Bipartite tracking of homogeneous and heterogeneous linear multi-agent systems

In this paper, we consider bipartite tracking of linear multi-agent systems with a leader. Both homogeneous and heterogeneous systems are investigated. The communication between agents is modelled by a directed signed graph, where the negative (positive) edges represent the antagonistic (cooperative) interactions among agents. Linear Quadratic Regulator (LQR)-based approach is used to derive the distributed protocol for the follower agent to achieve bipartite tracking of the leader. It is shown that solving the bipartite tracking problem over the structurally balanced signed graph is equivalent to solving the cooperative tracking problem over a corresponding graph with nonnegative edge weights. This bridges the gap between the newly raised bipartite tracking problem and the well-studied cooperative tracking problem. Three novel control protocols are proposed for both cooperative and bipartite output tracking of heterogeneous linear multi-agent systems. Numerical examples are given to show the effectiveness of our control protocols.     

Fully distributed bipartite output consensus of heterogeneous linear multiagent systems based on event‐triggered transmission mechanism

This study investigates the fully distributed bipartite output consensus issue of heterogeneous linear multiagent systems (HLMASs) based on event‐triggered transmission mechanism. Both the cooperative interaction and the antagonistic interaction between neighbor agents are considered. A fully distributed bipartite compensator consisting of time‐varying coupling gain and dynamic event‐triggered mechanism is first proposed to estimate the leader's states. Different from the existing schemes, the proposed compensator is independent of any global information of the network topology, is capable of achieving intermittent communication between neighbors, and is applicable for the signed communication topology. Then the distributed output feedback control protocol is developed such that the fully distributed bipartite event‐triggered output consensus problem can be achieved. Moreover, we extend the results in HLMASs without external disturbances to HLMASs with disturbances, which is more challenging in three cases (a) the disturbances are not available for measurement, (b) the disturbances suffered by each agent are heterogeneous, and (c) the disturbances are not required to be stable or bounded. It is proven that the proposed controllers fulfill the exclusion of Zeno behavior in two consensus problems. Finally, two examples are provided to illustrate the feasibility of the theoretical results.     

A unified approach to output synchronization of heterogeneous multi-agent systems via L2-gain design

In this paper, a unified design procedure is given for output synchronization of heterogeneous multi-agent systems (MAS) on communication graph topologies, using relative output measurements from neighbors. Three different control protocols, namely, full-state feedback, static output-feedback, and dynamic output-feedback, are designed for output synchronization. It is seen that a unified design procedure for heterogeneous MAS can be given by formulation and solution of a suitable local $\mathcal{L}{_2}$-gain design problem. Sufficient conditions are developed in terms of stabilizing the local agents'' dynamics, satisfying a certain small-gain criterion, and solving the output regulator equations. Local design procedures are presented for each agent to guarantee that these sufficient conditions are satisfied. The proposed control protocols require only one copy of the leader''s dynamics in the compensator, regardless of the dimensions of the outputs. This results in lower-dimensional compensators for systems with high-order outputs, compared to the $p$-copy internal model approach. All three proposed control protocols are verified using numerical simulations.     

Adaptive bipartite consensus control of high‐order multiagent systems on coopetition networks

In this paper, a bipartite consensus problem is considered for a high‐order multiagent system with cooperative‐competitive interactions and unknown time‐varying disturbances. A signed graph is used to describe the interaction network associated with the multiagent system. The unknown disturbances are expressed by linearly parameterized models, and distributed adaptive laws are designed to estimate the unknown parameters in the models. For the case that there is no exogenous reference system, a fully distributed adaptive control law is proposed to ensure that all the agents reach a bipartite consensus. For the other case that there exists an exogenous reference system, another fully distributed adaptive control law is also developed to ensure that all the agents achieve bipartite consensus on the state of the exogenous system. The stability of the closed‐loop multiagent systems with the 2 proposed adaptive control laws are analyzed under an assumption that the interaction network is structurally balanced. Moreover, the convergence of the parameter estimation errors is guaranteed with a persistent excitation condition. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed adaptive bipartite consensus control laws for the concerned multiagent system.     

