couple group consensus for second order multi agent systems with fixed and stochastic switching topologies abstract this paper deals with the couple group consensus problem for second order discrete time multi agent systems both the fixed topology case and the stochastic switching topology case are considered the couple group consensus problem is converted into the stability problem of the error system by a linear transformation for the fixed topology case we obtain two different conditions of couple group consensus for the stochastic switching topology case we obtain a necessary and sufficient condition of mean square couple group consensus algorithms are provided to design the allowable control gains finally simulation examples are given to show the usefulness of the theoretical results

reasonable properties for the ordering of fuzzy quantities ii as a continuation of the first part related to the first and second class of ordering approaches this paper deals with the fulfilment of reasonable properties in the third class of ordering approaches to do so we briefly introduce fuzzy relations on which the third class of approaches is based then we recall some transitivity related concepts and an ordering procedure based on a acyclic fuzzy relation acyclicity is a very weak restriction on a fuzzy relation we prove that many fuzzy relations used for the comparison of fuzzy quantities satisfy some conditions stronger than acyclicity so we give a widely applicable formulation to derive a total ranking order from a fuzzy relation with our formulation we examine all the ordering indices in the third class with respect to the proposed axioms in part i

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 l 2 gain output feedback control of homogeneous and heterogeneous systems the importance of static output feedback opfb design for aircraft control process control and elsewhere has been well documented since the 1960s since full state measurements are not usually available in practical systems this problem is compounded in the case of multi agent systems mas where each agent has its own state variable and measured outputs therefore this paper addresses the l 2 gain opfb synchronization of linear mas subject to external disturbances both homogeneous and heterogeneous mas are considered for homogeneous mas it is shown that the l 2 gain static opfb synchronization problem of mas can be cast into the l 2 gain static opfb problem for a set of decoupled systems that depend on the graph topology a modified riccati equation is introduced which gives the opfb gain and the coupling gain of the proposed static opfb control protocol for heterogeneous mas it is shown that the l 2 gain synchronization problem can be cast into the l 2 gain static opfb problem of a set of decoupled systems plus a coupling condition on their dynamic compensators that depends on the graph topology a certain novel gain matrix is introduced in the dynamics of the control protocol to improve the performance

new approach to synchronization analysis of linearly coupled ordinary differential systems in this paper a general framework is presented for analyzing the synchronization stability of linearly coupled ordinary differential equations lcodes the uncoupled dynamical behavior at each node is general and can be chaotic or otherwise the coupling configuration is also general with the coupling matrix not assumed to be symmetric or irreducible on the basis of geometrical analysis of the synchronization manifold a new approach is proposed for investigating the stability of the synchronization manifold of coupled oscillators in this way criteria are obtained for both local and global synchronization these criteria indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold furthermore the roles of the uncoupled dynamical behavior on each node and the coupling configuration in the synchronization process are also studied

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

travelling wave solutions of reduced super kdv equation a perspective from lame equation abstract reduced supersymmetric korteweg de vries super kdv equation is investigated in this paper with the help of an auxiliary lame equation and jacobi elliptic function travelling wave solutions of reduced super kdv equation are obtained in the form of jacobi elliptic periodic function meanwhile trigonal solutions and hyperbolic solutions are derived

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

lame equation and asymptotic higher order periodic solutions to nonlinear evolution equations based on an auxiliary lame equation and the perturbation method a direct method is proposed to construct asymptotic higher order periodic solutions to some nonlinear evolution equations it is shown that some asymptotic higher order periodic solutions to some nonlinear evolution equations in terms of jacobi elliptic functions are explicitly obtained with the aid of symbolic computation

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

fuzzy preference relations in models of decision making abstract analysis of x r models is considered as part of a general approach to solving optimization problems with fuzzy coefficients this approach involves a modification of traditional optimization methods and is associated with formulating and solving one and the same problem within the framework of mutually interrelated models by constructing equivalent analogs with fuzzy coefficients in objective functions alone the use of the approach allows one to maximally cut off dominated alternatives the subsequent contraction of the decision uncertainty region is based on reducing the problem to multiobjective choice of alternatives in a fuzzy environment three techniques for processing of fuzzy preference relations reflecting criteria of quantitative as well as qualitative character are discussed the results of the paper are universally applicable and are already being used to solve power engineering problems

