Distributed Consensus Tracking Control Of Multi-Agent Systems

In recent years, more and more researchers have focused their attention on the distributed cooperative control of multi-agent systems. It reveals emergence properties of many natural complex systems and also has broad applications in engineering. Consensus plays a critical role in the distributed cooperative control of multi-agent systems. Each agent needs to exchange the local information with its neighbors in order to achieve consensus. Since the multi-agent systems are always in complex environments, the communication topology might be time-varying, communication data might suffer measurement noises and communication delays and the agents’ dynamics might contain nonlinear and uncertain terms. All of these factors might lead to the unachievement of consensus. Thus, it is necessary to analyze the effects of these factors on consensus and to find some strategies to reduce the effects.This dissertation mainly discusses consensus tracking and containment control of high order multi-agent systems in directed graph, robust distributed containment control of high order multi-agent systems with nonlinear and uncertain terms, mean square containment control with measurement noises and communication delays and containment formation with collision avoidance. Main contributions of this dissertation are as follows:The consensus tracking of multi-agent systems with general linear dynamics and a leader of time-varying, bounded input under directed graph is studied. By constructing Lyapunov function appropriately and using “pseudo positive semi-definite” property of the Laplacian matrix, we prove that the consensus tracking problem can be solved. In most practical cases, the physical state of the system cannot be determined by direct observation. Instead, indirect effects of the internal state are observed by way of the system outputs. Thus, a state observer based distributed consensus tracking controller is designed. An adaptive consensus tracking protocol without knowing global information is also proposed. Due to the environment and movement of agents, the communication topology might change as time progresses, consensus tracking with switching directed topology is also studied. With extensions to multiple leaders, containment control of multi-agent systems with general linear dynamics under fixed and switching directed graph is also considered.Since the agents’ dynamics always contain nonlinear and uncertain terms, robust containment control problem for multi-agent systems with uncertain nonlinear dynamics is addressed. A distributed static containment controller based on neighbouring state is designed, a sufficient condition which guarantees the convergence of the protocol is given based on LMI. Furthermore, an adaptive containment control algorithm is developed without knowing any global information about the topology and the upper bound of the leaders’ state and control input.By using stochastic analysis tools and algebraic graph theory, the containment consensus control problem for multi-agent systems with measurement noises and time-varying communication delays under directed networks is addressed. We prove that the followers can converge to the convex hull spanned by the leaders in the sense of mean square if the allowed upper bound of the time-varying delays satisfies certain sufficient condition. Moreover, the time-varying delays are asymmetric for each follower agent, and the time-delay dependent consensus condition is derived.Current research on containment protocol didn’t consider the case that the followers’ state are overlapped or close, which will cause collision between each other. Based on graph theory, matrix analysis and nonlinear analysis, we propose the static and adaptive containment formation protocol, respectively. The necessary condition is also obtained by using Lyapunov method. Both the protocols can drive the position of the followers close to the convex hull formed by those of the leaders with collision avoidance. The proposed containment protocols are also shown to achieve velocity matching.Many existing works about flight formation all assume the airplane works in the level flight condition, while this dissertation studies the flight formation considering flight path angle. Two simplification of the flight dynamics are given to make consensus theory applicable to 3D flight formtaion. A distributed flight formation simulation system with autopilot hardware in the loop is also developed. The system can reduce the complexity and costs of the experiment, it also can overcome the pure software simulation’s shortcoming, which might diverge from reality.