A new algorithm for solving optimal control problems with hard control constraints, end-point inequality constraints, and a variable initial state

We (1993) previously introduced an algorithm to solve continuous-time optimal control problems where the control variables are constrained. It was later (1994) extended to solve optimal control problems with not only hard control constraints but also terminal-state constraints. In this paper, the algorithm is further extended to more general optimal control problems. This improved algorithm can solve optimal control problems which are subjected to control constraints, path constraints, end-point constraints, a variable initial state, and a variable vector of design parameters, within a fixed end-time or free end-time interval. The algorithm is based on a second-order approximation to the change of the cost functional due to changes in the control and in the initial state. Further approximation produces a simple convex functional. An exact penalty type of function is employed to penalize any violation of end-point inequality constraints. We then show that the solution of the minimization of the convex functional generates a descent direction of that exact penalty function