有向图中网络Euler-Lagrange系统的自适应协调跟踪

基于一致性理论, 在有向图中研究网络 Euler-Lagrange 系统的协调跟踪控制. 所有跟随智能体的动力学模型均为 Euler-Lagrange 方程. 在仅有部分跟随智能体能获取领航智能体信息的情形下, 同时考虑系统模型的参数不确定性, 设计分布式自适应控制律实现所有跟随智能体对领航智能体的跟踪. 针对领航智能体的运动状态, 考虑以下两种情形: 1) 领航智能体为固定点; 2) 领航智能体为动态点. 对第一种情形, 设计的控制律使得所有跟随智能体渐近交会于固定点; 对第二种情形, 首先对每个跟随智能体设计分布式连续估计器, 然后提出了分布式自适应控制律. 当每个跟随智能体均能获取领航智能体的加速度信息时, 设计的控制律能实现对领航智能体的渐近跟踪, 当跟随智能体不能获取领航智能体的加速度信息时, 跟踪误差是有界的. 最后通过仿真分析验证设计的控制算法是合理有效的.     

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.     

Consensus of nonlinear multi-agent systems with observer-based protocols

This paper is concerned with distributed pinning consensus problem for a class of nonlinear multi-agent system with observer-based protocols. Two types of state observers including local observer and distributed pinning observer are proposed for the single nonlinear agent with the first one designed by the local output information and the second one designed via the relative output information of its neighboring agents. According to the state information observed, a distributed pinning observer-based protocol is proposed for the leader-following consensus of the multi-agent system. Furthermore, two multi-step algorithms are presented to construct the observer gains and the protocol parameters for the proposed protocols respectively. It is shown that under the condition that the pinning joint communication topology contains a directed spanning tree, the sufficient criteria established can not only ensure the observation error to be globally asymptotically stable, but also guarantee the consensus of the multi-agent system to be solved asymptotically. Finally, two numerical examples are provided to demonstrate the effectiveness of the observer-based protocols.     

Fixed-time Consensus Tracking for Second-order Leader-follower Multi-agent Systems with Nonlinear Dynamics Under Directed Topology

In this paper, we address the fixed-time consensus tracking problem of second-order leader-follower multi-agent systems with nonlinear dynamics under directed topology. The consensus tracking algorithm consists of distributed observer and observer-based decentralized controller. The fixed-time distributed observer guarantees that each follower estimates the leader’s state under directed topology within a fixed time, where the upper bound of convergence time is independent on the initial conditions. The fixed-time decentralized controller makes each follower converge to the leader’s state in fixed time via tracking the distributed observer’s state and overcome the nonlinear dynamics without adding linear control terms. Finally, the numerical example is provided to illustrate the effectiveness of the results.

     

Robust consensus tracking of a class of second-order multi-agent dynamic systems

In this paper, we study the problem of robust consensus tracking for a class of second-order multi-agent dynamic systems with disturbances and unmodeled agent dynamics. Contrary to previous approaches, we design continuous distributed consensus protocols to enable global asymptotic consensus tracking. Our focus is on consensus protocol design and stability analysis which also leads to the derivation of sufficient conditions for consensus tracking. We first consider the case of undirected information exchange with a symmetric and positive definite information-exchange matrix. We develop an identifier for each agent to estimate the unknown disturbances and unmodeled agent dynamics. Based on the identifier, we develop a consensus tracking protocol to enable global asymptotic consensus tracking using local information obtained from neighboring agents. The closed-loop stability is proven using Lyapunov analysis theory and an invariance-like theorem. We then extend the approach to the case of directed information exchange, whose information-exchange matrix is only of full rank so that the approach for undirected graphs cannot be directly applied. We show that global asymptotic consensus tracking can still be enabled under the new derived sufficient conditions by designing a new identifier, which utilizes the estimated information exchanged from neighboring agents, and constructing a new Lyapunov function. Examples and numerical simulations are provided to validate the effectiveness of the proposed robust consensus tracking method.     

