Class Of Linear Multi-agent Systems Research Articles

Observer-based event-triggered leader-following control of a class of linear multi-agent systems

ABSTRACTThis paper addresses an observer-based consensus problem for leader-following control of a class of linear multi-agent systems (MASs) under a directed communication topology via event-triggered approaches. State observers are employed to tackle the scenario wherein inner information of the follower agents are not available for measurement. And then, an observer-based distributed leader-following control scheme is developed on the basis of event-triggered mechanisms. Further, to avoid continuous measurement information monitor, we present a technical approach for generation of the combinational information from their own neighbouring agents only at triggered instants. In theory, the stability of the resulting closed-loop system is rigorously investigated, and it is proven that all signals in the closed-loop system are bounded and Zeno behaviour is also excluded. Finally, simulation examples are presented for illustration of the theoretical claims.

Model-free optimal containment control of multi-agent systems based on actor-critic framework

Abstract This paper deals with the model-free optimal containment control problem for a class of linear multi-agent systems (MASs). In the existing results concerning containment control of MASs, the dynamics of the MASs is required to be completely known. Differently, in this paper, we propose a new distributed self-learning control scheme based on action dependent heuristic dynamic programming (ADHDP) to achieve containment control, where the model of MASs is no longer needed. The containment control problem is first transformed into a regulation problem on the dynamics of the designed local containment error. The policy iteration method based on the designed state-action value function (also called the Q-function) is introduced to deal with such a regulation problem. The convergence analysis of this policy iteration method is also given. Neural network (NN) based actor-critic framework is adopted to approximate the optimal Q-functions and the optimal control policies for facilitating the implementation of the proposed method. It shows that the approximated control policies achieve the containment control and satisfy the global Nash equilibrium. Finally, the simulation results are provided to demonstrate the effectiveness of the developed approach.

Robust consensus control for a class of multi-agent systems via distributed PID algorithm and weighted edge dynamics

This paper studies the robust proportional-integral-derivative (PID) consensus control for a class of linear multi-agent systems (MASs) with external disturbances. Different from the existing results, both the consensus analysis and the transient performance characteristics for high-order linear MASs are considered. Based on a factorization of Laplacian matrix, the initial MAS is firstly transformed into the so-called weighted edge dynamics, and then a design equivalence between the proposed PID consensus controller and the corresponding stabilizing controller for such weighted edge dynamics is presented via some graph theory results. Furthermore, by combining Lyapunov theory and Barbalat’s Lemma, it is proved that both the stabilization of weighted edge dynamics and the consensus of MAS can be guaranteed even in the presence of external disturbances. In particular, some relationships between the transient time performance of weighted edge dynamics and the PID design parameters are given. Finally, some numerical examples on LC oscillator network are provided to illustrate the validity of theoretical results.

Event-triggered cooperative robust practical output regulation for a class of linear multi-agent systems

In this paper, we consider the event-triggered cooperative robust practical output regulation problem for a class of linear minimum-phase multi-agent systems. We first convert our problem into the cooperative robust practical stabilization problem of a well defined augmented system based on the distributed internal model approach. Then, we design a distributed event-triggered output feedback control law together with a distributed output-based event-triggered mechanism to stabilize the augmented system, which leads to the solvability of the cooperative robust practical output regulation problem of the original plant. Our distributed control law can be directly implemented in a digital platform provided that the distributed triggering mechanism can monitor the continuous-time output information from neighboring agents.

Event-triggered Consensus Seeking under Non-uniform Time-Varying Delays

In this paper, we study consensus seeking for a class of linear multi-agent systems (MAS) subject to the inevitable imperfections of packet-based networked communication. These imperfections include unknown non-uniform time-varying transmission delays and limited communication resources. To reduce the utilization of communication resources, we propose a dynamic event-triggered control scheme resulting in aperiodic transmission of information between agents. The proposed framework leads to event-triggered controllers that guarantee the MAS to asymptotically reach consensus, strictly positive lower bounds on the inter-event times and robustness for unknown non-uniform time-varying delays in terms of maximum allowable delays.

Fixed-time consensus for multi-agent systems with discontinuous inherent dynamics over switching topology

ABSTRACTThis paper is concerned with the fixed-time consensus problem of multi-agent systems. Unlike conventional consensus-based investigations, where nonlinear inherent dynamics satisfying the Lipschitz continuous condition is assumed or simply no inherent dynamics is involved for each agent, we are dealing with a more general case: agents with discontinuous nonlinear inherent dynamics. By using non-smooth analysis and fixed-time stability techniques, distributed protocols are proposed to achieve the fixed-time consensus over fixed and switching topology. Then, for a class of linear multi-agent systems, a new distributed controller is proposed to further reduce the calculation cost while achieving the agreement. A distinctive feature of the work is that the estimation of settling time for consensus is independent of initial states of agents, which provides flexibility for applications implemented in unknown environment. Finally, numerical simulations are given to demonstrate the effectiveness of the theoretical results.

