Tracking Problems Of Multi-Agent Systems With Time-Varying Topologies

Multi-agent systems have become a hot research area in the recent two decades due to the wide applications to mobile robots, unmanned aerial vehicles (UAVs), au-tonomous underwater vehicles (AUVs) and satellites. Tracking problem of a target is a typical issue of multi-agent systems. Most of the works in the literature consider fixed or switching topologies no matter in case of second-order or high-order kinemat-ics. However, in practical, the velocity of each maneuvering agent is time-varying and the communication radius of each agent is finite. Therefore, the communication topol-ogy between the target and tracking agents may change from time to time, tracking problem of multi-agent systems under time-varying topology is of vital necessity. The main content of this thesis can be summarized as follows.(1)Some necessary and sufficient conditions for tracking of continuous multi-agent systems with nonlinear dynamics and transit variable topology are obtained. Transient variable topology means the variable topology shifts continuously rather than switches among several different structures. A necessary and sufficient condition associated with eigenvalues is given to ensure successful tracking of the nonlinear multi-agent system-s. Then, tracking problems of second-order and high-order multi-agent systems under transient variable topology are addressed. Some sufficient conditions and controller de-sign principles which ensure the successful tracking of multi-agent systems are deduced both for second-order and high-order case.(2)This thesis studies the multi-agent tracking problem of a high-order maneu-vering target under uncertain communication environments. Each tracking agent is assumed to be a high-order system and can only use its own and neighbours’ position, velocity and acceleration information to design its control input. In this work, the uncertain communication environments are modelled by a finite number of constant Laplacian matrices together with their corresponding scheduling functions. Sufficient conditions for the existence of a tracking strategy have been expressed in terms of the solvability of linear matrix inequalities.(3)Tracking problem for high-order agents under uncertain communication topol- ogy and time varying delays is investigated. In real-world systems, when information is exchanged between the agents and the target through the wireless communication network, time delays are inevitable. Through a set of simulations with various control parameters γ, the relationship between γ and the maximum allowable communication delays are tabulated. It verifies that appropriate time delays are in favor of the consen-sus of tracking systems to some extent.(4) Sliding mode control method is applied to solve this nonlinear tracking problem under a time-varying topology. It is well known that sliding mode control(SMC) is a robust control scheme due to its insensitivity to system uncertainty. Owing to its effectiveness and simplicity to implement in practice, SMC has been widely employed in many areas and it has been verified that the introduction of SMC can indeed help accomplish certain desired control performances for a group of agents. Therefore, the sliding model control method is employed to deal with the tracking problem of multi-agent system under a time-varying topology in this work. The proposed polytopic model structure makes it able to apply the sliding mode control scheme in a wider range. At the same time, the sliding mode control scheme shows advantage in terms of tracking time.(5)A class of multi-agent relay tracking systems, in which targets are caught by cooperative agents in a monitoring area, is considered. A certain domain is monitored by a large number of agents, which are capable of sensing and mobility. With the assistance of knowledge of Voronoi diagrams, the domain is divided into many Voronoi cells. Then, a cooperative relay tracking strategy is proposed such that during the tracking process, when a target enters a new Voronoi cell, the Voronoi site agent replaces one of the original tracking agents. This means that not only the topology but also the tracking agents switch, which is significantly different from the traditional switching topologies. With the introduction of redundant agents, this domain can deal with the situation that several targets share the same route.In addition, a class of nonlinear multi-agent tracking problems with unstable sub-systems is investigated. During the tracking process, the topology and tracking agents switch, which may lead the tracking system to be stable or unstable. The system switches either among consecutive stable subsystems and consecutive unstable subsys- tems or between stable and unstable subsystems. A tracking strategy guaranteeing overall successful tracking despite the existence of unstable subsystems is designed. Al-so, extended discussions are addressed on the case where the dynamics of agents are subject to disturbances and the disturbance attenuation level is achieved.In the end, main results presented in this thesis are summarized, and the possible extensions for future work are discussed.