A Newton-type Computing Technique for Optimal Control Problems

In this paper we propose some Newton-type algorithms for the numerical solution of both unconstrained and constrained discrete-time optimal control problems. The approach followed here is based on a suitable augmented Lagrangian function whose unconstrained minimization yields the solution of the optimal control problem and the associated multipliers. We show that the Hessian matrix of the augmented Lagrangian function has a sparse structure which allows the use of an efficient decomposition scheme for the computation of the Newton's direction. In addition, consistent approximations of the Newton's direction are described. These approximations may allow a further reduction of the computational cost. Two numerical examples are reported.