On The Distributed Leader-following Consensus Control Of Multi-agent Systems

During the past decade, as one of the central problems in control theory, the dis-tributed control of multi-agent systems has gained much attention due to its broad appli-cation backgrounds in many disciplines, such as computer sciences and biology. One main fundamental problem in multi-agent systems is the consensus problem that aims to design distributed control laws such that the states or outputs of all agents reach an agree-ment. It contains the consensus problem without a leader (i.e., leader-less consensus) and consensus problem with a leader, which is generally called leader-following consen-sus or distributed tracking problem. This dissertation focuses on the leader-following consensus problem of multi-agent systems. The main contents and contributions are summarized as follows.1. The leader-following consensus problem of second-order nonlinear multi-agent systems is investigated. First, the leader-following consensus problem of second-order integrator type nonlinear multi-agent systems and second-order strict-feedback nonlin-ear multi-agent systems are studied under directed communication topology. Under the assumption that the control input of the leader agent is equal to zero, the inverse opti-mal adaptive distributed tracking control problem is also studied. Second, the leader-following consensus problem of second-order nonlinear multi-agent systems with un-known but bounded disturbances is considered. Both state feedback and dynamic output feedback control laws are designed. Compared with the existence literatures, the nonlin-ear functions are not required to satisfy any globally Lipschitz growth or Lipschitz-like growth condition. Moreover, the adaptive consensus protocol is in a distributed fashion without using any global information such as the eigenvalues of the Laplacian matrix of underly topology and the agent’s own state. Therefore, the proposed control laws are in a fully distributed fashion.2. According to the methods developed for nonlinear multi-agent systems, the leader-following consensus problem of general linear multi-agent systems is investi-gated. First, the leader-following consensus problem of a class of high-order integrator type multi-agent systems is studied. Compared with the existing works, the proposed control law is independent of the eigenvalues of the Laplacian matrix of underly topol-ogy. Due to the complexity caused by the directed graph, the proposed protocol is nonlinear rather than the conventional linear protocol. It is proved that, for any directed communication graph that contains a spanning tree with the root node being the leader agent, the proposed control law solves the leader-following consensus problem. Sec-ond, by using linear system theory, we convert the leader-following consensus problem of general linear multi-agent systems into the leader-following consensus problem of some high-order integrator type multi-agent systems.3. The leader-following consensus problem of a class of nonlinear multi-agent systems in strict feedback form is studied. By introducing a novel distributed observer and employing the backstepping methodology, a distributed adaptive nonlinear control law is constructed using the relative output information between neighboring agents. For any directed communication graph that contains a spanning tree with the root node being the leader agent, the proposed control law solves the leader-following consensus problem.4. The robust leader-following consensus problem of a class of multi-agent sys-tems with unknown nonlinear dynamics and unknown but bounded disturbances under undirected communication topology is studied. First, by employing the robust inte-gral of the sign of the error technique, a distributed control law is designed for a class of high-order integrator type nonlinear multi-agent systems. The proposed protocol achieves semiglobally leader-following consensus. Second, the approach is extended to study a class of more general uncertain multi-agent systems. It is worth pointing out that the proposed distributed control law is continuous rather than discontinuous.5. The leader-following consensus problem of a class of heterogeneous second-order nonlinear multi-agent systems and the inverse optimal gain assignment distribut-ed control of a class of second-order multi-agent systems under Markovian switching topology are investigated. It is more difficult to design distributed control laws due to the complexity caused by Markovian switching topology. To study the inverse optimal gain assignment distributed control problem of multi-agent systems, the inverse opti-mal gain assignment problem of Markovian jump nonlinear systems is introduced. Two sufficient conditions are given for the solvability of this problem. Based on those two sufficient conditions, two distributed control laws are designed, which solve the inverse optimal gain assignment distributed control problem of multi-agent systems.