Cooperative observers and regulators for discrete‐time multiagent systems

Abstract

SUMMARYThis paper investigates the design of distributed observers for agents with identical linear discrete‐time state‐space dynamics networked on a directed graph interaction topology. The digraph is assumed to have fixed topology and contain a spanning tree. Cooperative observer design guaranteeing convergence of the estimates of all agents to their actual states is proposed. The notion of convergence region for distributed observers on graphs is introduced. It is shown that the proposed cooperative observer design has a robustness property. Application of cooperative observers is made to the synchronization problem. A command trajectory generator and pinning control are employed for synchronizing all the agents to a desired trajectory. Complete knowledge about the agent's state is not assumed. A duality principle is shown for observers and state feedback for distributed discrete‐time systems on graph topologies. Three different observer/controller architectures are proposed for dynamic output feedback regulator design, and they are shown to guarantee convergence of the estimate to the true state and synchronization of all the agents' states to the command state trajectory. This provides design methods for cooperative regulators based on a separation principle. It is shown that the observer convergence region and feedback control synchronizing region for discrete‐time systems are inherently bounded, so that the conditions for observer convergence and state synchronization are stricter than the results for the continuous‐time counterparts. This is in part remedied by using weighting of different feedback coupling gains for every agent. Copyright © 2012 John Wiley & Sons, Ltd.

Distributed consensus control for discrete-time linear multi-agent systems with reduced-order observer

“…In [29], the authors proposed three different architectures of controllers and observers to solve the leader-following multi-agent consensus problems. The approach of [29] were developed to solve the discrete-time consensus problem by [9]. The distributed reduced-order observer-based protocols were proposed by [19] for both continuous-time and discretetime multi-agent systems.…”

“…But the input u r (k) is regarded as a common policy, which is assumed to be known by all the following agents. In many references such as [9,16,24,29], u r is assumed to be u r = 0. The proposed reduced-order observer-based distributed consensus protocol for agent i concludes an observer with same form (5) and a feedback control law with form…”

Consensus stability of discrete-time descriptor multi-agent systems

“…By using repeatedly of (9), we havẽ According to (8), we haveP 11 >Ã T 1P 11Ã1 ≥ 0 which means that the Lyapunov inequality (8) has positive definite solu-tionP 11 . Thus,Ã 1 is Schur-stable.…”

“…This protocol has been provided by [11] to solve the discrete-time multi-agent consensus with general linear dynamics. Let e i (k) = x i (k) − x 0 (k) and e(k) = [e T 1 (k), e T 2 (k), ⋅⋅⋅ , e T n (k)] T .…”

“…The distributed state-feedback protocols were proposed to solve discrete-time consensus with general linear dynamics systems by [9,10]. The observer-based consensus protocols for the discrete-time multi-agent systems has been addressed by [11,12,13]. The descriptor system is also referred to as singular statespace system, generalized system, or implicit system [14].…”