多智能体系统自适应跟踪控制

基于带有非线性动态的二阶多智能体系统,研究了在有动态领导者条件下的跟踪一致性问题。假设跟随者只能获取邻居智能体的相对状态信息,只有一部分跟随者可以获得领导者的位置和速度信息,领导者的控制输入非零且不被任何一个跟随者可知。在通信拓扑为无向连通图的条件下,为了避免全局信息的不确定性,设计了分布式自适应控制协议。将系统的一致性问题转化为误差系统的一致性问题,通过Lyapunov稳定性理论和矩阵理论分析得到了该协议使系统达到一致的充分条件。最后用仿真例子证明了设计方法的有效性。     

Consensus of networked multi-agent systems with communication delays based on the networked predictive control scheme

The consensus problem of discrete-time networked multi-agent systems (NMASs) with a communication delay is investigated in this article, where the dynamics of agents described by discrete-time linear time-invariant systems can be either uniform or non-uniform. For the NMASs with a directed topology and constant delay, a novel protocol based on the networked predictive control scheme is proposed to compensate for communication delay actively. Using algebraic graph theories and matrix theories, necessary and/or sufficient conditions of achieving consensus are obtained, which indicates that, under the proposed protocol, the consensus is independent of the network delay and only dominated by agents' dynamics and communication topology. Meanwhile, the protocol design and consensus analysis are also presented in the case of no network delay. Simulation results are further presented to demonstrate the effectiveness of theoretical results.     

Leader-following scaled consensus of second-order multi-agent systems under directed topologies

ABSTRACT

This paper investigates the leader-following scaled consensus problem of second-order multi-agent systems under directed topologies. Three novel leader-following scaled consensus protocols are designed. First, a novel scaled consensus protocol is proposed. It can guarantee the velocity of each agent in one sub-group exactly follow that of a leader, and the follower agents achieve scaled consensus. Second, another proposed protocol enables the agents' positions and velocities of one sub-group accurately track those of a leader, and the follower agents achieve scaled consensus. Third, consider the case where the leader's states available to one or multiple followers and the leader travels with a varying velocity, a novel scaled consensus tracking protocol is proposed. Sufficient and necessary conditions are obtained to guarantee scaled consensus tracking for the three cases,respectively. Finally, simulation examples are made to verify the effectiveness of the theoretical results.     

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.     

Observer-based prescribed-time consensus control for heterogeneous multi-agent systems under directed graphs

This work studies the prescribed-time robust consensus tracking problem of heterogeneous multi-agent systems over directed graphs. Aiming at multi-agent systems with a static leader and only matched disturbances, a distributed observer-based consensus algorithm is developed, to ensure that the tracking errors converge to zero accurately in prescribed time. For the case of multi-agent systems with a dynamic leader and mismatched/matched disturbances, an adaptive strategy based on a distributed observer and a disturbance observer is designed by the dynamic damping reciprocal technology. Such strategy can avoid the numerical singularity, adapt to the situation that the upper bounds of the disturbances are unknown, and assure that the tracking errors converge to an adjustable neighborhood of zero within prescribed time. Finally, simulations are given to verify the effectiveness of the proposed control strategies.     

Consensus of linear multi-agent systems with reduced-order observer-based protocols

This paper considers the consensus problems for both continuous- and discrete-time linear multi-agent systems with directed communication topologies. Distributed reduced-order observer-based consensus protocols are proposed, based on the relative outputs of neighboring agents. A multi-step algorithm is presented to construct a reduced-order protocol, under which a continuous-time multi-agent system whose communication topology contains a directed spanning tree can reach consensus. This algorithm is further modified to achieve consensus with a prescribed convergence rate. These two algorithms have a favorable decoupling property. In light of the modified algebraic Riccati equation, an algorithm is then given to construct a reduced-order protocol for the discrete-time case.     

Admissible consensus for networked singular multi-agent systems with communication delays

This study concerns the admissible consensus problem for networked singular multi-agent systems with communication delays and agents described by general singular systems. Only the information of outputs is available through the network. An observer-based networked predictive control scheme (NPCS) is employed to compensate for the communication delays actively. Based on NPCS and dynamic compensator (dynamic output feedback), a novel protocol is proposed. Based on graph, algebra and singular system theory, the necessary and sufficient conditions are given to guarantee existence of the proposed protocol. The conditions depend on the topologies of singular multi-agent systems and the structure properties of each agent dynamics. Moreover, a consensus algorithm is provided to design the predictive protocol. A numerical example demonstrates the effectiveness of compensation for networked delays.     

