Cooperative control of nonlinear multi-agent systems in dynamical networks

Abstract

n the recent decade, the cooperative control of swarm robots has become a hot research topic in various fields and a multi-billion-dollar industry. The main objective of cooperative control is to design a distributed cooperative protocol for each agent in large-scale interconnected systems to accomplish a common task. Some specific recent examples include inspection, filming, formation light show, rescue and package delivery. This thesis is concerned with the fundamental problems of nonlinear multi-agent systems (MASs) in dynamical networks. Based on Lyapunov stability theory, matrix analysis, graph theory and convex optimization, several novel distributed controllers are designed, the consensus con-trol protocols are provided, and the state estimation protocols are also proposed with the new theories. Firstly, we tackle the observer-based consensus control problem of the nonlinear MASs that satisfies the general linear incremental (GLI) condition in a hybrid-varying directed network. In this part of the thesis, to relieve the constraints of the coupling networks and dynamics of the previous results of nonlinear MASs, we propose new sufficient conditions of the observability and controllability by means of the linear matrix inequalities (LMIs). Secondly, we investigate the leader-following consensus control of nonlinear MASs with discrete time-delays. A non-fragile controller algorithm is designed with control gain fluctuation. Furthermore, we derive some sufficient criteria for nonlinear MASs with discrete delays and control gain fluctuation by utilizing the theory of integral inequalities and free weighting matrices. In addition, we also research the Hopf bifurcation of a single agent with dis-tributed delays with the help of the Routh-Hurwitz criterion and then discuss the bifurcation consensus of multi-agent-based network congestion control systems, which can realize the bifurcation and the consensus at the same time by simulations. Finally, we study the finite-time adaptive consensus control problem of nonlinear MASs with mixed-delays. In this part, we focus on the case of nonlinear agent mod-eled by the most general nonlinear dynamics with both the mixed distributed and discrete time-delays. We present a sufficient criterion for the finite-time convergence together with a neural adaptive distributed algorithm, which is proven by the neural adaptive technique and the Lyapunov-Krasovskii function (LKF).