Issues on cooperative control of multi-agent systems
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This thesis studies cooperative control for a multi-agent system (MAS). That is, via decentralized protocols, agents in a MAS can achieve synchronization, consensus, or formation. Both homogeneous and heterogeneous MAS are considered. In homogeneous MAS, two kinds of time delays are identified: input delay, which is from computational limitations, and communication delay, which results from limitations on the communication between agents. For a MAS with unknown, nonuniform constant input delay, agents are assumed to be asymptotically null controllable, i.e., agents have all eigenvalues in the closed left-hand plane for continuous-time agents, or in the closed unit disc for discrete-time agents. An upper bound for the delay is obtained which explicitly depends on agent dynamics, and a low-gain based controller design is proposed without knowing exactly the network topology. For a MAS with unknown, nonuniform and arbitrarily large communication delay, a decentralized protocol is designed. Besides, a homogeneous time-varying MAS with full (partial) state coupling is dealt with, where the network graph switches within an infinite set of graphs with arbitrarily small dwell time. A high-gain based protocol is designed. In partial-state coupling, agents can be non-minimum-phase because of the communication among control states. In heterogeneous MAS, two kinds of agents are investigated: introspective agents ( i.e., agents have access to part of states), and non introspective agents. When agents are introspective and with external disturbances, three problems are addressed: H infinity almost output synchronization, H infinity almost regulated output synchronization, and H infinity almost formation. A decentralized protocol is designed to make the H infinity norm from the disturbances to the disagreement dynamics in the network arbitrarily small. When agents are non-introspective and with external disturbances, a time-varying MAS with linear or nonlinear agents is studied. A low-and-high gain protocol is designed to achieve almost regulated output synchronization while reducing the impact of disturbances on the regulation error. This low-and-high gain protocol also works for agents with external stochastic disturbance. Moreover, disturbances with know frequencies are also addressed. This thesis also studies squaring down of general multi-input-multi-output systems to invertible uniform rank systems via pre-and/or post compensators. This squaring down technique is used in the synchronization problem.