characterized as efforts to minimize entropy when suitably defined

adaptive coordinated tracking of multi agent systems with quantized information abstract in this paper we study the adaptive coordinated tracking problem for continuous time first order integrator systems with quantized information under switching undirected and fixed directed communication graphs respectively the combined effect of quantized relative information error and quantized absolute information error on the tracking result is investigated both the logarithmic quantizers and uniform quantizers are considered it is shown that when logarithmic quantizers are used exact coordinated tracking can still be achieved by properly choosing the design parameters in the controller while when uniform quantizers are used practical coordinated tracking can be achieved with tracking error bounds proportional to the quantizer parameter simulation examples are provided to illustrate the results

consensus of second order discrete time multi agent systems with fixed topology abstract this paper studies the consensus of second order discrete time multi agent systems with fixed topology first we formulate the problem and give some preliminaries then by algebraic graph theory and matrix theory the convergence of system matrix is analyzed our main results indicate that the consensus of second order system can be achieved if and only if the topology graph has a directed spanning tree and the values of the scaling parameters satisfy a range the eigenvalues of the corresponding laplacian matrix play a key role in reaching consensus finally numerical simulations are given to illustrate the results

observer design for tracking consensus in second order multi agent systems fractional order less than two this technical note studies the leader following tracking consensus problem of a class of multi agent systems where the dynamics of the leader is described by second order systems in order to track the states of the leader observers for the followers are designed by fractional order multi agent systems where the relative velocity information is unavailable it is interestingly found that the followers can track the leader with second order dynamics even if the fractional order is less than two by only using the position information of the local neighbors which is different from the existing results a novel fractional order observer is first proposed whose order is surprisingly less than the original leader system it is also shown that leader following consensus can be ensured if some carefully selected followers are informed and the relative position based protocols are appropriately designed with fractional order being between one and two a necessary and sufficient condition for the leader following consensus in multi agent systems without control input delay is proposed the results are then extended to the case with constant control input delay it is found that in both cases the real and imaginary parts of the eigenvalues of the augmented laplacian matrix of the topology play an important role in achieving consensus

consensus on complete riemannian manifolds in finite time abstract in view of the fact that prototypes of riemannian manifolds range from euclidean surfaces to lie groups operator spaces etc the paper explores common consensus schemes for connected complete riemannian manifolds after studying the restriction exponential map we introduce a local consensus protocol with switching communication topologies for the manifolds via the isometric mapping based on one of the euclidean consensus protocols equipped with the compression decompression functions we extend the local consensus protocol and put forth a global consensus algorithm for any such manifolds these consensus schemes can provide common solutions to the consensus problems arising from various nonlinear spaces or abstract spaces belonging to connected complete riemannian manifolds in particular they are simple and concise and can converge in finite time simulation on the unit sphere is provided to verify our consensus schemes and to demonstrate the usage of our proposed techniques

self triggered consensus for multi agent systems with zeno free triggers in this technical note a self triggered consensus algorithm for multi agent systems has been proposed each agent receives the state information of its neighbors and computes the average state of its neighborhood based on this average state the event trigger is designed to determine when the agent updates its control input and transmits the average state to its neighbors by specifying a strictly positive minimal inter event time for each agent zeno behavior can be avoided then by solving quadratic equations related to the event condition the self triggered consensus algorithm is developed by directly computing the event time instants with a set of iterative procedures it has been proved that with the proposed zeno free algorithm the agent group can achieve consensus asymptotically compared with the existing works the proposed algorithm is simpler in formulation and computation moreover it has been showed that agents need less time to achieve consensus with considerable reduction of the number of triggering events controller updates and information transmission as a result more energy can be saved using the proposed algorithm in practical multi agent systems

properties of measures of information in evidence and possibility theories abstract an overview of information measures recently introduced by several authors in the settting of shafer s theory of evidence is proposed new results pertaining to additivity and monotonicity properties of these measures of information are presented the interpretation of each measure of information as opposed to others is discussed the potential usefulness of measures of specificity or imprecision is suggested and a principle of minimal specificity is stated for the purpose of reconstructing a body of evidence from incomplete knowledge

