A fully distributed approach for consensus of multi-agent systems under multiple state-variables-dependent interaction topologies

In this paper, the consensus problem of multi-agent systems with general linear dynamics is studied. Motivated by the MIMO communication technique, a general framework is considered in which different state variables are exchanged in different independent interaction topologies. This novel framework could improve the control system design flexibility and potentially improve the system performance. Fully distributed consensus control laws are proposed and analyzed for the settings of fixed and switching multiple topologies. The control law can be applied using only local information. And the control gain can be designed depending on the dynamics of the individual agent. By transforming the overall multi-agent systems into cascade systems, necessary and sufficient conditions are provided to guarantee the consensus of the overall systems under fixed and switching state variable dependent topologies, respectively. Two simulation examples are provided to illustrate the effectiveness of the proposed theoretical results.     

Bounded average consensus for multi-agent systems with switching topologies by event-triggered persistent dwell time control

This paper is concerned with the consensus of multi-agent systems (MASs) with switching topologies. A norm-bounded event-trigger is designed where non-global information of the communication graph is involved. By directly employing the asynchronous event-triggered neighbor state information, a distributed persistent dwell time (PDT) based predictor-like consensus protocol is proposed. By the proposed scheme, the dynamics of local subsystems are allowed to be unstable during fast switching time intervals as well as the jump time instants, meanwhile, the bounded average consensus of overall MASs can be achieved. In addition, the Zeno-phenomena is naturally excluded. Numerical example is provided to demonstrate the effectiveness of the proposed method.     

Analysis of distributed consensus protocols with multi-equilibria under time-delays

In this paper, we propose a novel method for addressing the multi-equilibria consensus problem for a network of n agents with dynamics evolving in discrete-time. In this method, we introduce, for the first time in the literature, two concepts called primary and secondary layer subgraphs. Then, we present our main results on directed graphs such that multiple consensus equilibria states are achieved, thereby extending the existing single-state consensus convergence results in the literature. Furthermore, we propose an algorithm to determine the number of equilibria for any given directed graph automatically by a computer program. We also analyze the convergence properties of multi-equilibria consensus in directed networks with time-delays under the assumption that all delays are bounded. We show that introducing communication time-delays does not affect the number of equilibria of the given network. Finally, we verify our theoretical results via numerical examples.     

Event-triggered learning consensus of networked heterogeneous nonlinear agents with switching topologies

In this work, a lifted event-triggered iterative learning control (lifted ETILC) is proposed aiming for addressing all the key issues of heterogeneous dynamics, switching topologies, limited resources, and model-dependence in the consensus of nonlinear multi-agent systems (MASs). First, we establish a linear data model for describing the I/O relationships of the heterogeneous nonlinear agents as a linear parametric form to make the non-affine structural MAS affine with respect to the control input. Both the heterogeneous dynamics and uncertainties of the agents are included in the parameters of the linear data model, which are then estimated through an iterative projection algorithm. On this basis, a lifted event-triggered learning consensus is proposed with an event-triggering condition derived through a Lyapunov function. In this work, no threshold condition but the event-triggering condition is used which plays a key role in guaranteeing both the stability and the iterative convergence of the proposed lifted ETILC. The proposed method can reduce the number of control actions significantly in batches while guaranteeing the iterative convergence of tracking error. Both rigorous analysis and simulations are provided and confirm the validity of the lifted ETILC.     

Stability analysis of linear continuous-time delay-difference systems with multiple time-delays

This paper is concerned with the stability analysis of linear continuous-time delay-difference systems with multiple delays. Firstly, a new method for testing the L₂-exponential stability of the considered system is proposed, which is easier to use than the one in the existing literature. In view of the conservatism and the complexity of the obtained stability conditions in the existing literature, a complete Lyapunov–Krasovskii functional (LKF) is constructed by analyzing the relationship among the multiple delays. Sufficient conditions for both L₂-exponential stability and exponential stability are then derived based on the constructed LKFs, which are delay-independent. Exponential convergence rate for the considered system is also investigated by a new method, which is shown to be equivalent to the existing approach by using weighted LKFs. Robust stability under parameter uncertainties is also investigated. Numerical examples are provided to demonstrate the effectiveness and less conservativeness of the proposed method.     

