Research On Coordinated Control Of Cooperative–antagonistic Generalized Multi-agent Systems

In recent years,coordinated control of generalized multi-agent systems has attracted the attention of more and more scholars in the control field at home and abroad due to its extensive engineering background and broad potential applications in robotics,electricity,chemical engineering,aviation,aerospace and many other areas.Compared with normal multi-agent systems,generalized multi-agent systems are more complicated in structure and have many new characteristics,and hence the study of their coordinated control problem is more difficult and challenging.To data,many results have been obtained concerning the coordinated control of generalized multi-agent systems,yet the overwhelming majority of existing results focus on the generalized multi-agent systems which only include cooperative interactions among agents.However,in many practical multi-agent systems,such as biological systems,economic systems,and social networks,the interactions between agents can be not only cooperative but also antagonistic.Thus,it is of both theoretical and practical significance to study the coordinated control problem of generalized multi-agent systems in which both cooperative and antagonistic interactions coexist.This dissertation is devoted to study the problems of bipartite consensus tracking and bipartite containment control for linear cooperative-antagonistic generalized multi-agent systems in the leader-follower framework,by using tools from signed graph theory,matrix theory,linear generalized system theory,and coordinated control theory of multi-agent systems.The main contents of this dissertation are as follows.The problem of semi-global bipartite consensus tracking for continuous-time linear cooperative-antagonistic generalized multi-agent systems subject to input saturation under fixed signed graph topology is investigated.By exploiting a parametric generalized algebraic Riccati equation(GARE)-based low-gain feedback approach,a state feedback controller relying on the relative states of neighboring agents and an observer-based feedback controller are designed.By using generalized Lyapunov function method and linear matrix inequalities technique,sufficient conditions for the closed-loop system to achieve semi-global bipartite consensus tracking are derived.Numerical examples are given to illustrate the effectiveness of the proposed controllers.The bipartite containment control problem for both continuous-time and discretetime linear cooperative-antagonistic generalized multi-agent systems with multiple dynamic leaders under static signed digraph topology is studied,where each leader can be autonomous or dynamically evolving via interactions with its neighboring leaders.First,by using matrix-theoretic and graph-theoretic tools,some fundamental properties for the Laplacian and Perron matrices of weakly connected signed digraphs are established.Then,distributed control protocols based upon the relative states of neighboring agents are designed for both continuous-time and discrete-time cases.In addition,necessary and sufficient conditions ensuring the bipartite containment of the considered multi-agent systems under the proposed control protocols are derived by utilizing tools from matrix theory and linear generalized system theory.Finally,numerical simulations are provided to demonstrate the validity of the proposed results.The problem of observer-based bipartite containment control for continuous-time linear cooperative-antagonistic generalized multi-agent systems with multiple dynamic leaders under static signed digraph topology is investigated.By using different local output information,three different types of distributed observer-based control protocols are proposed.Multi-step algorithms for constructing the corresponding proposed protocols are also given.Based on the matrix theory and continuous generalized linear system theory,sufficient conditions for bipartite containment of the considered systems are obtained.The effectiveness of the three proposed control protocols is demonstrated by numerical examples.The observer-based bipartite containment control problem of discrete-time linear cooperative-antagonistic generalized multi-agent systems with multiple dynamic leaders under signed digraph topology is studied.In light of the modified discrete-time generalized Riccati equation method,three different distributed observer-based control protocols are designed utilizing different local output information.Meanwhile,algorithms for constructing the corresponding proposed protocols are presented.By using matrix theory and discrete linear generalized systems theory,sufficient conditions to ensure the bipartite containment of the considered generalized multi-agent systems are given.Numerical examples are presented to illustrate the effectiveness of the proposed control protocols.The problem of reduced-order observer-based bipartite containment control for both continuous-time and discrete-time linear cooperative-antagonistic generalized multi-agent systems with multiple dynamic leaders over static signed digraph topology is investigated.In light of the continuous-time generalized Riccati equation and generalized Sylvester equation methods,a distributed normal reduced-order observer-based control protocol relying upon the relative output information of neighboring agents is proposed for the continuous-time case,and sufficient condition is established via theoretical analysis.Furthermore,by using the modified discrete generalized Riccati equation and the generalized Sylvester equation methods,a distributed normal reduced-order observer-based control protocol using the relative outputs of neighboring agents is designed similarly for the discrete time case,and sufficient condition to ensure the bipartite containment of the considered generalized multi-agent systems is derived through theoretical analysis.Finally,two numerical examples are provided to validate the effectiveness of the proposed control protocols.