A feasible directions type algorithm for optimal control problems with hard state and control constraints

In this paper we describe an algorithm which solves optimal control problems with terminal equality and inequality constraints and with hard constraints on states and controls. The inequality constraints are treated via a feasible direction approach. It assures that if we start from a control which is feasible with respect to these constraints they remain satisfied during a run of the algorithm. Terminal equality constraints are tackled by an exact penalty function. In order to achieve better performance a second order correction step is applied to the equality constraints. A projection is used to treat efficiently simple control constraints. Usually this leads to a fast recognition of active control constraints at a solution. Moreover this significantly reduces the computational burden of solving direction finding subproblems because only ε-active control constraints are used in these subproblems. The algorithm is globally convergent in the sense that every accumulation point of the sequence generated by the algorithm satisfies necessary optimality conditions