Scalable Computation of Robust Control Invariant Sets of Nonlinear Systems
Lukas Schäfer, Felix Gruber, Matthias Althoff
Abstract
Ensuring robust constraint satisfaction for an infinite-time horizon is a challenging, yet crucial task when deploying safety-critical systems. In this article, we address this issue by synthesizing robust control invariant sets of perturbed nonlinear sampled-data systems. This task can be encoded as a nonconvex program that we approximate by a tailored, computationally efficient successive convexification algorithm. Based on the zonotopic representation of invariant sets, we obtain an updated candidate for the invariant set and the invariance-enforcing controller by solving a single convex program. To obtain a possibly large region of safe operation, our algorithm is designed so that the sequence of candidate invariant sets is volume-wise monotonically increasing. We demonstrate the efficacy and scalability of our approach using a broad range of nonlinear control systems from the literature with up to 20 dimensions.