An algorithm for solving control constrained optimal control problems

An algorithm, with an approach similar to the Han-Powell method in finite-dimensional optimization, is devised to solve continuous-time optimal control problems where the control variables are constrained. The algorithm is based on a second-order approximation to the change of the cost functional due to a change in the control. Further approximation of that summation produces a simple convex functional. It is then show that the solution of the minimization of the convex functional, subject to linearized system dynamics and the original control constraint, generates a descent direction of the original cost functional. Three examples are given in which the authors´ algorithm converges faster than its predecessors