nonzero bound on fiedler eigenvalue causes exponential growth of h infinity norm of vehicular platoon we consider platoons composed of identical vehicles and controlled in a distributed way that is each vehicle has its own onboard controller the regulation errors in spacing to the immediately preceeding and following vehicles are weighted differently by the onboard controller which thus implements an asymmetric bidirectional control scheme the weights can vary along the platoon we prove that such platoons have a nonzero uniform bound on the second smallest eigenvalue of the graph laplacian matrix the fiedler eigenvalue furthermore it is shown that existence of this bound always signals undesirable scaling properties of the platoon namely the h infinity norm of the transfer function of the platoon grows exponentially with the number of vehicles regardless of the controllers used hence the benefits of a uniform gap in the spectrum of a laplacian with an asymetric distributed controller are paid for by poor scaling as the number of vehicles grows

synchronization of identical linear dynamic systems subject to input saturation abstract this paper investigates the synchronization problem for a group of agents with identical linear dynamics subject to input saturation two classes of linear systems asymptotically null controllable with bounded control ancbc systems and double integrator systems are studied for ancbc systems it is shown that a linear protocol with the control gain obtained via parametric lyapunov equations can semiglobally synchronize the undirected topology provided that its augmented directed topology has a spanning tree for a special case of ancbc the double integrator systems it is established that if the augmented directed topology has a spanning tree then in the presence of input saturation using linear protocols with positive control gains can achieve global synchronization two numerical examples are given to demonstrate the effectiveness of the theoretical results

robust consensus tracking control for multiagent systems with initial state shifts disturbances and switching topologies this paper deals with the consensus tracking control issues of multiagent systems and aims to solve them as accurately as possible over a finite time interval through an iterative learning approach based on the iterative rule distributed algorithms are proposed for every agent using its nearest neighbor knowledge for which the robustness problem is addressed against initial state shifts disturbances and switching topologies these uncertainties are dynamically changing not only along the time axis but also the iteration axis it is shown that the matrix norm conditions can be developed to achieve the convergence of the considered consensus tracking objectives for which necessary and sufficient conditions are presented in terms of linear matrix inequalities to guarantee their feasibility in the sense of the spectral norm furthermore simulation examples are given to illustrate the effectiveness and robustness of the obtained consensus tracking results

distributed robust consensus control of multi agent systems with heterogeneous matching uncertainties this paper considers the distributed consensus problem of linear multi agent systems subject to different matching uncertainties for both the cases without and with a leader of bounded unknown control input due to the existence of nonidentical uncertainties the multi agent systems discussed in this paper are essentially heterogeneous for the case where the communication graph is undirected and connected based on the local state information of neighboring agents a fully distributed continuous adaptive consensus protocol is designed under which the consensus error is uniformly ultimately bounded and exponentially converges to a small adjustable bounded set for the case where there exists a leader whose control input is unknown and bounded a distributed adaptive consensus protocol is proposed to ensure the boundedness of the consensus error a sufficient condition for the existence of the proposed protocols is that each agent is stabilizable

q oscillator realizations of the quantum superalgebras slq m n andospq m 2n realizations of the quantum superalgebras corresponding to thea m n b m n c n 1 andd m n series are given in terms of the creation and annihilation operators ofq deformed bose and fermi oscillators

finite dimensional irreducible representations of the quantum superalgebra u q gl n 1 it is shown that every finite dimensional irreducible module over the general linear lie superalgebragl n 1 can be deformed to an irreducible module ofu q gl n 1 aq analogue of the universal enveloping algebra ofgl n 1 the results are extended also to all kac modules which in the atypical cases remain indecomposible within each module expressions for the transformations of the gel fand zetlin basis under the action of the algebra generators are written down an analogoue of the poincare birkhoff witt theorem is formulated

