Infinite horizon nonlinear optimal control and approximation.
详细信息
文摘
In this dissertation, we consider fundamental problems of existence, convergence, and approximations for infinite horizon nonlinear optimal control problems with unbounded performance indices. In the framework of optimal control, new sufficient conditions of Caratheodory-Hamilton-Jacobi type for both overtaking and weak overtaking optimality are presented and compared with known results from the calculus of variations setting. Using local structural properties of a related control Hamiltonian and tools for an associated Hamilton-Jacobi equation, conclusions are drawn on aspects of existence of overtaking and weak overtaking optimal controls, convergence of optimal controls and trajectories, and approximations of strong and weak overtaking optimal controls. New results and extension for the linear-quadratic optimal tracking problem are obtained, and an application to an optimal gain scheduling problem is investigated. Both similarities and differences among known results and alternative approaches to overtaking, weak overtaking, and strong optimal control problems are discussed. In summary, this dissertation focuses on optimal control aspects of overtaking optimality with both analysis and design perspectives.