Robust cooperative control and optimization of multi-agent systems - Sun, Chao (2018)
Multi-agent systems have been extensively studied in modern control theory due to their wide range of applications in robotics, transportation networks, and smart grid, etc. In this thesis, we investigate control and optimization problems in networked multi-agent systems from the perspectives of distributed coordinated control, distributed optimization and game algorithm design, and network controllability. In the first part of this thesis, we study robust cooperative control of multi-agent systems. Firstly, we consider the robust finite-time connectivity-preserving consensus tracking and formation control problems. An integral sliding mode based framework is proposed to simultaneously achieve disturbance rejection, finite-time convergence, and connectivity preservation for double-integrators with bounded disturbances and a virtual leader. The result is further extended to formation tracking. Secondly, we propose a continuous filter-based consensus protocol for a class of high-order multi-agent systems to deal with model uncertainties and disturbances in the agent dynamics. Sufficient conditions are given to guarantee asymptotic consensus tracking results. An output feedback control algorithm is further proposed by using only position information. In the second part, we study distributed optimization and game algorithm design problems. Firstly, we consider distributed quadratic optimization problem where the optimal solution and the objective functions are both assumed to be time-varying. When there exists a local compact convex constraint set for each agent, by using projected gradient methods, we prove that the tracking errors are uniformly ultimately bounded (UUB) with arbitrarily small bounds. Next, we consider a distributed Nash equilibrium seeking problem for a nonsmooth noncooperative game. Each player has a convex cost function and is subject to multiple shared constraints. The objective is to design a Nash equilibrium seeking law such that each player minimizes its own cost function in a distributed way. Both class-C2 objective functions and locally Lipschitz objective functions are studied. In the third part, the network controllability problem is investigated. Specifically, we study the controllability of a class of antagonistic networks with not only positive weights but also negative ones. This kind of network model has a wide range of applications in social network science. Nodes connected with a positive edge can be viewed as “friends” and linked with a negative edge can be viewed as “enemies”. We present a necessary condition to characterize the controllability and analyze the relationship between an antagonistic network and an all-positive network in terms of controllability.