Output Feedback Cooperative Control for Linear Uncertain Multi-Agent Systems With Nonidentical Relative Degrees

In this technical note, we present an output feedback control for the cooperative robust output regulation problem of a class of heterogeneous minimum phase linear uncertain multi-agent systems with the arbitrary large plant uncertainty and the arbitrary nonidentical relative degrees. To estimate the system state, we propose a novel distributed observer that contains two distinct parts, where the first part is of the distributed form to estimate the regulated error, while the second part is a modified version of the standard reduced-order high-gain observer by replacing the regulated error with its estimation given in the first part. Our design significantly extends some current literatures in that it strictly removes the assumption of the identical relative degree, and hence applies to a much larger class of linear multi-agent systems.

Robust Unknown Input Observer-Based Fault Estimation of Leader–Follower Linear Multi-agent Systems

In this paper, the problem of the robust unknown input observer for a class of linear multi-agent systems and its application to fault estimation are considered. First, an undirected graph is used to represent the communication topology of a leader---follower linear multi-agent system. Then, using relative output estimation errors among agents, an unknown input observer is proposed to achieve fault estimation for the global augmented system in which the actuator or sensor fault vector is taken as an auxiliary state vector. A multi-constrained design algorithm based on linear matrix inequality technique is also designed to obtain gain matrices of unknown input observer. Simulation results show the effectiveness and advantages of the proposed robust unknown input observer method for fault estimation of multi-agent systems.

H ∞ control for a class of multi‐agent systems via a stochastic sampled‐data method

In this study, the stochastic sampled-data approach is developed to deal with the H ∞ control problem for a class of linear multi-agent systems. For each agent, signals should be transmitted to the control input, including not only its own measurements, but also the output information received from the neighbour agents. The relationships of information communications between the whole multi-agents are totally reflected by a weighted directed graph with a fixed topology structure. To the addressed problem, the author's focus is to design an output feedback controller for each agent such that, for the external energy bounded disturbances, the exponential stability in the mean square sense and interference rejection ability under consideration can be guaranteed. By assuming that the sampling period of each agent switches between two values in a probabilistic way, the stochastic sampling phenomenon is well characterised in every sampling tasks. In virtue of Lyapunov theory and semi-definite programming method, sufficient conditions are derived to ensure the exponential stability as well as H ∞ performance, and the feedback controllers are also designed by solving some certain matrix inequalities. Finally, a numerical simulation is given to demonstrate the validness of the proposed control strategy.

Robust consensus for linear multi-agent systems with mixed uncertainties

This paper studies the robust consensus problem for a class of linear multi-agent systems (MASs) with polytopic uncertainties and external disturbances. The uncertainties appear in both the dynamics of each agent and the topology of the overall network. Based on Lyapunov stability theory, the robust consensus problem is converted to the robust H∞ stabilization of the error system. With the aid of the homogeneous parameter-dependent (HPD) Lyapunov functions and sum of squares (SOS) technique, the robust consensus problem is further formulated as an SOS programming. Sufficient conditions to achieve robust consensus with disturbance rejection capability are presented in terms of SOS constraints. As an extension, the robust consensus problem for discrete-time MASs is studied in a similar way. Numerical examples are provided to illustrate the effectiveness of the approach.

Distributed node-to-node consensus of multi-agent systems with time-varying pinning links

In this paper, the distributed node-to-node consensus problem is addressed for a class of linear multi-agent systems with time-varying pinning links by using relative state feedback. The coordination goal in the present work is to make the states of each follower track those of its corresponding leader asymptotically where only a small fraction of followers can sense the states of their corresponding leaders through some switched communication channels. By using tools from M-matrix theory and stability analysis of switched systems theory, it is theoretically shown that such a node-to-node consensus in the closed-loop multi-agent systems can be guaranteed if each follower can be directly or indirectly influenced by at least one leader over some uniformly bounded time intervals, with the inner coupling matrix as well as the coupling strength being appropriately designed. Distributed node-to-node consensus for multi-agent systems with general Lipschitz-type nonlinear dynamics is also investigated. Numerical simulations are finally performed to verify the effectiveness of the theoretical results.

Cooperative output regulation of multi-agent systems coupled by dynamic edges

This paper investigates a new class of linear multi-agent systems, in which nodes are coupled by dynamic edges in the sense that each edge has a dynamic system attached. The outputs of the edge dynamic systems combine to form the external input of the node dynamic system, which is called neighboring input; while the outputs of the node dynamic systems are inputs of the edge dynamic systems that therefore can not be directly controlled. Distributed controllers for nodes are presented to realize output synchronization and output cooperation. Output cooperation makes the outputs of nodes realize some cooperation that here is specified as making the neighboring input track a predefined trajectory. The controllers depending on local state and neighboring inputs are designed by combining the feedback passivity theory and the internal model principle. A simulation example on the cooperated current control of an electrical network illustrates the potential applications of the analytic results.