Numerical experiments on transformation techniques for minimax problems of optimal control
Kuo, Yan Min
Master of Arts
A transformation technique is employed in order to convert mini max 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 TT. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the vector parameter in 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 considered in this 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 interval of integration is normalized to unit length. Four test problems characterized by known analytical solutions are solved numerically. It is found that the combination of transformation technique and sequential gradient-restoration algorithm yields numerical solutions which are quite close to the known analytical solutions. In particular, the converged values of the minimax performance index agree well with the known analytical values.