Average consensus in networks of dynamic agents with uncertain topologies and time-varying delays

In this paper, we study average consensus problem in networks of dynamic agents with uncertain topologies as well as time-varying communication delays. By using the linear matrix inequality method, we establish several sufficient conditions for average consensus in the existence of both uncertainties and delays. Several linear matrix inequality conditions are presented to determine the allowable upper bounds of time-varying communication delays and uncertainties. Numerical examples are worked out to illustrate the theoretical results.     

Scaled consensus problem for multi-agent systems with semi-Markov switching topologies: A view from the probability

This paper investigates the stochastic scaled consensus problem for multi-agent systems with semi-Markov switching topologies. Sufficient conditions are established to guarantee the addressed system to realize the scaled consensus with probability one, which means that all agents’ states almost surely reach a dictated proportion. Here, the semi-Markov process concerned is much more general than those utilized in the recent literature, which can be characterized by two important factors: (1) the transition probability matrix, and (2) the polytropical distribution functions of sojourn times. In addition, pinning scaled consensus protocol is designed by employing the pinning control technique, where only the root nodes of the union set of all the topologies are chosen to be pinned, and the final desired state value of the considered system can be realized with probability one. Finally, numerical simulations are provided to illustrate validity of the obtained main results.     

Positive consensus for multi-agent systems with average dwell time switching

This paper considers the positive consensus for a class of multi-agent systems (MASs) with average dwell time (ADT) switching. First, sufficient and necessary conditions are derived for preserving the positivity of the closed-loop MASs. Second, the performance analysis of the consensus error system is accomplished by using the multiple Lyapunov functions (MLFs) approach, and an ADT switching technique designs the corresponding controlled switching signal. Then, both leaderless and leader-following positive consensus are achieved. Furthermore, to reduce the computational complexity, a novel leader-following positive consensus criterion is derived in the form of linear programming (LP). Finally, simulation examples are given to illustrate the effectiveness of the proposed method.     

Mean-square consensus of hybrid multi-agent systems with noise and nonlinear terms over jointly connected topologies

This paper studies the mean-square consensus of second-order hybrid multi-agent systems over jointly connected topologies. Systems with time-varying delay and multiplicative noise are considered. The date sampling control technique is adopted. Through matrix transformation, a positive definite matrix transformed by the Laplacian matrix is obtained, where the Laplacian matrix is a connected subgraph divided by the jointly connected topologies. By using graph theory, matrix theory and Lyapunov stability theory, sufficient conditions and the upper bound of time delays for the mean-square consensus are obtained. Finally, several simulations are presented to demonstrate the validity of the control method.     

Event-based consensus for second-order multi-agent systems with actuator saturation under fixed and Markovian switching topologies

This paper studies the event-based consensus problem of second-order multi-agent systems with actuator saturation under fixed topology and Markovian switching topologies. By a model transformation, the consensus problem is first converted into the stability problem of the error system. Using discontinuous Lyapunov functional approach, two sufficient conditions on the consensus are derived for second-order multi-agent systems with fixed topology and Markovian switching topologies, respectively. The discontinuous Lyapunov functions take full account of the characteristics of the sawtooth delay, and thus lead to a less conservative consensus criterion. It is shown that the consensus condition depends on the parameters of sampling period, Laplacian matrix, and event-triggered parameter. In addition, this paper provides an effective method to co-design both the consensus controller and the event-triggered parameter. Finally, two numerical examples are provided to illustrate the effectiveness and feasibility of the proposed algorithm.     