hybrid control for connectivity preserving flocking in this technical note we address the combined problem of motion and network topology control in a group of mobile agents with common objective the flocking behavior of the group instead of assuming network connectivity we enforce it by means of distributed topology control that decides on both deletion and creation of communication links between agents adapting the network to the group s spatial distribution with this protocol ensuring network connectivity a decentralized motion controller aligns agent velocity vectors and regulates inter agent distances to maintain existing network links the stability of the flocking controller is established in continuous time by means of an observability argument on a quadratic form of the graph laplacian that exploits the time delay between link deletion and creation caused by the topology control protocol which induces a dwell time between network switches

on dissipative stochastic equations in a hilbert space a general existence and uniqueness theorem for solutions of linear dissipative stochastic differential equation in a hilbert space is proved the dual equation is introduced and the duality relation is established proofs take inspirations from quantum stochastic calculus however without using it solutions of both equations provide classical stochastic representation for a quantum dynamical semigroup describing quantum markovian evolution the problem of the mean square norm conservation closely related to the unitality non explosion of the quantum dynamical semigroup is considered and a hyperdissipativity condition ensuring such conservation is discussed comments are given on the existence of solutions of a nonlinear stochastic differential equation introduced and discussed recently in physical literature in connection with continuous quantum measurement processes

uniqueness of information measure in the theory of evidence abstract an evidence distribution on a set x assigns non negative weights to the subsets of x such weights must sum to one and the empty set is given weight 0 an information measure can be defined for such an evidence distribution if m i are the weights assigned to subsets a i and a i are the cardinalities of these subsets then the function m i log a i satisfies all the usual axioms of an information measure in this paper we show that conversely these axioms are sufficient to characterize uniquely the above measure it can be thus considered as the main uncertainty function for the theory of evidence we demonstrate that using only the properties of symmetry additivity and subadditivity the problem of uniqueness can be reduced to finding linear functionals on the space of functions analytic at origin we surmise that under a suitable continuity hypothesis all such functionals can be represented as linear combinations of the coefficients of taylor series our function then represents the first derivative evaluated at 0 an alternative approach is then discussed we assume a form of branching property suggested by the monotonicity considerations now the properties of symmetry additivity and subadditivity together with branching again offer the unique characterization of the information function no continuity assumption whatsoever is needed and the proof is entirely elementary

on the rendezvous problem for multiple nonholonomic agents in this note a decentralized feedback control strategy that drives a system of multiple nonholonomic unicycles to a rendezvous point in terms of both position and orientation is introduced the proposed nonholonomic control law is discontinuous and time invariant and using tools from nonsmooth lyapunov theory and graph theory the stability of the overall system is examined similarly to the linear case the convergence of the multi agent system relies on the connectivity of the communication graph that represents the inter agent communication topology the control law is first defined in order to guarantee connectivity maintenance for an initially connected communication graph moreover the cases of static and dynamic communication topologies are treated as corollaries of the proposed framework

the constrained rayleigh quotient with a general orthogonality constraint and an eigen balanced laplacian matrix the greatest lower bound and applications in cooperative control problems mathematically the rayleigh quotient is defined as the quadratic function of a symmetric matrix and a nonzero usually unconstrained variable vector in this paper we consider the constrained rayleigh quotient in which the variable vector has the orthogonality constraint i e it is constrained to be orthogonal to a nonzero vector this nonzero vector is called the orthogonality constraint vector or abbreviated as the oc vector for the variable vector the matrix for the rayleigh quotient is an eigen balanced eb laplacian matrix a tighter lower bound of the constrained rayleigh quotient has many implications in mathematics as well as in cooperative control problems the main contributions in this paper are as follows first we provide the greatest lower bound or the infimum of the constrained rayleigh quotient with respect to a general oc vector and the eb laplacian matrix whose results are novel and better than the existing results then we interpret the physical meaning of our results in an insightful geometric form and characterize the properties of the results finally as an example to illustrate the merit of the tighter lower bound of the constrained rayleigh quotient we consider the scale of the agents driving by a fundamental consensus protocol and show that the convergence rate of the agents scale is characterized by the greatest lower bound of the constrained rayleigh quotient

