Computing Robust Control Invariant Sets of Nonlinear Systems Using Polynomial Controller Synthesis

Deploying nonlinear sampled-data systems in safety-critical applications requires us to ensure robust con-straint satisfaction for an infinite time horizon. To maximize the region of safe operation, we aim to compute a robust control invariant set with maximum volume. In this work, we propose an iterative optimization-based algorithm that com-putes a sequence of candidate invariant sets, which is volume-wise monotonically increasing. By leveraging polynomialization-based techniques from reach ability analysis and controller synthesis, our approach outperforms linearization-based approaches, especially for higher-dimensional systems. We show that the computational complexity of each iteration of our algorithm is polynomial in the state dimension and demonstrate its broad applicability using several examples from the literature with up to 10 dimensions.