An exact penalty function algorithm for control problems with state and control constraints

This paper describes an exact penalty function algorithm for solving control problems with state, control, and terminal constraints and establishes its convergence properties. A convex optimal control problem is defined whose solution yields a search direction which satisfies the control constraints and reduces a first-order estimate of the exact penalty function. Step length is determined using an Armijo-like procedure. An adaptive procedure for adjusting the penalty parameter completes the algorithm.