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

consensus and its ℒ 2 gain performance of multi agent systems with intermittent information transmissions this article addresses the consensus problem for cooperative multiple agents with nonlinear dynamics on a fixed directed information network where each agent can only communicate with its neighbours intermittently a class of control algorithms is first introduced using only intermittent relative local information by combining tools from switching systems and lyapunov stability theory some sufficient conditions are established for consensus of multi agent systems without any external disturbances under a fixed strongly connected topology theoretical analyses are further provided for consensus of multi agent systems in the presence of external disturbances it is shown that a finite 2 gain performance index for the closed loop multi agent systems can be guaranteed if the coupling strength of the network is larger than a threshold value determined by the average communication rate and the generalised algebraic connectivity of the strongly connected topology the results are then extended to consensus

distributed adaptive consensus and output tracking of unknown linear systems on directed graphs this paper considers both the distributed consensus control and output tracking problems of a group of unknown linear subsystems using the relative output information of neighboring subsystems each system is a minimum phase siso system with relative degree one and unknown parameters and the interaction graph among the subsystems is directed for the case where the directed graph is strongly connected a distributed adaptive protocol is designed to achieve consensus for the case where there exists an arbitrary constant reference signal a distributed adaptive controller together with an internal model are presented to achieve output tracking in the sense that the subsystem outputs asymptotically follow a reference constant the proposed adaptive protocols are independent of the parameters of the subsystems only use the relative outputs of neighboring subsystems and hence are fully distributed

finite dimensional representations of the quantum superalgebra uq gl 3 2 in a reduced uq gl 3 2 contains implies uq gl 3 1 contains implies uq gl 3 basis for generic q we give expressions for the transformations of all essentially typical finite dimensional modules of the hopf superalgebra uq ql 3 2 the latter is a deformation of the universal enveloping algebra of the lie superalgebra gl 3 2 the basis within each module is similar to the gel fand zetlin basis for gl 5 we write down expressions for the transformations of the basis under the action of the chevalley generators

an explicit unconditionally stable variable time step method for one dimensional stefan problems modelling of heat conduction processes with phase changes benefits from the application of variable time step methods when the behaviour of the moving boundary is not known a priori due to convergence and stability constraints only implicit difference equations have been used with these methods implicit methods show a significant loss of accuracy and exhibit convergence difficulties when used for relatively slow or rapid moving boundary problems

induced representations of the multiparameter hopf superalgebras uuq gl m n and uuq sl m n we construct the induced holomorphic representations of the multiparameter hopf superalgebras uuq gl m n and uuq sl m n the first superalgebra we constructed earlier as the dual of the multiparameter quantum deformation of the supergroup gl m n the second superalgebra is a hopf subalgebra of the first for a special choice of the parameters the representations are labelled by m n integer numbers respectively m n 1 complex numbers and act in the space of formal power series of m n m n 1 2 non commuting variables of which mn are odd and the rest are even these variables generate a q deformation of a flag supermanifold of the supergroup gl m n respectively sl m n

character formulas for irreducible modules of the lie superalgebras sl m n kac distinguished between typical and atypical finite dimensional irreducible representations of the lie superalgebras sl m n and provided an explicit character formula appropriate to all the typical representations here the range of validity of some character formulas for atypical representations that have been proposed are discussed several of them are of the kac weyl type but then it is proved that all formulas of this type fail to correctly give the character of one particular atypical representation of sl 3 4 having ruled out therefore all such formulas a completely new extension of the kac weyl character formula is proposed the validity of this formula in the case of all covariant tensor irreducible representations is proved and some evidence in support of the conjecture that it covers all irreducible representations of sl m n is presented

distributed static output feedback control for state synchronization in networks of identical lti systems this paper studies state synchronization of multi agent systems with disturbances using distributed static output feedback opfb control the bounded l 2 gain synchronization problem using distributed static opfb is defined and solved the availability of only output measurements restricts the local controls design while the communication graph topology restricts global information flow among the agents it is shown here that these two types of restriction can be dealt with in a symmetric manner and lead to two similar conditions guaranteeing the existence of bounded l 2 gain static opfb one condition is on the output measurement matrix on a local scale and the other on the graph laplacian matrix on a global scale under additional conditions a distributed two player zero sum game using static opfb is also solved and leads to distributed nash equilibrium on the communication graph as a special case the static opfb globally optimal control is given a new class of digraphs satisfying the above condition on the graph laplacian is studied the synchronizing region for distributed static opfb control is exposed and found to be conical different than the infinite right half plane synchronizing region for distributed state feedback

