Convex Interpolation Control with Formal Guarantees for Disturbed and Constrained Nonlinear Systems

Abstract

A new control method for nonlinear systems is presented which solves reach-avoid problems by interpolating optimal solutions using convex combinations. It also provides formal guarantees for constraint satisfaction and safety. Reach-avoid problems are important control tasks, which arise in many modern cyber-physical systems, including autonomous driving and robotic path planning. We obtain our control policy by computing the optimal input trajectories for finitely many extreme states only and combining them using convex combinations for all states in a continuous set. Our approach has very low online computation complexity, making it applicable for fast dynamical systems. Iterating through our approach leads to a new form of feedback control with formal guarantees in the presence of disturbances. We demonstrate the new control method for a control problem in automated driving and show the advantages compared to a classical control method.