Research On Several Containment Problems Of Multi-agent Systems

In recent years, distributed cooperative control of multi-agent systems has received considerable attention due to its broad applications in engineering. Generally speaking,the main aim of multi-agent systems is to design a distributed control law for each agent using local information from its neighbors, such that the multi-agent systems can achieve prescribed collective behaviors such as maintaining a formation, swarming, rendezvousing,or reaching a consensus. Consensus is one of the most important and fundamental issues in the cooperative control of multi-agent systems. In some multi-agent systems, there exist one or even multiple leaders. When there is a leader in the multi-agent systems, the consensus problem becomes a distributed tracking problem or a leader-following consensus problem. When there are multiple leaders in the multi-agent systems, the consensus problem becomes a containment control problem. The objective is to design a control law for each follower to ensure that all the followers will move into the convex hull formed by the leaders. This dissertation studies containment control problems of the multi-agent systems in many cases. The main contents of this dissertation include:Chapter 1 is preface, the historical background and the significance of the multi-agent systems are introduced. The recent developments of the multi-agent systems and some knowledge of algebra graph theory are given. Finally, the main work of this dissertation is introduced.Chapter 2 discusses L2- L∞containment control problem of multi-agent systems with multiple stationary leaders and external disturbances. Furthermore, the interaction topology is Markovian switching and nonuniform time-varying delays are considered. By using a model transformation, the containment control problem of the multi-agent systems is turned into a normal L2- L∞control problem. Based on the theory in stochastic stability for time-delays systems, su?cient conditions in terms of a set of linear matrix inequalities(LMIs) are given to ensure that all the followers will move into the convex hull formed by the leaders in mean square sense with a prescribed L2- L∞performance.Chapter 3 investigates the containment control problem of second-order discrete-time multi-agent systems with Markovian missing data in actuators and one step networkinduced time delay. The process of missing data from the controller to actuator is modeled by a homogeneous, finite-state, discrete-time Markov chain. We first discuss the containment control problem for the case when all the elements of the transition probability matrix are completely known, then the result is extended to a more general case with only partially known transition probabilities. The distributed control protocol with one step time delay is proposed. Based on the stochastic Lyapunov-Krasovskii functional method, su?cient conditions in terms of a set of matrix inequalities are given to guarantee that the states of all the followers asymptotically converge to the convex hull formed by the corresponding states of the leaders in mean square sense. A cone complementary linearization algorithm is used to obtain the control gains.Chapter 4 discusses the formation-containment control problem of second-order multiagent systems with only sampled position data. We assume that there exist interactions among leaders and the leader’s neighbors are only leaders. In reality, the velocity of each agent is impossible or very di?cult to measure, two di?erent control protocols with only sampled position information are proposed for followers and leaders, respectively. By algebraic graph theory and matrix theory, su?cient conditions are given to guarantee that the leaders achieve a desired formation, meanwhile, the followers asymptotically converge into the convex hull formed by the the leaders’ final positions, i.e., the multi-agent systems achieve formation-containment.Chapter 5 discusses the formation-containment control problem of second-order multiagent systems with small sampling delay. In reality, sampling delay induced by the signal sampling process often exists due to all kinds of reasons, two di?erent control protocols with sampling delay are proposed for followers and leaders, respectively. By algebraic graph theory and matrix theory, su?cient conditions are given to guarantee that the leaders achieve a desired formation, meanwhile, the followers asymptotically converge into the convex hull formed by the the leaders’ final positions, i.e., the multi-agent systems achieve formation-containment.Chapter 6 summarizes the main results of this dissertation and point out the further research.