Leader‐following consensus with disturbance rejection for uncertain Euler‐Lagrange systems over switching networks

In this paper, the leader‐following consensus with disturbance rejection problem of uncertain Euler‐Lagrange systems is studied by the adaptive distributed observer approach. We first present a key lemma that guarantees the existence of an exponentially convergent adaptive distributed observer for linear leader systems without exponential growing modes over jointly connected switching and directed communication networks. This lemma also provides a specific Lyapunov function for the error dynamics of the adaptive distributed observer, which will play a crucial role in establishing one of the main results. A special case of this result where there is no disturbance will extend the existing result for a neutrally stable leader system and undirected communication networks to the case where the communication networks are directed and the leader's positional signal includes the class of ramp signals. Two examples will be given to demonstrate the effectiveness of the new results.     

Leader-following consensus of linear discrete-time multi-agent systems subject to jointly connected switching networks

In this paper, we further study the leader-following consensus problem for a class of linear discrete-time multi-agent systems subject to jointly connected switching digraphs. We first establish a stability result for a class of linear switched systems under a more relaxed assumption than those in the literature. Then, we apply this stability result to obtain the solution to our problem, which contains previous results as special cases. Finally, we apply our result to an example that cannot be handled by any existing result.     

Adaptive output tracking of linear uncertain discrete-time networked systems over switching topologies

ABSTRACT

In this paper, we study the asymptotic output tracking problem for a class of minimum phase uncertain linear discrete-time multi-agent systems over jointly connected digraphs. As the systems contain arbitrarily large uncertain parameters, the robust feedback control technique does not work. We develop a distributed adaptive control law composed of a distributed observer and a purely decentralised adaptive control law. We first establish a stability result for a class of linear switched systems, which extends the existing results. This stability result leads to a novel distributed observer for the leader system which estimates the leader's signal using the output of the leader system locally and passes the estimated leader's signal to each follower. We then further show that the distributed adaptive control law solves our problem under some mild conditions. An example is used to illustrate the effectiveness and generality of our approach.     

Containment in leader–follower networks with switching communication topologies

We study bipartite, first-order networks where the nodes take on leader or follower roles. Specifically, we let the leaders’ positions be static and assume that leaders and followers communicate via an undirected switching graph topology. This assumption is inspired by the swarming behavior of silkworm moths, where female moths intermittently release pheromones to be detected by the males. The main result presented here states that if the followers execute the linear agreement protocol, they will converge to the convex hull spanned by the leaders’ positions as long as the time-varying undirected graph defining the communication among all agents is jointly connected. The novelty of this research is that we use LaSalle’s Invariance Principle for switched systems, and additionally, the result is shown to hold for arbitrary state dimensions.     

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.     

Decentralized observers with consensus filters for distributed discrete-time linear systems

This paper presents a decentralized observer with a consensus filter for the state observation of discrete-time linear distributed systems. Each agent in the distributed system has an observer with a model of the plant that utilizes the set of locally available measurements, which may not make the full plant state detectable. This lack of detectability is overcome by utilizing a consensus filter that blends the state estimate of each agent with its neighbors’ estimates. It is proven that the state estimates of the proposed observer exponentially converge to the actual plant states under arbitrarily changing, but connected, communication and pseudo-connected sensing graph topologies. Except these connectivity properties, full knowledge of the sensing and communication graphs is not needed at the design time. As a byproduct, we obtained a result on the location of eigenvalues, i.e., the spectrum, of the Laplacian for a family of graphs with self-loops.     

通信时延和联合连通拓扑下多刚体系统分布式姿态一致性控制

本文研究了通信时延和联合连通切换拓扑条件下的多刚体系统分布式姿态一致性控制问题. 通过构建有 效的辅助向量并选择合适的Lyapunov-Krasovskii函数, 分别对恒定通信时延和时变通信时延两种不同情况下的控 制器进行了设计. 数值仿真结果表明, 本文提出的方法能够有效地解决这类分布式姿态一致性控制问题. 多刚体; 姿态一致性; 联合连通拓扑; 时变时延; Lyapunov函数     

Output feedback quantized observer‐based synchronization of linear multi‐agent systems over jointly connected topologies

The synchronization problem of linear over‐actuated multi‐agent systems with unmeasurable states is studied in this paper, under both limited communication data rate and switching topology flows. A class of adaptive quantized observer‐based encoding–decoding schemes and a class of certainty equivalence principle‐based control protocols are proposed. By developing the graph‐based space decomposition technique and analyzing the closed‐loop quantized dynamic equations, it is shown that if the network topology flow is jointly connected, the communication channels are periodic active, and the agent dynamics is observable, and with the orthogonal system matrix, the proposed communication and control protocols can ensure the closed‐loop system to achieve synchronization exponentially fast with finite bits of information exchange per step. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive tracking control of leader-following linear multi-agent systems with external disturbances