coordination of multi agent systems on interacting physical and communication topologies abstract a new framework is given for coordination of multi agent systems that are interconnected by a physical coupling digraph the edges of this graph represent physical couplings between agents that are fixed due to dynamical interactions on top of the physical graph distributed control protocols are designed where the allowed communications between agents for control purposes are prescribed by a second fixed communication digraph the physical and communication digraphs are generally different and the combination of these two graphs forms a cyber physical system the interactions between physical and communication graphs are the focus of this paper we consider different interactions between two graphs including the case when their pinned laplacian commutes the case of the communication graph with diagonalizable pinned laplacian and the case of two general graphs moreover within each graph the relations between the agents can be either collaborative or antagonistic to capture this the theory of bipartite consensus is used coordination protocols for different cases are designed that are distributed with respect to the communication graph and overcome the detrimental effects of the signed physical graph the proposed control methods are illustrated by simulation examples

centre and representations of at roots of unity quantum groups at the roots of unity have the property that their centre is enlarged polynomial equations relate the standard deformed casimir operators and the new central elements these relations are important from a physical point of view since they correspond to relations between quantum expectation values of observables that have to be satisfied on all physical states in this paper we establish these relations in the case of the quantum lie superalgebra in the course of the argument we find and use a set of representations such that any relation satisfied on all the representations of the set is true in this set is a subset of the set of all the finite dimensional irreducible representations of which we classify and describe explicitly

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

distributed robust control of linear multi agent systems with parameter uncertainties this article considers the distributed robust control problems of uncertain linear multi agent systems with undirected communication topologies it is assumed that the agents have identical nominal dynamics while subject to different norm bounded parameter uncertainties leading to weakly heterogeneous multi agent systems distributed controllers are designed for both continuous and discrete time multi agent systems based on the relative states of neighbouring agents and a subset of absolute states of the agents it is shown for both the continuous and discrete time cases that the distributed robust control problems under such controllers in the sense of quadratic stability are equivalent to the h control problems of a set of decoupled linear systems having the same dimensions as a single agent a two step algorithm is presented to construct the distributed controller for the continuous time case which does not involve any conservatism and meanwhile decouples the feedback gain design from the commun

iterative control for networked heterogeneous multi agent systems with uncertainties this note addresses the convergence of iterative control for networked heterogeneous multi agent systems where each agent has potentially different dynamics and dissimilar uncertainties the major contribution of this work is to quantify the acceptable modeling uncertainty for ensuring convergence of the proposed iterative approach for collaborative tracking convergence conditions are established for the case when inversion based iterative control of each individual agent designed separately independent of the iterative controllers of the other agents are conjoined using a network graph structure

optimal design for synchronization of cooperative systems state feedback observer and output feedback this technical note studies synchronization of identical general linear systems on a digraph containing a spanning tree a leader node or command generator is considered which generates the desired tracking trajectory a framework for cooperative tracking control is proposed including full state feedback control observer design and dynamic output feedback control the classical system theory notion of duality is extended to networked systems it is shown that unbounded synchronization regions that achieve synchronization on arbitrary digraphs containing a spanning tree can be guaranteed by using linear quadratic regulator based optimal control and observer design methods at each node

numerical solution of the time fractional reaction diffusion equation with a moving boundary abstract a fractional reaction diffusion model with a moving boundary is presented in this paper an efficient numerical method is constructed to solve this moving boundary problem our method makes use of a finite difference approximation for the temporal discretization and spectral approximation for the spatial discretization the stability and convergence of the method is studied and the errors of both the semi discrete and fully discrete schemes are derived numerical examples motivated by problems from developmental biology show a good agreement with the theoretical analysis and illustrate the efficiency of our method

