A Primal-Dual Augmented Lagrangian Method for Optimal Control of Linear-Quadratic Problem with Time Varying Systems

Abstract

In this paper we are concerned with time-varying optimal control problems whose cost is quadratic and whose state is a differential equation and with general boundary conditions. The basic new idea of this paper is to propose a primal-dual augmented Lagrangian method, embedded with a sequential quadratic programming(SQP) for the solution of such problems.The benefit of this approach is that the quality of the dual variables is monitored explicitly during the solution of the subproblem. Moreover, the formulation of a penalized matrix in the primal-dual variables with mesh-refinement strategy guarantees the reliability of the algorithm. Numerical experiments verify the efficiency of the proposed method.

Keywords: Optimal control,primal-dual methods, augmented Lagrangian methods, conjugate gradient method, sequential quadratic programming.