Consensus tracking control of discrete‐time second‐order agents over switching signed digraphs with arbitrary antagonistic relations

This article studies the problem of consensus tracking control for second‐order agents in multiagent systems over switching signed digraphs. Compared with the existing consensus tracking works on the structurally balanced signed digraph where the antagonistic relations exist only between two independent subgroups, this article explores a more general case for the first time, in the sense that the antagonistic relation is allowed between any two agents. On the basis of the design of a cooperation‐antagonism environment‐based distributed algorithm, suitable model transformation vectors are utilized to convert the stability of original system into a product convergence problem of time‐varying superstochastic matrices. By analyzing the convergence, algebraic conditions between positive and negative weights are established to ensure that all followers can eventually reach the leader's state under switching signed digraphs with arbitrary antagonistic relations. Simulation examples are provided to demonstrate the effectiveness of our results.     

Output feedback semiglobal practical consensus of linear systems with relative state‐dependent uncertainties

This paper proposes an output feedback consensus control law for linear multiagent systems with relative state‐dependent uncertainties. To achieve output feedback control and uncertainty attenuation, the theories of extended high‐gain observer and structural decomposition are employed. Under the proposed control scheme, semiglobal practical consensus is achieved in the sense that the synchronization errors are ultimately bounded. Besides, the synchronization errors can be kept arbitrarily small by a proper choice of tuning parameters. Finally, a simulation example is provided to verify the theoretical results.     

Observer‐predictor feedback for consensus of discrete‐time multiagent systems with both state and input delays

This article is concerned with the consensus problem for discrete‐time multiagent systems with both state and input delays. Single observer‐predictor‐based protocols and multiple observer‐predictors feedback protocols are simultaneously established to predict the future state such that the input delay that can be arbitrarily large yet bounded is completely compensated. It is shown that the consensus of the multiagent system can be achieved by the single/multiple observer‐predictors feedback protocol. Moreover, sufficient conditions guaranteeing the consensus of the multiagent system are provided in terms of the stability of some simple observer‐error systems, and the separation principle is discovered. Finally, a numerical example is worked out to illustrate the effectiveness of the proposed approaches.     

Bipartite consensus of multi‐agent systems over signed graphs: State feedback and output feedback control approaches

This paper studies bipartite consensus problems for continuous‐time multi‐agent system over signed directed graphs. We consider general linear agents and design both state feedback and dynamic output feedback control laws for the agents to achieve bipartite consensus. Via establishing an equivalence between bipartite consensus problems and the conventional consensus problems under both state feedback and output feedback control approaches, we make direct application of existing state feedback and output feedback consensus algorithms to solve bipartite consensus problems. Moreover, we propose a systematical approach to design bipartite consensus control laws. Copyright © 2016 John Wiley & Sons, Ltd.     

Cooperative output regulation of heterogeneous multiagent systems based on event‐triggered control with fixed and switching topologies

This paper addresses the cooperative output regulation problem of multiagent systems with fixed and switching topologies. Each agent is a heterogeneous linear system, and the output of the exosystem can be available to only a subset of agents. For the agents that can directly access the exosystem, a common observer based on an event‐triggered strategy is constructed to estimate the exogenous signal for feedback control design. For the rest of the agents, estimators based on an event‐triggered mechanism to acquire the estimation value of the exogenous signal are designed under some essential assumptions. A decentralized event‐triggered formulation is considered first by applying a Lyapunov function for a fixed topology. Furthermore, a topology‐dependent triggering condition and the average dwell‐time switching law are deduced simultaneously by using multiple Lyapunov functions for switching topologies. Under communication constraints, we propose observer‐based and estimator‐based feedback controllers to solve the cooperative output regulation problem using available local information among agents. Two examples are finally provided to verify the effectiveness of the proposed theoretical results.     

