Direct Data-Driven Design of LPV Controllers and Polytopic Invariant Sets With Cross-Covariance Noise Bounds

We propose a direct data-driven method for the concurrent computation of polytopic robust control invariant (RCI) sets and the associated invariance-inducing control laws for linear parameter-varying (LPV) systems. We present a data-based covariance parameterization of the gain-scheduled controller and the closed-loop dynamics and show that by assuming bounded cross-covariance noise, the invariance condition can be formulated as a set of data-based LMIs such that the number of decision variables are independent of the length of the dataset. These LMIs are combined with polytopic state-input constraints in a convex semi-definite program to maximize the volume of the RCI set. A numerical example demonstrates the computational effectiveness of the proposed method in synthesizing RCI sets even with large datasets.