Gradient Algorithms for the Optimization of Dynamic Systems

Abstract

Abstract : Recent advances in the area of gradient methods for optimal control problems are reviewed. Single-subarc problems are treated. Specifically, two classes of optimal control problems, called Problem P1 and Problem P2 for easy identification, are solved. Problem P1 consists of minimizing a functional I which depends on the n-vector state x(t), the m-vector control u(t), and the p-vector parameter 3.14. The state is given at the initial point. At the final point, the state and the parameter are required to satisfy q scalar relations. Problem P2 differs from Problem P1 in that the state, the control, and the parameter are required to satisfy k additional scalar relation along the interval of integration. Algorithms of the sequential gradient-restoration type are given for both Problem 1 and Problem 2. Problem P2 enlarges the number and variety of problems of optimal control which can be treated by gradient-restoration algorithms. Eight numerical examples are presented to illustrate the performance of the algorithms associated with Problem P1 and Problem P2. The numerical results show the feasibility as well as the convergence characteristics of these algorithms.