Event‐triggered output consensus for heterogeneous multiagent systems with fixed and switching directed topologies

This paper studies the event‐triggered output consensus problem of heterogeneous linear multiagent systems characterized via fixed and switching directed graphs. With proper state‐dependent triggering functions, two new event‐triggered output consensus control schemes are proposed for each agent to achieve consensus. Notably, under the proposed control protocols, continuous communication among agents is not required in both controllers updating and triggering threshold detection, which means being completely continuous communication free. The communication instances are reduced significantly, and the periodic or high‐frequency communication is restrained. It is also ensured that events cannot be triggered infinitely in finite time (ie, the Zeno behavior is elegantly avoided). Meanwhile, the simulation examples are given to illustrate the theoretical analysis.     

Synchronization of nonlinear heterogeneous cooperative systems using input–output feedback linearization

In this paper, input–output feedback linearization is used to design distributed controls for multi-agent systems with nonlinear and heterogeneous non-identical dynamics. Using feedback linearization, the nonlinear and heterogeneous dynamics of agents are transformed to identical linear dynamics and non-identical internal dynamics. Based on the dependence of agent outputs on agent inputs, feedback linearization may lead to a first-order or high-order tracking synchronization problem. The controller for each agent is designed to be fully distributed such that each agent only requires its own information and the information of its neighbors. The effectiveness of the proposed control protocols are verified by simulation on a microgrid test system.     

Output Consensus of Heterogeneous Multi-agent Systems under Directed Topologies via Dynamic Feedback

This paper discusses the problem of dynamic output consensus for heterogeneous multi-agent systems (MAS) with fixed topologies. All the agents possess unique linear dynamics, and only the output information of each agent is delivered throughout the communication digraphs. A series of conditions and protocols are set for reaching the consensus. With the proper feedback controllers, the output consensus of the overall system is guaranteed. An application illustrates the theorems.     

Adaptive consensus control for stochastic nonlinear multiagent systems with full state constraints

In this paper, the consensus tracking problem is investigated for stochastic nonlinear multiagent systems with full state constraints and time delays. The barrier Lyapunov functions proposed for single‐agent constrained systems are constructively extended to solve the consensus problem for multiagent systems with the full state constraints. Some Lyapunov‐Krasovskii functionals are introduced to compensate for state time delays, which are inherent in the complicated nonlinear systems. Based on the variable separation technique, the difficulty arising from the nonstrict‐feedback structure is overcome. Under a directed communication topology, the distributed neuroadaptive control protocols are proposed to guarantee that all the follower agents follow the trajectory of the leader agent and the full state constraints are not violated. The effectiveness of the proposed distributed adaptive control approach is verified via simulation examples.     

Distributed event-triggered optimal bipartite consensus control for multiagent systems with input delay via reinforcement learning method

In this article, an optimal bipartite consensus control (OBCC) scheme is proposed for heterogeneous multiagent systems (MASs) with input delay by reinforcement learning (RL) algorithm. A directed signed graph is established to construct MASs with competitive and cooperative relationships, and model reduction method is developed to tackle input delay problem. Then, based on the Hamilton–Jacobi–Bellman (HJB) equation, policy iteration method is utilized to design the bipartite consensus controller, which consists of value function and optimal controller. Further, a distributed event-triggered function is proposed to increase control efficiency, which only requires information from its own agent and neighboring agents. Based on the input-to-state stability (ISS) function and Lyapunov function, sufficient conditions for the stability of MASs can be derived. Apart from that, RL algorithm is employed to solve the event-triggered OBCC problem in MASs, where critic neural networks (NNs) and actor NNs estimate value function and control policy, respectively. Finally, simulation results are given to validate the feasibility and efficiency of the proposed algorithm.     

