Self-Organizing and Optimal Control for Nonlinear Systems

OF THE DISSERTATION Self-Organizing and Optimal Control for Nonlinear Systems by Wenjie Dong Doctor of Philosophy, Graduate Program in Electrical Engineering University of California, Riverside, June 2009 Professor Jay A. Farrell, Chairperson Vehicle formation control is one of important research topics in transportation. Control of uncertain nonlinear systems is one of fundamental problems in vehicle control. In this dissertation, we consider this fundamental control problem. Specially, we considered selforganizing based tracking control of uncertain nonaffine systems and optimal control of uncertain nonlinear systems. In tracking control of nonaffine systems, a self-organizing online approximation based controller is proposed to achieve a prespecified tracking accuracy, without using high-gain control nor large magnitude switching. For optimal control of uncertain nonlinear systems, we considered point-wise min-norm optimal control of uncertain nonlinear systems and approximately optimal control of uncertain nonlinear systems. In point-wise non-norm optimal control, optimal regulation and optimal tracking controllers were proposed with the aid of locally weighted learning observers. By introducing control Lyapunov functions and redefining the optimal criterions, analytic controllers were proposed and were optimal in the sense of min-norm. In approximately optimal control of uncertain nonlinear systems, adaptive optimal controllers were proposed with the aid of vi iterative approximation techniques and adaptive control. By iteratively learning, the difficulty of solving Hamilton-Jacobian-Bellman (HJB) equation is overcome. The proposed adaptive optimal algorithms can be applied to solve optimal control problem of a large class of nonlinear systems. To show effectiveness of the proposed controllers for above problems, simulations were done in computers.