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

a new numerical algorithm for 2d moving boundary problems using a boundary element method phase change problems are of practical importance and can be found in a wide range of engineering applications in the present paper two proposed numerical algorithms are developed the first one is general for phase change problems while the second one is for ablation problems the boundary elements method is used as a mathematical tool in conjunction with the proposed algorithms two test examples were solved and the results agree with the physics of the problems

brief paper synchronization in networks of identical linear systems the paper investigates the synchronization of a network of identical linear state space models under a possibly time varying and directed interconnection structure the main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected the result can be interpreted as a generalization of classical consensus algorithms stronger conditions are shown to be sufficient but to some extent also necessary to ensure synchronization with the diffusive static output coupling often considered in the literature

disconnected synchronized regions of complex dynamical networks this technical note addresses the synchronized region problem which is converted to a more convenient matrix stability problem for complex dynamical networks for any natural number n the existence of a network with n disconnected synchronized regions is theoretically proved and numerically demonstrated this shows the intrinsic complexity of the network synchronization problem convexity characteristic of stability for relevant matrix pencils is further discussed a smooth chua s circuit network is finally discussed as an example for illustration

on the composition factors of kac modules for the lie superalgebras sl m n in the classification of finite dimensional modules of lie superalgebras kac distinguished between typical and atypical modules kac introduced an induced module the so called kac module v with highest weight which was shown to be simple if is a typical highest weight if is an atypical highest weight the kac module is indecomposable and the simple module v can be identified with a quotient module of v in the present paper the problem of determining the composition factors of the kac modules for the lie superalgebra sl m n is considered an algorithm is given to determine all these composition factors and conversely an algorithm is given to determine all the kac modules containing a given simple module as a composition factor the two algorithms are presented in the form of conjectures and illustrated by means of detailed examples strong evidence in support of the conjectures is provided the combinatorial way in which the two algorithms are intertwined is both surprising and interesting and is a convincing argument in favor of the solution to the composition factor problem presented here

decentralized stabilizability of multi agent systems under fixed and switching topologies abstract the paper studies decentralized stabilizability for multi agent systems with general linear dynamics the stabilizability problem is formulated in a way that the protocol performance can be evaluated by means of the stabilizability region and the feedback gain for fixed topology it is proved that the system is stabilizable if and only if external control inputs are exerted on some indicated agents the result is further shown to be a prerequisite for subsequent design of the corresponding decentralized external self feedback control which is also necessary and sufficient based on this two methods are presented to find the agents under which stabilizability can be reached and the region of stabilizability is given to evaluate the protocol performance for switching interaction topology it is shown that the system is stabilizable even if each of its subsystems is not finally the results are employed to cope with the decentralized set point formation control problem for which some necessary and or sufficient conditions are developed numerical simulations are presented to demonstrate the effectiveness of the proposed results

optimisation and adaptation of synchronisation controllers for networked second order infinite dimensional systems abstractthe adaptation and optimisation of synchronisation control for networked second order distributed parameter systems are considered the objective is to design output feedback controllers guaranteeing agreement between the states of the n systems that individually track a reference model the controller structure involves feedback terms consisting of the pairwise difference of the measurements of the second order systems as well as coupling terms that enforce consensus placing the closed loop networked systems in aggregate form allows for further optimisation of the synchronisation gains using the aggregate systems closed loop energy as a suitable optimisation measure the search for the synchronisation gains reduces to the minimisation of the optimisation index which eventually is described by the trace of the solution to a parameterised lyapunov operator equation considering the adaptation of the synchronisation gains offers an alternative to optimisation the adaptation is based on lyapuno

distributed consensus control for linear multi agent systems with discontinuous observations this article addresses the distributed consensus problem of linear multi agent systems with discontinuous observations over a time invariant undirected communication topology under the assumption that each agent can only intermittently share its outputs with the neighbours a class of distributed observer type of protocols are designed and utilised to achieve consensus by using appropriate matrix decomposition it is shown that consensus in the closed loop multi agent systems under a connected topology can be converted to the simultaneous asymptotic stability of a set of switching systems whose dimensions are the same as each agent from a multiple lyapunov functions approach it is proved that there exists a protocol to guarantee consensus if the communication time rate is larger than a threshold value furthermore a distributed pinning control method is employed to solve the consensus problem on an arbitrary given topology which needs not be connected particularly the questions of what kind of agen

