Multiple-subarc approach for solving minimax problems of optimal control

[摘要] Numerical solutions of minimax problems of optimal control are obtained through a multiple-subarc approach, used as a sequel to a single-subarc approach. The problems are solved by means of the sequential gradient-restoration algorithm. Firsts transformation technique is employed in order to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations. The transformation requires the proper augmentation of the state vector x(t),the control vector u(t),and the parameter vector ir. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the vector parameter is being optimized. The transformation technique is then employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer. The algorithm developed in the thesis belongs to the class of sequential gradient-restoration algorithms. The sequential gradient-restoration algorithm is made up of a sequence of two-phase cycles,each cycle consisting of a gradient phase and a restoration phase. The principal property of this algorithm is that it produces a sequence of feasible suboptimal solutions. Each feasible solution is characterized by a lower value of the minimax performance index than any previous feasible solution. To facilitate numerical implementation, the intervals of integration are normalized to unit length. Several numerical examples are presented to illustrate the present approach. For comparison purposes, the analytical solutions, the single-subarc solutions, and the multiple-subarc solutions are presented. Key Words. MLnimax problems, ndnimax optimal control, numerical methods, continuous approach, single-subarc approach, multiple-subarc approach, transformation techniques, sequential gradient-restoration algorithms.

[发布机构] Rice University