Computation of robust positively invariant set based on direct data-driven approach

A direct data-driven approach for computing the robust positively invariant sets of a discrete-time system is presented in this study. By transforming the invariance conditions into a set of tractable linear matrix inequality problems and combining them with a semidefinite programming problem, we maximize the volume of invariant sets without violating state constraints. Based on two equivalence conditions of invariance, we investigate two algorithms using the one-step method to maximize the volume of the invariant sets. Ultimately, we opted for Algorithm 1, which is more succinct and effective. To further reduce conservatism, we propose an iterative algorithm based on Algorithm 1. The effectiveness of the proposed algorithm is verified through numerical examples.