An iterative algorithm for volume maximization of N-step backward reachable sets for constrained linear time-varying systems

In this paper, we consider the computation of robust N-step backward reachable sets for state- and input con- strained linear time-varying systems with additive uncertainty. We propose a method to compute a linear, time-varying control law that maximizes the volume of the robust N-step reachable set for the closed-loop system. The proposed method is an extension of recent developments and involves the recursive solution of N semi-definite programs (SDP). We demonstrate the performance of the proposed method on the lateral control problem for emergency maneuvers of autonomous vehicles and compare it to results obtained when backward reachability is applied to the same system and a naively designed controller.