Strong variation algorithms for optimal control problems with control and terminal inequality constraints

This paper presents several new algorithms for solving optimal control problems with general constraints on the control and inequality constraints on the terminal state. The algorithms are of the differential dynamic programming (strong variation) type. Thus the algorithms generate, at each iteration, a new control which is equal to a "minimising" control u on a subset I??(u) ?? T and equal to the old control u elsewhere, where ?? =??(I??u) is the step length and T ?? [0,1]; this enables control constraints to be easily handled. Terminal inequality constraints are dealt with by incorporating features of non-linear programming algorithms of the feasible directions type. Convergence is proved using general results due to Polak and Klessig.