decentralized estimation of laplacian eigenvalues in multi agent systems in this paper we present a decentralized algorithm to estimate the eigenvalues of the laplacian matrix that encodes the network topology of a multi agent system we consider network topologies modeled by undirected graphs the basic idea is to provide a local interaction rule among agents so that their state trajectory is a linear combination of sinusoids oscillating only at frequencies function of the eigenvalues of the laplacian matrix in this way the problem of decentralized estimation of the eigenvalues is mapped into a standard signal processing problem in which the unknowns are the finite number of frequencies at which the signal oscillates

accelerated distributed average consensus via localized node state prediction this paper proposes an approach to accelerate local linear iterative network algorithms asymptotically achieving distributed average consensus we focus on the class of algorithms in which each node initializes its ldquostate valuerdquo to the local measurement and then at each iteration of the algorithm updates this state value by adding a weighted sum of its own and its neighbors state values provided the weight matrix satisfies certain convergence conditions the state values asymptotically converge to the average of the measurements but the convergence is generally slow impeding the practical application of these algorithms in order to improve the rate of convergence we propose a novel method where each node employs a linear predictor to predict future node values the local update then becomes a convex weighted sum of the original consensus update and the prediction convergence is faster because redundant states are bypassed the method is linear and poses a small computational burden for a concrete theoretical analysis we prove the existence of a convergent solution in the general case and then focus on one step prediction based on the current state and derive the optimal mixing parameter in the convex sum for this case evaluation of the optimal mixing parameter requires knowledge of the eigenvalues of the weight matrix so we present a bound on the optimal parameter calculation of this bound requires only local information we provide simulation results that demonstrate the validity and effectiveness of the proposed scheme the results indicate that the incorporation of a multistep predictor can lead to convergence rates that are much faster than those achieved by an optimum weight matrix in the standard consensus framework

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

where do we stand on measures of uncertainty ambiguity fuzziness and the like abstract it is argued in this paper that the theory of fuzzy sets involves at least four fundamentally different types of uncertainty each of these types requires a measure by which the degree of uncertainty of that type can be determined two main categories of uncertainty are connected with the terms vagueness or fuzziness and ambiguity in general vagueness is associated with the difficulty of making sharp or precise distinctions in the world ambiguity on the other hand is associated with one to many relations i e situations with two or more alternatives that are left unspecified while the concept of a fuzzy set represents a basic mathematical framework for dealing with vagueness the concept of a fuzzy measure is a general framework for dealing with ambiguity several classes of measures of vagueness usually referred to as measures of fuzziness have been proposed in the literature each class is based on some underlying conception of the degree of fuzziness a general set of requirements for measures of fuzziness is formulated followed by an overview of the measures proposed in the literature measures of ambiguity are discussed within the framework of plausibility and belief measures although it does not cover all fuzzy measures this framework is sufficiently broad for most practical purposes and represents a generalization of both probability theory and possibility theory it is argued that three complementary measures of ambiguity should be employed one of them is obtained by generalizing the hartley measure of uncertainty it measures the degree of nonspecificity in individual situations described by the various belief and plausibility measures the other two are obtained by generalizing the well known shannon measure of uncertainty they measure the degree of dissonance and the degree of confusion in evidence respectively basic mathematical properties of these measures are overviewed it is also argued that each of the four types of uncertainty measures which are fundamentally different from each other can be used for measuring structural syntactic information in the same sense as the hartley and shannon measures have been used in this respect as such these measures are potentially powerful tools for dealing with systems problems such as systems modelling analysis simplification or design

distributed geodesic control laws for flocking of nonholonomic agents we study the problem of flocking and velocity alignment in a group of kinematic nonholonomic agents in 2 and 3 dimensions by analyzing the velocity vectors of agents on a circle for planar motion or sphere for 3 d motion we develop a geodesic control law that minimizes a misalignment potential and results in velocity alignment and flocking the proposed control laws are distributed and will provably result in flocking when the underlying proximity graph which represents the neighborhood relation among agents is connected we further show that flocking is possible even when the topology of the proximity graph changes over time so long as a weaker notion of joint connectivity is preserved

