Convexifying State-Constrained Optimal Control Problem

Abstract

This paper presents a method that convexifies state-constrained optimal control problems in the control-input space. The proposed method enables convex programming methods to find the globally optimal solution even if costs and control constraints are non-convex in control and convex in state, dynamics is non-affine in control and convex in state, and state constraints are convex in state. Under the above conditions, generic methods do not guarantee to find optimal solutions, but the proposed method does. The proposed approach is demonstrated in a sixteen-dimensional navigation example.