A Sequential Quadratic Programming Perspective on Optimal Control

Abstract: This paper offers a unified perspective on different approaches to the solution of optimal control problems through the lens of constrained sequential quadratic programming. In particular, it allows us to find the relationships between Newton's method, the iterative LQR (iLQR), and Differential Dynamic Programming (DDP) approaches to solve the problem. It is shown that the iLQR is a principled SQP approach, rather than simply an approximation of DDP by neglecting the Hessian terms, to solve optimal control problems that can be guaranteed to always produce a cost-descent direction and converge to an optimum; while Newton's approach or DDP do not have similar guarantees, especially far from an optimum. Our empirical evaluations on the pendulum and cart-pole swing-up tasks serve to corroborate the SQP-based analysis proposed in this paper.