high dimensional kuramoto models on stiefel manifolds synchronize complex networks almost globally abstract the kuramoto model of coupled phase oscillators is often used to describe synchronization phenomena in nature some applications e g quantum synchronization and rigid body attitude synchronization involve high dimensional kuramoto models where each oscillator lives on the n sphere or so n these manifolds are special cases of the compact real stiefel manifold st p n using tools from optimization and control theory we prove that the generalized kuramoto model on st p n converges to a synchronized state for any connected graph and from almost all initial conditions provided p n satisfies p 2 3 n 1 and all oscillator frequencies are equal this result could not have been predicted based on knowledge of the kuramoto model in complex networks over the circle in that case almost global synchronization is graph dependent it applies if the network is acyclic or sufficiently dense this paper hence identifies a property that distinguishes many high dimensional generalizations of the kuramoto models from the original model

consensus optimization on manifolds the present paper considers distributed consensus algorithms that involve n agents evolving on a connected compact homogeneous manifold the agents track no external reference and communicate their relative state according to a communication graph the consensus problem is formulated in terms of the extrema of a cost function this leads to efficient gradient algorithms to synchronize i e maximizing the consensus or balance i e minimizing the consensus the agents a convenient adaptation of the gradient algorithms is used when the communication graph is directed and time varying the cost function is linked to a specific centroid definition on manifolds introduced here as the induced arithmetic mean that is easily computable in closed form and may be of independent interest for a number of manifolds the special orthogonal group so n and the grassmann manifold text it grass p n are treated as original examples a link is also drawn with the many existing results on the circle

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

curve shortening and the rendezvous problem for mobile autonomous robots if a smooth closed and embedded curve is deformed along its normal vector field at a rate proportional to its curvature it shrinks to a circular point this curve evolution is called euclidean curve shortening and the result is known as the gage hamilton grayson theorem motivated by the rendezvous problem for mobile autonomous robots we address the problem of creating a polygon shortening flow a linear scheme is proposed that exhibits several analogues to euclidean curve shortening the polygon shrinks to an elliptical point convex polygons remain convex and the perimeter of the polygon is monotonically decreasing

distributed formation control of multi agent systems using complex laplacian the paper concentrates on the fundamental coordination problem that requires a network of agents to achieve a specific but arbitrary formation shape a new technique based on complex laplacian is introduced to address the problems of which formation shapes specified by inter agent relative positions can be formed and how they can be achieved with distributed control ensuring global stability concerning the first question we show that all similar formations subject to only shape constraints are those that lie in the null space of a complex laplacian satisfying certain rank condition and that a formation shape can be realized almost surely if and only if the graph modeling the inter agent specification of the formation shape is 2 rooted concerning the second question a distributed and linear control law is developed based on the complex laplacian specifying the target formation shape and provable existence conditions of stabilizing gains to assign the eigenvalues of the closed loop system at desired locations are given moreover we show how the formation shape control law is extended to achieve a rigid formation if a subset of knowledgable agents knowing the desired formation size scales the formation while the rest agents do not need to re design and change their control laws

distributed adaptive consensus output regulation of network connected heterogeneous unknown linear systems on directed graphs this technical note deals with output regulation of network connected linear systems under directed connection graphs the subsystem dynamics are unknown and heterogeneous the desired output signal generated by a linear exosystem is only available to some subsystems and the others will estimate the exosystem state through the network connections for obtaining regulation errors the exosystem is parametrised in a specific form such that it has a skew symmetric system matrix whose property is further explored in the estimation of exosystem state and in the estimation of the desired feed forward control inputs for output regulation the unknown subsystem parameters are dealt with by the adaptive laws driven by the estimated regulation errors the proposed adaptive control strategy is fully distributed in the sense that the control design only uses the information in the connected neighbourhood without reference to the eigenstructure of the associated laplacian matrix as long as the connection graph is strongly connected

on global leader following consensus of identical linear dynamic systems subject to actuator saturation abstract this paper studies the leader following consensus problem for a group of agents with identical linear systems subject to control input saturation we focus on two classes of linear systems neutrally stable systems and double integrator systems for neurally stable systems we establish that global consensus can be achieved by linear local feedback laws over a fixed communication topology and with proper choices of relative potential functions global consensus can also be achieved over a switching communication topology for double integrator systems we establish that global consensus can be achieved by linear local feedback laws over a fixed communication topology and with the help of a simple saturation function in the local feedback laws global consensus can also be achieved over a switching communication topology simulation results illustrate the theoretical results