pinning control of scale free dynamical networks abstract recently it has been demonstrated that many large complex networks display a scale free feature that is their connectivity distributions have the power law form in the present work control of a scale free dynamical network by applying local feedback injections to a fraction of network nodes is investigated the specifically and randomly pinning schemes are considered the specifically pinning of the most highly connected nodes is shown to require a significantly smaller number of local controllers as compared to the randomly pinning scheme the method is applied to an array of chua s oscillators as an example

pinning synchronization of directed networks with switching topologies a multiple lyapunov functions approach this paper studies the global pinning synchronization problem for a class of complex networks with switching directed topologies the common assumption in the existing related literature that each possible network topology contains a directed spanning tree is removed in this paper using tools from m matrix theory and stability analysis of the switched nonlinear systems a new kind of network topology dependent multiple lyapunov functions is proposed for analyzing the synchronization behavior of the whole network it is theoretically shown that the global pinning synchronization in switched complex networks can be ensured if some nodes are appropriately pinned and the coupling is carefully selected interesting issues of how many and which nodes should be pinned for possibly realizing global synchronization are further addressed finally some numerical simulations on coupled neural networks are provided to verify the theoretical results

irreducible finite dimensional representations of the lie superalgebra gl n 1 in a gel fand zetlin basis all finite dimensional irreducible representations of the general linear lie superalgebra gl n 1 are studied for each representation a concept of a gel fand zetlin basis is defined expressions for the transformation of the basis under the action of the generators are written down

coordination of multiagents interacting under independent position and velocity topologies we consider the coordination control for multiagent systems in a very general framework where the position and velocity interactions among agents are modeled by independent graphs different algorithms are proposed and analyzed for different settings including the case without leaders and the case with a virtual leader under fixed position and velocity interaction topologies as well as the case with a group velocity reference signal under switching velocity interaction it is finally shown that the proposed algorithms are feasible in achieving the desired coordination behavior provided the interaction topologies satisfy the weakest possible connectivity conditions such conditions relate only to the structure of the interactions among agents while irrelevant to their magnitudes and thus are easy to verify rigorous convergence analysis is preformed based on a combined use of tools from algebraic graph theory matrix analysis as well as the lyapunov stability theory

cooperative optimal control for multi agent systems on directed graph topologies this note brings together stability and optimality theory to design distributed cooperative control protocols that guarantee consensus and are globally optimal with respect to a positive semi definite quadratic performance criterion a common problem in cooperative optimal control is that global optimization problems generally require global information which is not available to distributed controllers optimal control for multi agent systems is complicated by the fact that the communication graph topology interplays with the agent system dynamics in the note we use an inverse optimality approach together with partial stability to consider the cooperative consensus and pinning control agents with identical linear time invariant dynamics are considered communication graphs are assumed directed and having fixed topology structured quadratic performance indices are derived that capture the topology of the graph which allows for global optimal control that is implemented using local distributed protocols a new class of digraphs is defined that admits a distributed solution to the global optimal control problem namely those with simple graph laplacian matrices

a conservative finite element method for one dimensional stefan problems with appearing and disappearing phases abstract a one dimensional stefan problem involving several phases solid liquid vapor which can appear and disappear is considered a numerical method for such problems is described and numerically tested it is derived from a previous method of the same authors for one phase problems it is a front tracking method based on finite elements in space and time the treatment of the boundary conditions and the computation of the moving boundaries guarantee the exact conservation of heat energy the numerical experiments demonstrate the accuracy and efficiency of the method moreover they show that the appearing interfaces start smoothly with a vanishing initial speed to the authors knowledge this property has not been mathematically proved

finite dimensional irreducible representations of the quantum supergroup uq gl m n finite dimensional irreducible representations of the quantum supergroup uq gl m n at both generic q and q being a root of unity are investigated systematically within the framework of the induced module construction the representation theory is rather similar to that of gl m n at generic q but drastically different when q is a root of unity in the latter case atypicality conditions of highest weight irreducible representations irreps are substantially altered and such finite dimensional irreps arise that do not have highest weight and or lowest weight vectors as concrete examples the irreps of uq gl 2 1 are classified

