A projected SQP method for nonlinear optimal control with quadratic convergence

In this paper, we propose a discrete-time Sequential Quadratic Programming (SQP) algorithm for nonlinear optimal control problems. Using the idea by Hauser of projecting curves onto the trajectory space, the introduced algorithm has guaranteed recursive feasibility of the dynamic constraints. The second essential feature of the algorithm is a specific choice of the Lagrange multiplier update. Due to this ad hoc choice of the multiplier, the algorithm converges locally quadratically. Finally, we show how the proposed algorithm connects standard SQP methods for nonlinear optimal control with the Projection Operator Newton method by Hauser.

I. Introduction

Optimal control problems are of special interest within the control community and find numerous applications in academia as well as in practice and industry. Throughout the literature, many different approaches to solve these problems have been presented, in continuous and in discrete-time.