a common framework for complete and incomplete attitude synchronization in networks with switching topology in this paper we study attitude synchronization for elements in the unit sphere in mathbb r scriptscriptstyle scriptscriptstyle 3 and for elements in the three dimensional 3 d rotation group for a network with switching topology the agents angular velocities are assumed to be the control inputs and a switching control law for each agent is devised that guarantees synchronization provided that all elements are initially contained in a region which we identify later in the paper the control law is decentralized and it does not require a common orientation frame among all agents we refer to synchronization of unit vectors in mathbb r scriptscriptstyle 3 as incomplete synchronization and of 3 d rotation matrices as complete synchronization our main contribution lies in showing that these two problems can be analyzed under a common framework where all agents dynamics are transformed into unit vectors dynamics on a sphere of appropriate dimension

persistent flows in deterministic chains this paper studies the role of persistent flows in the convergence of infinite backward products of stochastic matrices of deterministic chains over networks with nonreciprocal interactions between agents an arc describing the interaction strength between two agents is said to be persistent if its weight function has an infinite l 1 norm convergence of the infinite backward products to a rank one matrix of a deterministic chain of stochastic matrices is equivalent to achieving consensus at the node states we discuss two balance conditions on the interactions between agents which generalize the arc balance and cut balance conditions in the literature respectively the proposed conditions require that such a balance should be satisfied over each time window of a fixed length instead of at each time instant we prove that in both cases global consensus is reached if and only if the persistent graph which consists of all the persistent arcs contains a directed spanning tree the convergence rates of the system to consensus are also provided in terms of the interactions between agents having taken place the results are obtained under a weak condition without assuming the existence of a positive lower bound of all the nonzero weights of arcs and are compared with the existing results illustrative examples are provided to validate the results and show the critical importance of the nontrivial lower boundedness of the self confidence of the agents

finite time consensus using stochastic matrices with positive diagonals we discuss the possibility of reaching consensus in finite time using only linear iterations with the additional restrictions that the update matrices must be stochastic with positive diagonals and consistent with a given graph structure we show that finite time average consensus can always be achieved for connected undirected graphs for directed graphs we show some necessary conditions for finite time consensus including strong connectivity and the presence of a simple cycle of even length

on the consensus of homogeneous multi agent systems with arbitrarily switching topology abstract in this paper we investigate the consensus problem under arbitrary switching for homogeneous multi agent systems with switching communication topology by assuming that each agent is described by a single input stabilizable state space model and that the communication graph is connected at every time instant under these assumptions we construct a common quadratic positive definite lyapunov function for the switched system describing the evolution of the disagreement vector thus showing that the agents always reach consensus in addition the proof leads to the explicit construction of a constant state feedback matrix that allows the multi agent system to achieve consensus

designing fully distributed consensus protocols for linear multi agent systems with directed graphs this technical note addresses the distributed consensus protocol design problem for multi agent systems with general linear dynamics and directed communication graphs existing works usually design consensus protocols using the smallest real part of the nonzero eigenvalues of the laplacian matrix associated with the communication graph which however is global information in this technical note based on only the agent dynamics and the relative states of neighboring agents a distributed adaptive consensus protocol is designed to achieve leader follower consensus in the presence of a leader with a zero input for any communication graph containing a directed spanning tree with the leader as the root node the proposed adaptive protocol is independent of any global information of the communication graph and thereby is fully distributed extensions to the case with multiple leaders are further studied

network flows that solve linear equations we study distributed network flows as solvers in continuous time for the linear algebraic equation mathbf z mathbf h mathbf y each node i has access to a row mathbf h i mathrm t of the matrix mathbf h and the corresponding entry z i in the vector mathbf z the first consensus projection flow under investigation consists of two terms one from standard consensus dynamics and the other contributing to projection onto each affine subspace specified by the mathbf h i and z i the second projection consensus flow on the other hand simply replaces the relative state feedback in consensus dynamics with projected relative state feedback without dwell time assumption on switching graphs we prove that all node states converge to a common solution of the linear algebraic equation if there is any the convergence is global for the consensus projection flow while local for the projection consensus flow in the sense that the initial values must lie on the affine subspaces if the linear equation has no exact solutions we show that the node states can converge to a ball around the least squares solution whose radius can be made arbitrarily small through selecting a sufficiently large gain for the consensus projection flow for a fixed bidirectional graph semi global convergence to approximate least squares solutions is also demonstrated for switching balanced directed graphs under suitable conditions it is also shown that the projection consensus flow drives the average of the node states to the least squares solution with a complete graph numerical examples are provided as illustrations of the established results