Semi‐global bipartite output consensus of heterogeneous multi‐agent systems subject to input saturation by finite‐time observer

In this paper, the semi‐global bipartite output consensus problem of heterogeneous linear multi‐agent systems is studied. Compared with related works, both cooperative interactions and antagonistic interactions between agents are considered, and the input saturation on each follower is taken into account. First, two distributed finite‐time observers are designed to recover the leader's state. Particularly, the setting time can be independent of any initial states. Due to the antagonistic interactions, estimation values are the same as the leader's state in modulus but may not in sign. Then, the low‐gain feedback technique is used to develop the distributed control law for each follower. Moreover, we summarize a framework for solving the semi‐global bipartite output consensus problem of heterogeneous multi‐agent systems subject to input saturation. Finally, examples are given to illustrate the results.     

基于自适应分布式滤波观测器的多智能体系统编队控制

本文考虑了全局指令系统输出信息受到信道扰动情况下线性多智能体系统的编队控制问题.首先,基于协作式输出调节理论框架对线性多智能体系统的编队控制问题进行数学建模.其次,针对受到信道扰动的全局指令系统输出信息,提出了一类基于受扰输出的自适应分布式滤波观测器,在降低网络信息交换量的同时消除扰动的影响.最后,设计了输出反馈确定等价控制律,解决了线性多智能体系统的分布式编队控制问题.给出了数值仿真结果检验控制性能.     

Output sign‐consensus of heterogeneous multiagent systems over fixed and switching signed graphs

This paper investigates output sign‐consensus of multiagent systems over directed signed graphs. In signed graphs, the sign of each edge stands for either hostile interaction (associated with positive sign) or antagonistic interactions (associated with negative sign) among agents. Agent dynamics are heterogeneous, allowing coexistence of distinct agent dynamics in one group. Heterogeneity in this paper also implies that the states of different agents may have different dimensions, but their outputs should have the same dimension. Distributed control laws are designed for both fixed and switching graph topologies. For fixed topology, the graph is assumed to be eventually positive. For switching topology, the graph needs to be jointly eventually positive, which extends the well‐known concept of joint connectivity by taking dwell time into consideration.     

Model‐free adaptive formation control for unknown multiinput‐multioutput nonlinear heterogeneous discrete‐time multiagent systems with bounded disturbance

Based on the model‐free adaptive control, the distributed formation control problem is investigated for a class of unknown heterogeneous nonlinear discrete‐time multiagent systems with bounded disturbance. Two equivalent data models to the unknown multiagent systems are established through the dynamic linearization technique considering the circumstances with measurable and unmeasurable disturbances. Based on the obtained data models, two distributed controllers are designed with only using the input/output and disturbance data of the neighbor agents system. The tracking error of the closed‐loop system driven by the proposed controllers is shown to be bounded by the contraction mapping principle and inductive methods. An example illustrates the effectiveness of the proposed two distributed controllers.     

Output consensus for heterogeneous multiagent systems with Markovian switching network topologies

This paper investigates the output consensus problem of heterogeneous continuous‐time multiagent systems under randomly switching communication topologies. The switching mechanism is governed by a time‐homogeneous Markov process, whose states correspond to all possible communication topologies among agents. A novel dynamic consensus controller is proposed. The controller gains are designed based on the information of the expectation graph and the solutions to regulator equations. Furthermore, a necessary and sufficient condition is presented for output consensus of the controlled multiagent system in mean square sense. Finally, a simulation example is provided to corroborate the effectiveness of the proposed controller.     

Leader-follower consensus for a class of nonlinear multi-agent systems

This paper deals with the leader-follower consensus problem for a class of nonlinear multiagent systems. All agents have identical nonlinear dynamics in the strict feedback form with Lipschitz growth condition. Both full state consensus protocol and dynamic output consensus protocol are provided. It is shown that under a connected undirected information communication topology, the proposed protocols can solve the leader-follower consensus problem. Two consensus protocol design procedures are presented and a numerical example is given to illustrate the proposed protocols.