Data-Driven Min-Max MPC for LPV Systems with Unknown Scheduling Signal

TL;DR

This paper introduces a novel data-driven min-max MPC approach for LPV systems with unknown scheduling signals, ensuring stability and constraint satisfaction using only input-state data and QMI descriptions.

Contribution

It develops a new data-driven characterization of system matrices for LPV systems with unknown scheduling signals, enabling robust control without offline scheduling data.

Findings

Guarantees recursive feasibility and stability.

Ensures constraint satisfaction in closed-loop operation.

Effective in simulation for systems with unknown scheduling signals.

Abstract

This paper presents a data-driven min-max model predictive control (MPC) scheme for linear parameter-varying (LPV) systems. Contrary to existing data-driven LPV control approaches, we assume that the scheduling signal is unknown during offline data collection and online system operation. Assuming a quadratic matrix inequality (QMI) description for the scheduling signal, we develop a novel data-driven characterization of the consistent system matrices using only input-state data. The proposed data-driven min-max MPC minimizes a tractable upper bound on the worst-case cost over the consistent system matrices set and over all scheduling signals satisfying the QMI. The proposed approach guarantees recursive feasibility, closed-loop exponential stability and constraint satisfaction if it is feasible at the initial time. We demonstrate the effectiveness of the proposed method in simulation.