An algorithm for solving optimal control problems with control and terminal-state constraints

The authors (1993) introduced an algorithm to solve continuous-time optimal control problems where the control variables are constrained. In this paper, the algorithm is extended to solve optimal control problems with not only hard control constraints but also terminal-state constraints. An exact penalty type of function is employed to penalize any violated terminal-state constraints. The authors then show that the solution of the minimization of a convex functional, subject to a linearized system dynamics, the original control constraints, and the linearized terminal-state constraints, generates a descent direction of the exact penalty function. Iteration after iteration, the algorithm monotonically decreases the value of that penalty function until all the terminal-state constraints are satisfied and the cost functional is minimized. Also, the capability of handling terminal-state constants allows the algorithm to handle, in an approximate way, path constraints as well. Two examples are given to show the effectiveness of the algorithm