Learning event-triggered controllers for linear parameter-varying systems from data

TL;DR

This paper develops data-driven event-triggered control strategies for LPV systems, providing stability verification, robust control solutions, and extensions to trajectory tracking, validated through numerical simulations.

Contribution

It introduces a novel data-driven approach for event-triggered LPV control with stability guarantees and robust tracking, using feasible data representations and semidefinite programming.

Findings

Stability certificates for data-driven LPV control are derived.

Robust control solutions are obtained via semidefinite programming.

The methods are validated through numerical simulations.

Abstract

Nonlinear dynamical behaviours in engineering applications can be approximated by linear-parameter varying (LPV) representations, but obtaining precise model knowledge to develop a control algorithm is difficult in practice. In this paper, we develop the data-driven control strategies for event-triggered LPV systems with stability verifications. First, we provide the theoretical analysis of ${\theta}$-persistence of excitation for LPV systems, which leads to the feasible data-based representations. Then, in terms of the available perturbed data, we derive the stability certificates for event-triggered LPV systems with the aid of Petersen's lemma in the sense of robust control, resulting in the computationally tractable semidefinite programmings, the feasible solutions of which yields the optimal gain schedulings. Besides, we generalize the data-driven eventtriggered LPV control methods to the scenario of reference trajectory tracking, and discuss the robust tracking stability accordingly. Finally, we verify the effectiveness of our theoretical derivations by numerical simulations.