Abstract
This paper presents a strong variation algorithm for solving optimal control problems whose dynamics are described by ordinary differential equations with discontinuous right-hand sides.
It is proved that the accumulation points of the sequence of controls generated by the algorithm, if exist, satisfy maximum principle type necessary conditions for optimality. The major difficulties which arise from the existence of “separating hyperplanes” dividing the state space into subregions are that state trajectories do not necessarily exist on the whole time interval, and that adjoint variables may have the jump-discontinuities at hyperplane passing times. Both of the existence of state trajectories and jump-phenomena of adjoint variables are discussed in detail. Moreover, two examples with separating hyperplanes are shown to illustrate the effectiveness of the present algorithm.