multi vehicle consensus with a time varying reference state in this paper we study the consensus problem in multi vehicle systems where the information states of all vehicles approach a time varying reference state under the condition that only a portion of the vehicles e g the unique team leader have access to the reference state and the portion of the vehicles might not have a directed path to all of the other vehicles in the team we first analyze a consensus algorithm with a constant reference state using graph theoretical tools we then propose consensus algorithms with a time varying reference state and show necessary and sufficient conditions under which consensus is reached on the time varying reference state the time varying reference state can be an exogenous signal or evolve according to a nonlinear model these consensus algorithms are also extended to achieve relative state deviations among the vehicles an application example to multi vehicle formation control is given as a proof of concept

passivity as a design tool for group coordination we pursue a group coordination problem where the objective is to steer the differences between output variables of the group members to a prescribed compact set to stabilize this set we study a class of feedback rules that are implementable with local information available to each member when the information flow between neighboring members is bidirectional we show that the closed loop system exhibits a special interconnection structure which inherits the passivity properties of its components by exploiting this structure we develop a passivity based design framework which results in a broad class of feedback rules that encompass as special cases some of the existing formation stabilization and group agreement designs in the literature the passivity approach offers additional design flexibility compared to these special cases and systematically constructs a lurie type lyapunov function for the closed loop system we further study the robustness of these feedback laws in the presence of a time varying communication topology and present a persistency of excitation condition which allows the interconnection graph to lose connectivity pointwise in time as long as it is established in an integral sense

consensus in directed networks of agents with nonlinear dynamics this technical note studies the consensus problem for cooperative agents with nonlinear dynamics in a directed network both local and global consensus are defined and investigated techniques for studying the synchronization in such complex networks are exploited to establish various sufficient conditions for reaching consensus the local consensus problem is first studied via a combination of the tools of complex analysis local consensus manifold approach and lyapunov methods a generalized algebraic connectivity is then proposed to study the global consensus problem in strongly connected networks and also in a broad class of networks containing spanning trees for which ideas from algebraic graph theory matrix theory and lyapunov methods are utilized

quasi rational function solutions of an elliptic equation and its application to solve some nonlinear evolution equations abstract using the differential transformation method and the homogeneous balance method some new solutions of an auxiliary elliptic equation are obtained these solutions possess the forms of rational functions in terms of trigonometric functions hyperbolic functions exponential functions power functions elliptic functions and their operation and composite functions and so on which are so called quasi rational function solutions based on these new quasi rational functions solutions a direct method is proposed to construct the exact solutions of some nonlinear evolution equations with the aid of symbolic computation the coupled kdv mkdv equation and broer kaup equations are chosen to illustrate the effectiveness and convenience of the suggested method for obtaining quasi rational function solutions of nonlinear evolution equations

consensus of second order multi agent systems with delayed nonlinear dynamics and intermittent communications this article investigates the second order consensus problem of multi agent systems with inherent delayed nonlinear dynamics and intermittent communications each agent is assumed to obtain the measurements of relative states between its own and the neighbours only at a sequence of disconnected time intervals a new kind of protocol based only on the intermittent measurements of neighbouring agents is proposed to guarantee the states of agents to reach second order consensus under a fixed strongly connected and balanced topology by constructing a common lyapunov function it is shown that consensus can be reached if the general algebraic connectivity and communication time duration are larger than their corresponding threshold values respectively finally simulation examples are provided to verify the effectiveness of the theoretical analysis

distributed observer design for bounded tracking control of leader follower multi agent systems in a sampled data setting this paper studies the observer based bounded tracking control problem of second order multi agent systems in a disturbance environment via sampled data control two sampled data protocols are introduced under the assumption that the dynamic leader is only available to a portion of agents and distributed observers are designed to estimate the velocity of the active leader for the fixed communication topology case necessary and sufficient conditions of bounded consensus tracking are obtained by using the matrix analysis method for the switching communication topology case we prove that system can achieve bounded tracking by applying the common lyapunov function and perturbation theory simulation examples are given to illustrate the effectiveness of our 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

vsop fuzzy numbers and their fuzzy ordering abstract in this paper we extend the conventional fuzzy numbers and introduce a new fuzzy number system named vector space of ordered pairs vsop then we axiomatically define the fuzzy comparison relations and on vsop starting from the requirements of fuzzy ordering and vector ordering a concept of grading functions is introduced to prove some interesting properties of the fuzzy comparison relations we also introduce a concept of grading component operators which construct a new grading function from given grading functions and prove the necessary and sufficient condition of the grading component operators the fuzzy comparison relations constructed here are not only for vsop fuzzy numbers but are also directly applicable to conventional fuzzy numbers examples of fuzzy comparison relations which are applicable to conventional fuzzy numbers are also described

