Data-Driven Model Predictive Control for Linear Time-Periodic Systems

TL;DR

This paper introduces a data-driven predictive control method for unknown linear time-periodic systems, extending existing techniques for LTI systems and demonstrating robustness to noise through simulations.

Contribution

It generalizes DeePC and SPC to LTP systems using behavioral systems theory, including a generalized fundamental lemma and an algorithm matching standard MPC performance.

Findings

Algorithm matches standard MPC results for deterministic LTP systems

Robust to noisy data in stochastic MIMO LTP systems

Validated through extensive simulations

Abstract

We consider the problem of data-driven predictive control for an unknown discrete-time linear time-periodic (LTP) system of known period. Our proposed strategy generalizes both Data-enabled Predictive Control (DeePC) and Subspace Predictive Control (SPC), which are established data-driven control techniques for linear time-invariant (LTI) systems. The approach is supported by an extensive theoretical development of behavioral systems theory for LTP systems, culminating in a generalization of the fundamental lemma. Our algorithm produces results identical to standard Model Predictive Control (MPC) for deterministic LTP systems. Robustness of the algorithm to noisy data is illustrated via simulation of a regularized version of the algorithm applied to a stochastic multi-input multi-output LTP system.