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

TL;DR

This paper introduces a data-driven method to compute robust invariant sets and gain-scheduled controllers for LPV systems directly from a single trajectory, bypassing the need for system identification.

Contribution

It presents a novel approach that uses a single data trajectory to synthesize RCI sets and controllers without intermediate model identification.

Findings

Effective with limited data samples under excitation conditions

Generates small RCI sets for LPV systems

Avoids traditional model identification steps

Abstract

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. A data-set consisting of a single state-input-scheduling trajectory is gathered from the system, which is directly utilized to compute polytopic RCI set and controllers by solving a semidefinite program. The proposed method does not require an intermediate LPV model identification step. Through a numerical example, we show that the proposed approach can generate RCI sets with a relatively small number of data samples when the data satisfies certain excitation conditions.