Tracking Control Of Nonlinear Multi-AgentSystems Over Digraphs

Distributed control of nonlinear multi-agent systems has been extensively investigated in the system and control community,mainly due to its ubiquitous applications.Leader-follower tracking control is a class of fundamental problems of multi-agent systems over digraphs.This dissertation mainly considers cooperative tracking control of multi-agent systems with hysteresis inputs and collective behaviors and distributed control of nonlinear multi-agent over signed digraphs.Main contributions of this dissertation are highlighted as follows.First,the cooperative tracking control problem of nonlinear multi-agent systems with hysteresis inputs is studied over nonnegative digraphs.The digraph contains a spanning tree with a unique root node being the leader.Each agent is modeled by a higher-order nonlinear system in strict-feedback form with the hysteresis input.By using backstepping technique,a class of distributed adaptive control laws are proposed.For the output feedback approach,the state observer and the nonlinear disturbance observer are respectively developed to estimate unavailable states and unknown compounded disturbances.For the state feedback approach,the use of multiple Nussbaum functions is developed to handle the unknown time-varying virtual control coefficients,and a distributed control law with the global neural networks is proposed to guarantee the global ability.The control laws are designed to guarantee the uniformly ultimately bounded stability,and the cooperative tracking can be achieved with bounded residual errors.Additionally,the bipartite tracking control problem of higher-order nonlinear multi-agent systems is investigated over signed digraphs.The signed digraph that is structurally balanced contains a spanning tree with a unique root node being the leader.Each agent is modeled by a higher-order nonlinear system in strict-feedback form with unknown dynamics.By using backstepping technique,a distributed adaptive control law is proposed to guarantee the prescribed performance of local neighborhood error.A class of distributed low-complexity state and output feedback control laws which are simple and approximation-free,utilizing the local errors incorporating with the prescribed performance metrics,are respectively proposed to achieve the bipartite tracking.The control laws are designed to guarantee the uniformly ultimately bounded stability,and the bipartite tracking can be achieved with bounded residual errors,and both transient and steady state performances of tracking errors can also be guaranteed.Furthermore,the bipartite containment tracking control problem of nonlinear multi-agent systems with matched conditions is studied over signed digraphs,regardless of whether the digraphs are structurally balanced or unbalanced.For each follower,there exists at least one leader that has a directed path to that follower.Each agent is modeled by the nonlinear systemwith matching uncertainty.By utilizing algebraic Riccati method,the distributed adaptive state feedback and output feedback control laws are respectively proposed,which guarantee that all followers can converge to the convex hull spanning by the leaders' trajectories as well as their signed symmetric trajectories.As a consequence,the theoretical results of this dissertation mainly extend and improve the existing results for distributed tracking control problems of nonlinear multi-agent systems,which provide the valuable control strategies to solve practical problems,and thus they are not only of theoretical significance,but also of practical importance.