In this paper, the consensus problem for leader-following linear multi-agent systems with external disturbances is investigated. Brownian motions are used to describe exogenous disturbances. A distributed tracking controller based on Riccati inequalities with an adaptive law for adjusting coupling weights between neighbouring agents is designed for leader-following multi-agent systems under fixed and switching topologies. In traditional distributed static controllers, the coupling weights depend on the communication graph. However, coupling weights associated with the feedback gain matrix in our method are updated by state errors between neighbouring agents. We further present the stability analysis of leader-following multi-agent systems with stochastic disturbances under switching topology. Most traditional literature requires the graph to be connected all the time, while the communication graph is only assumed to be jointly connected in this paper. The design technique is based on Riccati inequalities and algebraic graph theory. Finally, simulations are given to show the validity of our method.     

Event‐triggered tracking control of heterogeneous multiagent systems based on two kinds of observers with asymmetric delay

In this paper, we consider the output tracking problem of a multiagent system with asymmetric delays and a switching topology. The multiagent system contains a leader and some followers, the dynamics of which are heterogeneous, and the output of the leader is available to only a subset of followers. We propose two types of observers to estimate states of the leader and reduce communication cost. For the informed followers that can directly obtain information of the leader, a common observer is given to reduce the complexity of observer design. Meanwhile, for the rest of the followers, a distributed observer with asymmetric communication delays for each follower is designed. The observer error system is transformed into a switched system. Through designing the average dwell‐time switching law and constructing multiple Lyapunov functionals, some sufficient conditions for stability of the observer error system are obtained. Furthermore, a distributed controller for followers based on the relative information is developed to track the output of the leader. Finally, an example is given to validate the effectiveness of the proposed results.     

Observer-based distributed coordinated tracking control for multiple simple-pendulum network systems with time-varying delays

For networked control systems consisting of multiple simple-pendulums driven by corresponding DC motors with time-varying communication and input delays, a distributed coordinated controller via observer-based output feedback is designed to solve the tracking problem under both fixed and jointly-connected switching topologies. Firstly, the linearized dynamic model for multiple nonlinear simple-pendulum network systems with DC motors is presented, and the distributed coordinated tracking problem considering time-varying input delays is mathematically described. Then the distributed observer-based tracking control protocol with time-varying communication and input delays is proposed, and simultaneously, both the observer gain and feedback gain are designed. Two examples are simulated to demonstrate consensus tracking for three types of states, i.e., swing angles, angular velocities of multiple simple-pendulums and armature currents of DC motors can be completed utilizing the developed coordinated tracking control with fixed and jointly connected topologies.     

Bipartite Formation Tracking for Multi-Agent Systems Using Fully Distributed Dynamic Edge-Event-Triggered Protocol

In this study, the bipartite time-varying output formation tracking problem for heterogeneous multi-agent systems (MASs) with multiple leaders and switching communication networks is considered. Note that the switching communication networks may be connected or disconnected. To address this problem, a novel reduced-dimensional observer-based fully distributed asynchronous dynamic edge-event-triggered output feedback control protocol is developed, and the Zeno behavior is ruled out. The theoretical analysis gives the admissible switching frequency and switching width under the proposed control protocol. Different from the existing works, the control protocol reduces the dimension of information to be transmitted between neighboring agents. Moreover, since an additional positive internal dynamic variable is introduced into the triggering functions, the control protocol can guarantee a larger inter-event time interval compared with previous results. Finally, a simulation example is given to verify the effectiveness and performance of the theoretical result.      

Semi‐global cooperative output regulation of a class of nonlinear uncertain multi‐agent systems under switching networks

In this paper, we consider the semi‐global cooperative output regulation problem for a class of nonlinear uncertain multi‐agent systems under switching networks. At first, we study the nonadaptive case when the exosystem has no parametric uncertainties and construct a common Lyapunov function to achieve the output regulation for general switching connected networks. Next, we study the case when the exosystem contains some parametric uncertainties. To solve the problem, we establish a stability result for a class of time‐varying system, which is then used in the design of distributed adaptive internal model‐based control. Then we construct multiple Lyapunov functions for the switching signal with its average dwell time lower bounded by a given constant. Throughout the paper, we treat the closed‐loop multi‐agent system from the viewpoint of singular perturbation. In fact, the singular perturbation‐based method provides an effective tool to handle the multi‐agent system under switching networks. Finally, we give numerical simulations based on Duffing systems and flexible manipulator systems to illustrate the effectiveness of our method. Copyright © 2017 John Wiley & Sons, Ltd.     

