Data-Driven Computation of Robust Invariant Sets and Gain-Scheduled Controllers for Linear Parameter-Varying Systems

We present a direct data-driven approach to synthesize robust control invariant (RCI) sets and their associated gain-scheduled feedback control laws for linear parameter-varying (LPV) systems subjected to bounded disturbances. The proposed method utilizes a single state-input-scheduling trajectory to compute polytopic RCI sets, without requiring a model of the system. The problem is formulated in terms of a set of sufficient data-based LMI conditions that are then combined in a semi-definite program to maximize the volume of the RCI set, while respecting the state and input constraints. We demonstrate through a numerical example that the proposed approach can generate RCI sets with a relatively small number of data samples when the data satisfies certain excitation conditions.Comment: 7 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:2303.1815