Global finite-time attitude consensus tracking control for a group of rigid spacecraft

The problem of finite-time attitude consensus for multiple rigid spacecraft with a leader–follower architecture is investigated in this paper. To achieve the finite-time attitude consensus, at the first step, a distributed finite-time convergent observer is proposed for each follower to estimate the leader's attitude in a finite time. Then based on the terminal sliding mode control method, a new finite-time attitude tracking controller is designed such that the leader's attitude can be tracked in a finite time. Finally, a finite-time observer-based distributed control strategy is proposed. It is shown that the attitude consensus can be achieved in a finite time under the proposed controller. Simulation results are given to show the effectiveness of the proposed method.     

Distributed finite‐time tracking of multiple Euler–Lagrange systems without velocity measurements

This paper investigates the distributed finite‐time tracking problem of networked agents with multiple Euler–Lagrange dynamics. To achieve finite‐time tracking, a distributed finite‐time protocol is first proposed on the basis of both relative position and relative velocity measurements. By using tools from homogeneous theory, it is theoretically shown that the proposed protocol can guarantee finite‐time tracking in the presence of control input constraints. On the basis of the state feedback analysis and with the aid of second‐order sliding‐mode observer approach, a new class of finite‐time tracking protocols based only on the relative position measurements is developed and employed. It is proved that the multiple agents equipped with the designed protocols can track the target location in finite time. Furthermore, a decentralized finite‐time protocol based on a distributed estimator is proposed to solve the finite‐time tracking problems with a dynamic leader. The effectiveness of the theoretical results is finally illustrated by numerical simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Disturbance observer–based consensus tracking for nonlinear multiagent systems with switching topologies

This paper considers the leader‐follower consensus tracking problem for nonlinear multiagent systems with external disturbances and switching topologies. A distributed disturbance observer is constructed to estimate the disturbances suffered by the followers. Then, a distributed consensus protocol is proposed for the consensus tracking problem with disturbance rejection under a fixed directed topology based on the disturbance observer. Next, this result is extended to the case in which the switching communication topology only frequently but not always contains a directed spanning tree. By selecting the parameters appropriately such that the communication time satisfies various preset conditions, it is theoretically proven that the consensus tracking with disturbance rejection can also be achieved by the multiagent systems. Finally, a simulation example is presented to demonstrate the performance of the proposed control scheme.     

Finite‐time consensus tracking for harmonic oscillators using both state feedback control and output feedback control

This paper investigates the distributed finite‐time consensus‐tracking problem for coupled harmonic oscillators. The objective is to guarantee a team of followers modeled by harmonic oscillators to track a dynamic virtual leader in finite time. Only a subset of followers can access the information of the virtual leader, and the interactions between followers are assumed to be local. We consider two cases: (i) The followers can obtain the relative states between their neighbors and their own; and (ii) Only relative outputs between neighboring agents are available. In the former case, a distributed consensus protocol is adopted to achieve the finite‐time consensus tracking. In the latter case, we propose a novel observer‐based dynamic protocol to guarantee the consensus tracking in finite time. Simulation examples are finally presented to verify the theoretical analysis. Copyright © 2012 John Wiley & Sons, Ltd.     

Observer-based consensus in networks of discrete-time switched linear dynamics under a fixed topology

This paper considers the consensus problem of discrete-time switched linear multi-agent systems under a fixed communication topology. An observer-based protocol with sampled data is proposed for solving such a problem. Assume that the digraph has a directed spanning tree and that all switched subsystem of each agent are stabilisable and detectable. It is shown that the proposed protocol solves the consensus problem when the sampling period is sufficiently small and the average dwell time of the switching signal is sufficiently large. Moreover, to reduce the conservatism, a sufficient condition for consensus is obtained to design the feedback gain matrices and the observer gain matrices by linear matrix inequalities, which guarantee that consensus can be achieved when the sampling period and the average dwell time are in the general case. Finally, the effectiveness of the theoretical results is demonstrated through an example.     

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.     

Homogeneous finite-time consensus tracking of high-order-integrator agents by parametric approach

Finite-time consensus tracking of high-order-integrator multi-agent systems (MAS) is investigated under an undirected topology. When the leader's control input is known to all followers, the homogeneous finite-time control for a high-order integrator is extended to a distributed protocol for the corresponding MAS, and a set of control gains are found by the parametric approach for robust control, such that the multiple agents are simultaneously stabilised in finite time by keeping all characteristic polynomials Hurwitz. When it is only known to the leader's neighbouring followers, a distributed observer is presented for each follower to estimate it in finite time, and the combined observer-based protocol achieves finite-time consensus tracking in a fully distributed fashion. Simulation examples illustrate the effectiveness of the proposed scheme.