Two consensus problems for discrete-time multi-agent systems with switching network topology

In this paper, we study both the leaderless consensus problem and the leader-following consensus problem for linear discrete-time multi-agent systems under switching network topology. Under the assumption that the system matrix is marginally stable, we show that these two consensus problems can be solved via the state feedback protocols, provided that the dynamic graph is jointly connected. Our result will contain several existing results as special cases. The proof is based on the stability analysis of a class of linear discrete-time switched systems which may have some independent interest.     

Intermittent observer-based consensus control for multi-agent systems with switching topologies

In this paper, we focus on the consensus problem for leaderless and leader–followers multi-agent systems with periodically intermittent control. The dynamics of each agent in the system is a linear system, and the interconnection topology among the agents is assumed to be switching. We assume that each agent can only share the outputs with its neighbours. Therefore, a class of distributed intermittent observer-based consensus protocols are proposed for each agent. First, in order to solve this problem, a parameter-dependent common Lyapunov function is constructed. Using this function, we prove that all agents can access a prescribed value, under the designed intermittent controller and observer, if there are suitable conditions on communication. Second, based on the investigation of the leader-following consensus problem, we design a new distributed intermittent observer-based protocol for each following agent. Finally, we provide an illustrative example to verify the effectiveness of the proposed approach.     

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

In this paper, we discuss average consensus problem in undirected networks of dynamic agents with fixed and switching topologies as well as multiple time-varying communication delays. By employing a linear matrix inequality method, we prove that all the nodes in the network achieve average consensus asymptotically for appropriate communication delays if the network topology is connected. Particularly, several feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time-varying communication delays. Numerical examples are given to demonstrate the effectiveness and the sharpness of the theoretical results.     

Distributed finite-time consensus of nonlinear systems under switching topologies

In this paper, the finite time consensus problem of distributed nonlinear systems is studied under the general setting of directed and switching topologies. Specifically, a contraction mapping argument is used to investigate performance of networked control systems, two classes of varying topologies are considered, and distributive control designs are presented to guarantee finite time consensus. The proposed control scheme employs a distributed observer to estimate the first left eigenvector of graph Laplacian and, by exploiting this knowledge of network connectivity, it can handle switching topologies. The proposed methodology ensures finite time convergence to consensus under varying topologies of either having a globally reachable node or being jointly strongly connected, and the topological requirements are less restrictive than those in the existing results. Numerical examples are provided to illustrate the effectiveness of the proposed scheme.     

Consensus control of multi‑manipulator systems based on disturbance observer under Markov switching topologies

In this paper, to solve the consensus control problem of multi-manipulator systems under Markov switching topologies, we propose a distributed consensus control strategy based on disturbance observer. In multi-manipulator systems, external disturbance described by heterogeneous exogenous systems is considered, and all communication topologies are directed. First, a disturbance observer is presented to suppress the influence of unknown external disturbance, and the equivalent compensation is introduced into the control protocol in multi-manipulator systems. Then, a novel control protocol based on neighbor information is designed, which guarantees that multi-manipulator systems reach consensus under Markov switching topologies. Finally, two simulation examples verify the validity of the theoretical result.     

Consensus of output-coupled high-order linear multi-agent systems under deterministic and Markovian switching networks

Consensus problem for high-order multi-agent systems is considered under deterministic and Markovian switching topologies. Only relative output information of agents is assumed to be available through the networks. First, a necessary and sufficient condition for achieving a consensus under a fixed communication network is presented. Based on this result and the stability of switched systems, a high-order multi-agent system with the proposed low-gain controller is shown to reach a consensus under deterministic switching network if the total time when the network is disconnected is, in some senses, smaller than the total time of the network being connected. Furthermore, the conditions sufficient for a high-order multi-agent system to reach an almost sure and mean-square consensus, under Markovian switching networks, are presented. Finally, illustrative examples are given to demonstrate the results.     

Semi‐global regulation of output synchronization for heterogeneous networks of non‐introspective,invertible agents subject to actuator saturation

In this paper, we consider the semi‐global regulation of output synchronization problem for heterogeneous networks of invertible linear agents subject to actuator saturation. That is, we regulate the output of each agent according to an a priori specified reference model. The network communication infrastructure provides each agent with a linear combination of its own output relative to that of neighboring agents, and it allows the agents to exchange information about their own internal observer estimates while some agents have access to their own outputs relative to the reference trajectory.Copyright © 2012 John Wiley & Sons, Ltd.