cooperative adaptive fuzzy tracking control for networked unknown nonlinear multiagent systems with time varying actuator faults in this paper the cooperative adaptive fault tolerant fuzzy tracking control caftftc problem of networked high order multiagent with time varying actuator faults is studied and a novel caftftc scheme is proposed to guarantee that all follower nodes asymptotically synchronize a leader node with tracking errors converging to a small adjustable neighborhood of the origin in spite of actuator faults the leader node is modeled as a higher order nonautonomous nonlinear system it acts as a command generator giving commands only to a small portion of the networked group each follower is assumed to have nonidentical unknown nonlinear dynamics and the communication network is also assumed to be a weighted directed graph with a fixed topology a distributed robust adaptive fuzzy controller is designed for each follower node such that the tracking errors are cooperative uniform ultimate boundedness cuub moreover these controllers are distributed in the sense that the controller designed for each follower node only requires relative state information between itself and its neighbors the adaptive compensation term of the optimal approximation errors and external disturbances is adopted to reduce the effects of the errors and disturbances which removes the assumption that the upper bounds of unknown function approximation errors and disturbances should be known analysis of stability and parameter convergence of the proposed algorithm are conducted that are based on algebraic graph theory and lyapunov theory comparing with results in the literature the caftftc scheme can minimize the time delay between fault occurrence and accommodation and reduce its adverse effect on system performance in addition the ftc scheme requires no additional fault isolation model which is necessary in the traditional active ftc scheme finally an example is provided to validate the theoretical results

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

finite dimensional representations of the quantum superalgebra u q gl n m and related q identities explicit expressions for the generators of the quantum superalgebrau q gl n m acting on a class of irreducible representations are given the class under consideration consists of all essentially typical representations for these a gel fand zetlin basis is known the verification of the quantum superalgebra relations to be satisfied is shown to reduce to a set ofq number identities

tracking algorithms for multiagent systems this paper is devoted to the consensus tracking issue on multiagent systems instead of enabling the networked agents to reach an agreement asymptotically as the time tends to infinity the consensus tracking between agents is considered to be derived on a finite time interval as accurately as possible we thus propose a learning algorithm with a gain operator to be determined if the gain operator is designed in the form of a polynomial expression a necessary and sufficient condition is obtained for the networked agents to accomplish the consensus tracking objective regardless of the relative degree of the system model of agents moreover the h analysis approach is introduced to help establish conditions in terms of linear matrix inequalities lmis such that the resulting processes of the presented learning algorithm can be guaranteed to monotonically converge in an iterative manner the established lmi conditions can also enable the iterative learning processes to converge with an exponentially fast speed in addition we extend the learning algorithm to address the relative formation problem for multiagent systems numerical simulations are performed to demonstrate the effectiveness of learning algorithms in achieving both consensus tracking and relative formation objectives for the networked agents

an analysis of solidification problems by the boundary element method the problem of interest in this paper is the calculation of the motion of the solid liquid interface and the time dependent temperature field during solidification of a pure metal an iterative implicit algorithm has been developed for this purpose using the boundary element method bem with time dependent green s functions and convolution integrals the bem approach requires discretization of only the surface of the solidifying body thus the numerical method closely follows the physics of the problems and is intuitively very appealing the formulation and the numerical scheme presented here are general and can be applied to a broad range of moving boundary problems emphasis is given to two dimensional problems comparison with existing semi analytical solutions and other numerical solutions from the literature reveals that the method is fast accurate and without major time step limitations

a suboptimality approach to distributed linear quadratic optimal control this note is concerned with a suboptimal version of the distributed linear quadratic optimal control problem for multiagent systems given a multiagent system with identical agent dynamics and an associated global quadratic cost functional our objective is to design distributed control laws that achieve consensus and whose cost is smaller than an a priori given upper bound for all initial states of the network that are bounded in norm by a given radius a centralized design method is provided to compute such suboptimal controllers involving the solution of a single riccati inequality of dimension equal to the dimension of the agent dynamics and the smallest nonzero and the largest eigenvalue of the laplacian matrix furthermore we relax the requirement of exact knowledge of the smallest nonzero and largest eigenvalue of the laplacian matrix by using only lower and upper bounds on these eigenvalues finally a simulation example is provided to illustrate our design method