consensusability of multi agent systems with time varying communication delay abstract this paper studies the consensusability problem of continuous time multi agent systems with time varying communication delay in undirected network we design a consensus protocol based on the low gain solution of a parametric algebraic riccati equation are and not use the precise information of the amount of time varying delay by studying the joint effect of agent dynamic and network topology sufficient conditions are given for consensus when all poles of the system matrix are on the closed left half plane in case of non zero poles on the imaginary axis maximal admissible upper bound of the time varying delay is given in terms of both the agent dynamic and network topology otherwise consensus can be achieved for the time varying delay with arbitrarily large upper bound finally simulation results are presented to demonstrate the effectiveness of the theoretical results

on the equivalence and condition of different consensus over a random network generated by i i d stochastic matrices our objective is to find a necessary and sufficient condition for consensus over a random network generated by i i d stochastic matrices we show that the consensus problem in all different types of convergence almost surely in probability and in lp for every p 1 are actually equivalent thereby obtain the same necessary and sufficient condition for all of them the main technique we used is based on the stability in a projected subspace of the concerned infinite sequences

the deformed consensus protocol this paper studies a generalization of the standard continuous time consensus protocol obtained by replacing the laplacian matrix of the communication graph with the so called deformed laplacian the deformed laplacian is a second degree matrix polynomial in the real variable s which reduces to the standard laplacian for s equal to unity the stability properties of the ensuing deformed consensus protocol are studied in terms of parameter s for some special families of undirected and directed graphs and for arbitrary graph topologies by leveraging the spectral theory of quadratic eigenvalue problems examples and simulation results are provided to illustrate our theoretical findings

equilibria and steering laws for planar formations abstract this paper presents a lie group setting for the problem of control of formations as a natural outcome of the analysis of a planar two vehicle formation control law the vehicle trajectories are described using the planar frenet serret equations of motion which capture the evolution of both the vehicle position and orientation for unit speed motion subject to curvature steering control the set of all possible relative equilibria for arbitrary g invariant curvature controls is described where g se 2 is a symmetry group for the control law and a global convergence result for the two vehicle control law is proved an n vehicle generalization of the two vehicle control law is also presented and the corresponding relative equilibria for the n vehicle problem are characterized work is on going to discover stability and convergence results for the n vehicle problem

on the structure of covariant dynamical semigroups abstract dynamical semigroups in b h without the norm continuity assumption are investigated by introducing the notion of form generator giving the mathematical expression for the idea of markovian master equation it is shown that any form generator on b h admits a standard representation and the non uniqueness of this representation is described the equations for the components of the standard representation of a covariant form generator are deduced in terms of low order cohomology of the symmetry group in particular noncommutative levy khinchin type formulae for the shift covariant form generators are obtained relations with previous works on characterisation of the unbounded generator of a dynamical semigroup are discussed

seeking consensus in networks of linear agents communication noises and markovian switching topologies the stochastic consensus problem of linear multi input multi output mimo multi agent systems mass with communication noises and markovian switching topologies is studied in this technical note the agent s full state is first estimated by the state observer and then the estimated state is exchanged with neighbor agents through a noisy communication environment the communication topology is randomly switching and the switching law is described by a continuous time markovian chain then a consensus protocol is proposed for this mas and some sufficient conditions are obtained for ensuring the mean square and almost sure consensus in addition if the communication topology is fixed some necessary and sufficient conditions for the mean square consensus can be obtained according to whether or not each agent in the system has parents

