Reachable set computation of linear systems with nonconvex constraints via convex optimization

This paper addresses the reachable set computation of a linear system with a nonconvex control constraint and other convex control and state constraints. We propose to convexify the nonconvex constraint by a relaxation technique. We prove that the reachable set of the relaxed constrained system at any given final time is equal to that of the original constrained system at the same final time under certain assumptions, and interestingly it holds even though the admissible control set is expanded. The theoretical result can enable us to use convex optimization to efficiently and accurately compute the reachable set of the original constrained system. We will verify and apply the theoretical result to reachable set computation via two planetary precision landing examples.