Leader-following consensus considering effects of agents on each other via impulsive control: A topology dependent average dwell time approach

This paper intends to investigate the consensus problem of a nonlinear multi-agent system with new nonlinear terms added to the dynamics of each agent in the leader-following framework with impulsive control. The main contribution of this paper is introducing these new terms expressing the effect of each agent on neighbor agents. The new terms called effect terms (ETs) are considered with time-varying delay. Moreover, the communication interactions among all agents are addressed by a set of consensusable and unconsensusable switching topologies. In particular, the topology-dependent average dwell time (TDADT), one of the significant practical analysis methods for switched systems, has been calculated for each topology. The globally uniformly exponentially stability (GUES) for the consensus error dynamics is analyzed by employing algebraic graph theory and a multiple discontinuous Lyapunov function approach (MDLF) regarding separate Lyapunov functions for impulse instants. Furthermore, sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to ensure that consensus can be achieved. Finally, the effectiveness of the theoretical analysis is corroborated by a numerical example.     

Event-triggered bipartite consensus for nonlinear multi-agent systems under switching topologies: A time-varying gain method

In this paper, the event-triggered bipartite consensus problem is investigated for nonlinear multi-agent systems under switching topologies, only part of topologies contain directed spanning tree rooted at the leader. First, a dynamic bipartite compensator is constructed based on relative output information to provide control signal. Then, the time-varying gain method is adopted to propose a compensator-based event-triggered control protocol without Zeno behavior. Notably, the control protocol proposed achieves the bipartite consensus while reducing update frequency effectively. Moreover, a low conservative switching law is designed by the topology-dependent average dwell time strategy, which fully considers the differences among topologies and provides an independent average dwell time for each topology. As an extension, the nonlinear multi-agent systems with non-zero input of leader are further studied. Finally, a practical example is presented to demonstrate the feasibility of proposed control protocol.     

Improved results on consensus of nonlinear MASs with nonhomogeneous Markov switching topologies and DoS cyber attacks

In this paper, the issue of leader-following consensus for nonlinear multi-agent systems (NMASs) suffered from uncertain nonhomogeneous Markov switching (UNMS) and denial-of-service (DoS) cyber attacks is studied. In contrast with the existing results on NMASs with a fixed topological structure, the communication topology is governed by an UNMS jump process, where the transition rates (TRs) of UNMS are considered to be partially known or completely unknown. Also, the changes of communication topologies caused by frequently DoS cyber attacks are taken into consideration, which will destroy the chains of communication and lead to network paralysis in NMASs. In view of this, based on the stochastic technique and multiple Lyapunov functional protocol, mean-square leader-following consensus conditions related to NMASs with the UNMS and DoS cyber attacks are proposed. Finally, the effectiveness of the presented theoretical results is validated by numerical example.     

Finite frequency range robust iterative learning control of linear discrete system with multiple time-delays

This paper uses repetitive process stability theory to design robust iterative learning control law for linear discrete systems with multiple time-delays and polytopic uncertainty. Both dynamic and static forms of the control law are considered and used when designing robust iterative learning control schemes. Also, based on the generalized Kalman-Yakubovich-Popov Lemma, the proposed design procedures a required frequency attenuation over a finite frequency range and the monotonic trial-to-trial error convergence. Moreover, linear matrix inequality techniques are applied to formulate the convergence conditions and to obtain formulas for the control law designs. Finally, an illustrative numerical simulation example is given and concludes the paper.     

A geometrical approach to problems of pursuit-evasion games

In this paper it is shown that a class of pursuit-evasion games can be treated more simply by the geometrical approach with the topological properties of the reachable region and by the method of functional analysis. Conditions for capture and optimal strategies are derived. A numerical example is given to show both the optimal open-loop strategies of players and the optimal trajectories of the game.     

Distributed dynamic event-triggered consensus control for multi-agent systems under fixed and switching topologies

This paper is devoted to the dynamic event-triggered consensus problem of general linear multi-agent systems under fixed and switching directed topologies. Two distributed dynamic event-triggered strategies, where internal dynamic variables are involved, are introduced for each agent to achieve consensus asymptotically. Compared with the existing static triggering strategies, the purposed dynamic triggering strategies result in larger inter-execution times and less communication energy among agents. In addition, neither controller updates nor triggering threshold detections require continuous communication in the purposed control strategies. It is also proven that the Zeno behavior is strictly ruled out under fixed and switching directed topologies. Finally, the effectiveness of the theoretical analysis is demonstrated by numerical simulations.