second order consensus of networked thrust propelled vehicles on directed graphs this technical note addresses the second order consensus problem of multiple underactuated thrust propelled vehicles tpvs on directed graphs containing a directed spanning tree we propose an adaptive control approach to resolve this problem and the proposed controller does not rely on the commonly used backstepping methodology and the exact knowledge of the mass properties of the tpvs in addition the resultant complexity is reduced and the requirement on the interaction graph is relaxed using an input output analysis we show that the proposed controller realizes second order consensus of the tpvs i e the position and velocity consensus errors between the tpvs converge to zero and moreover the velocities of the tpvs converge to the weighted average of their initial values the performance of the proposed control approach is shown by a numerical simulation

brief paper robust consensus of multi agent systems with diverse input delays and asymmetric interconnection perturbations the consensus problem of second order multi agent systems with diverse input delays is investigated based on the frequency domain analysis decentralized consensus conditions are obtained for the multi agent system with symmetric coupling weights then the robustness of the symmetric system with asymmetric perturbation is studied a bound of the largest singular value of the perturbation matrix is obtained as the robust consensus condition simulation examples illustrate the design procedure of consensus protocols and validate the correctness of the results

control of a driftless bilinear vector field on n sphere in this paper we consider a multi input driftless bilinear system evolving on the n dimensional sphere s n we first provide examples drawn from rigid body mechanics that provide the motivation for the control of bilinear systems on s n for the general framework we establish the global controllability on s n and propose two linear control laws on s n that achieve asymptotic stabilization of an equilibrium point with an almost global domain of attraction further the asymptotically stable closed loop system trajectories are shown to be arcs on the geodesics of s n for a particular choice of the equilibrium point next we propose two linear time varying control laws to achieve trajectory tracking on s n and show the asymptotic stability of the tracking error a distributed control is designed for the consensus of multiagent bilinear systems on s n with an undirected tree as the communication graph the consensus manifold is shown to have an almost global domain of attraction

multi agent second order average consensus with prescribed transient behavior the problem of consensus reaching with prescribed transient behavior for a group of double integrator agents is addressed the information exchange of the multi agent system is described by a static communication network we initially set time dependent constraints on the transient response of the relative positions between neighboring agents and we propose a distributed control law consisting of a proportional term of the transformed error and an additional damping term based on absolute velocities measurements we also design an agreement protocol that can additionally achieve prescribed performance for a combined error of positions and velocities under a sufficient condition for the damping gains the proposed nonlinear time dependent distributed controllers guarantee that the predefined constraints are not violated and that consensus is achieved with a convergence rate independent of the underlying communication graph furthermore connectivity maintenance can be ensured by appropriately designing the performance bounds theoretical results are supported by simulations

on discrete time convergence for general linear multi agent systems under dynamic topology this note aims to develop the nonnegative matrix theory in particular the product properties of infinite row stochastic matrices which is widely used for multiple integrator agents to deal with the convergence analysis of general discrete time linear multi agent systems mass with the proposed approach it is finally shown both theoretically and by simulation that the consensus for all the agents can be reached exponentially fast under relaxed conditions i e the individual uncoupled system is allowed to be strictly unstable in the discrete time sense and it is only required that the joint of the communication topologies has a spanning tree frequently enough moreover a least convergence rate as well as an upper bound for the strictly unstable mode which are independent of the switching mode of the system are specified as well

synchronization and balancing on the n torus in this paper we study the behavior of a network of n agents each evolving on the circle we propose a novel algorithm that achieves synchronization or balancing in phase models under mild connectedness assumptions on the possibly time varying and unidirectional communication graphs the global convergence analysis on the n torus is a distinctive feature of the present work with respect to previous results that have focused on convergence in the euclidean space

generators of quantum markov semigroups quantum markov semigroups qmss originally arose in the study of the evolutions of irreversible open quantum systems mathematically they are a generalization of classical markov semigroups where the underlying function space is replaced by a non commutative operator algebra in the case when the qms is uniformly continuous theorems due to the works of lindblad commun math phys 48 119 130 1976 stinespring proc am math soc 6 211 216 1955 and kraus ann phys 64 311 335 1970 imply that the generator of the semigroup has the form l a n 1 vn avn ga ag where vn and g are elements of the underlying operator algebra in the present paper we investigate the form of the generators of qmss which are not necessarily uniformly continuous and act on the bounded operators of a hilbert space we prove that the generators of such semigroups have forms that reflect the results of lindblad and stinespring we also make some progress towards forms reflecting kraus result finally we look at