observer based distributed consensus for general nonlinear multi agent systems with interval control inputs in this paper observer based distributed consensus for general nonlinear multi agent systems with interval control inputs under strongly connected balanced topology is encountered when the relative states of agents are unavailable or undesirable theoretical analysis method is further extended to the case of general nonlinear multi agent systems under switching setting moreover tracking problem on the leader follower scenario is also explicitly investigated under a mutual assumption that the communication graph which represents the interaction among agents contains a directed spanning tree with the leader as its root it is shown that the consensus for underlying considered multi agent systems can be desirable as long as the data missing rate does not exceed a certain threshold finally simulation examples are presented to effectively corroborate the analytical findings

multi agent zero sum differential graphical games for disturbance rejection in distributed control this paper addresses distributed optimal tracking control of multi agent linear systems subject to external disturbances the concept of differential game theory is utilized to formulate this distributed control problem into a multi player zero sum differential graphical game which provides a new perspective on distributed tracking of multiple agents influenced by disturbances in the presented differential graphical game the dynamics and performance indices for each node depend on local neighbor information and disturbances it is shown that the solution to the multi agent differential graphical games in the presence of disturbances requires the solution to coupled hamilton jacobi isaacs hji equations multi agent learning policy iteration pi algorithm is provided to find the solution to these coupled hji equations and its convergence is proven it is also shown that l 2 bounded synchronization errors can be guaranteed using this technique an online pi algorithm is given to solve the zero sum game in real time a simulation example is provided to show the effectiveness of the online approach

state agreement for continuous time coupled nonlinear systems two related problems are treated in continuous time first the state agreement problem is studied for coupled nonlinear differential equations the vector fields can switch within a finite family associated to each vector field is a directed graph based in a natural way on the interaction structure of the subsystems generalizing the work of moreau under the assumption that the vector fields satisfy a certain subtangentiality condition it is proved that asymptotic state agreement is achieved if and only if the dynamic interaction digraph has the property of being sufficiently connected over time the proof uses nonsmooth analysis second the rendezvous problem for kinematic point mass mobile robots is studied when the robots fields of view have a fixed radius the circumcenter control law of ando e ieee trans robotics automation 15 1999 pp 818 828 is shown to solve the problem the rendezvous problem is a kind of state agreement problem but the interaction structure is state dependent

fuzzy sets and models of decision making abstract results of research into the use of fuzzy sets for handling various forms of uncertainty in optimization problems related to the design and control of complex systems are presented much attention is given to considering the uncertainty of goals that is associated with a multicriteria character of many optimization problems the application of a multicriteria approach is needed to solve 1 1 problems in which solution consequences cannot be estimated on the basis of a single criterion that involves the necessity of analyzing a vector of criteria and 2 2 problems that may be considered on the basis of a single criterion but their unique solutions are not achieved because the uncertainty of information produces so called decision uncertainty regions and the application of additional criteria can serve as a convincing means to contract these regions according to this two classes of models x m and x r models are considered with applying the bellman zadeh approach and techniques of fuzzy preference relations to their analysis the consideration of x r models is associated with a general approach to solving a wide class of optimization problems with fuzzy coefficients this approach consists in formulating and analyzing one and the same problem within the framework of interrelated models with constructing equivalent analogs with fuzzy coefficients in objective functions alone it allows one to maximally cut off dominated alternatives the subsequent contraction of the decision uncertainty region is associated with reduction of the problem to multicriteria decision making in a fuzzy environment with its analysis applying one of two techniques based on fuzzy preference relations the results of the paper are of a universal character and are already being used to solve problems of power engineering

a general approach to solving a wide class of fuzzy optimization problems results of research into the use of fuzzy sets for handling various forms of uncertainty in the optimal design and control of complex systems are presented a general approach to solving a wide class of optimization problems containing fuzzy coefficients in objective functions and constraints is described it involves a modification of traditional mathematical programming methods and is associated with formulating and solving one and the same problem within the framework of mutually conjugated models this approach allows one to maximally cut off dominated alternatives from below as well as from above the subsequent contraction of the decision uncertainty region is associated with reduction of the problem to multicriteria decision making in a fuzzy environment the general approach is applied within the context of a fuzzy discrete optimization model that is based on a modification of discrete optimization algorithms prior to application of these algorithms there is a transition from a model with fuzzy coefficients in objective functions and constraints to an equivalent analog with fuzzy coefficients in objective functions alone the results of the paper are of a universal character and are already being used to solve problems of power engineering

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