Abstract:

We introduce a set-based, globally optimal con- troller for a specific class of nonlinear robust optimal control problems (ROCP). Traditional dynamic programming methods for solving nonlinear ROCP to global optimality require space discretization, leading to the well-known curse of dimensional- ity. In this paper, we establish sufficient conditions under which a convex relaxation of the dynamic programming recursion for a nonlinear ROCP is lossless, meaning it recovers the globally optimal solution of the original, non-convex recursion. We propose a computationally tractable, space discretization- free, almost lossless implementation of our approach using constrained zonotopes and a series of convex one-step optimal control problems. Additionally, we provide a suboptimality bound for the controller derived from our method for a standard nonlinear ROCP.