Research For Controller Design Of Linear Multi-agent Systems

With the popularity of intelligent devices and the fast development of communication techonology,the distributed cooperative control of networked multiagent system has recently been a hotspot within the control community.In the real world,numerous individuals can be modeled as nodes,and the connections between the individuals can be described by edges,and then produce a graph or network.A multi-agent system is a cooperative control system framework,within which information is exchanged based on networks.Thus,such a system is the high integration of network,communication and control.Due to the lack of global information of network,each agent can only use its neighboring information to reach specific global goals,so the essence of multi-agent coordination control is local interaction and global emergence.This dissertation investigates general linear multi-agent systems,and designs distributed controller in order to reach the consensus tracking or containment.System subtraction is used to translate the consensus tracking problem of homogeneous multiagent systems into the stabilization problem in terms of a single system.Then,we comprehensively use matrix theory,switching system theory,adaptive theory and saturation control theory to implement convergence analysis.The output regulation framework is artfully used to address the containment control problem of heterogeneous multi-agent systems.The main content and contributions of this dissertation are stated as follows.1.The consensus tracking problem of general linear multi-agent systems with Lipschitz nonlinear terms has been addressed.Because system states are difficult to acquire and signal transmission is not continuous,we propose a new protocol design based on intermittent communications and an observer.By using combined tools from the matrix theory,the switching theory and the averaging approach,a sufficient criterion is established,under which the consensus tracking of nonlinear multi-agent systems can be achieved.The obtained results reveal the relationships among the communication rate,the convergence rate and the dwell time of switching topologies.2.To mitigate the dependence of the constant coupling weights in protocols on global topology graphs,we propose an adaptive coupling weights design scheme over directed networks.The key idea is to assign a time-varying and self-adjusting coupling weight to each agent,and simultaneously combine a monotone increasing function for increasing the design degree of freedom.Under this design philosophy,an adaptive state feedback protocol and an adaptive output feedback protocol are respectively proposed to reach the consensus tracking of general linear multi-agent systems.By using matrix theory and artful Lyapunov function,a sufficient criterion is established,under which the consensus tracking over directed graphs is reached.The highlight of our protocols is that they do not rely on any global topology graphs,and this work provides a new perspective for designing an adaptive protocol over directed graphs.3.The low gain feedback method that addresses consensus tracking for multi-agent systems with input saturation often results in the contradiction between initial regions and convergence speed.To alleviate this contradiction,a gain scheduled approach is proposed and it aims at improving the convergent performance of the consensus tracking for multi-agent systems subject to the saturator saturation.Specifically,based on a specific scalar differential equation,the gain parameter is dynamically scheduled and its value continuously increases,which increases the feedback gain and enhaces the convergence speed.Our main contribution is to propose a two layers protocol design framework consisting of a control layer and a scheduling layer.In the control layer,distributed protocols are implemented on each agent to realize the consensus tracking,while in the schedule layer,the gain parameter is scheduled larger to accelerate consensus convergence.Finally,the obtained results are extended to the case where the leader's control input is bounded.To suppress the effect of bounded input,the discontinuous protocol and its continuous approximation counterpart are designed for achieving the exact-consensus tracking and the quasi-consensus tracking,respectively.Theoretical analysis and simulations show that,compared with the low gain feedback method,the gain scheduled approach proposed here can possess higher convergence speed.4.The output regulation problem aims to design a feedback control law for given plant,which can not only maintain the stability of the closed-loop system,but also achieve asymptotic tracking of a class of reference signals and reject a class of disturbance signals.Thus,the framework of the output regulation is more general.Within this framework,we consider the containment problem of heterogeneous linear multi-agent systems with directed graphs.First,via dynamic compensator techniques,the containment problem can be converted into cooperative output regulation problem.Moreover,we artfully construct regulation equations,whose solutions are also given explicitly.Under some mild assumptions on agent dynamics and network topology,we respectively propose the distributed dynamic adaptive state feedback and adaptive output feedback protocols for realizing containment control,i.e.,driving followers into the moving convex hull spanned by leaders.The results are applied to containment control of a network of heterogeneous agents,where the followers are described by mass-damper spring systems,and the leaders are specified by harmonic oscillators.