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Data-Driven Predictive Control with Adaptive Disturbance Attenuation for Constrained Systems

Nan Li, Ilya Kolmanovsky, Hong Chen

TL;DR

The paper addresses data-driven design of constrained $\\mathcal{H}_{\\infty}$-type control for unknown linear time-invariant systems. It combines data-driven synthesis with moving-horizon MPC to enforce time-domain constraints while adaptively attenuating disturbances from $w$ to $y_1$ using forecasted energy bounds. The main contributions are an LMI-based synthesis yielding $K = YQ^{-1}$ under Assumption 1, recursive feasibility and stability guarantees for online moving-horizon operation (Theorem 2), and a numerical example demonstrating constraint satisfaction and improved disturbance rejection relative to fixed-gain designs. This framework enables robust performance under noisy data and transient disturbances with practical computational feasibility.

Abstract

In this paper, we propose a novel data-driven predictive control approach for systems subject to time-domain constraints. The approach combines the strengths of H-infinity control for rejecting disturbances and MPC for handling constraints. In particular, the approach can dynamically adapt H-infinity disturbance attenuation performance depending on measured system state and forecasted disturbance level to satisfy constraints. We establish theoretical properties of the approach including robust guarantees of closed-loop stability, disturbance attenuation, constraint satisfaction under noisy data, as well as sufficient conditions for recursive feasibility, and illustrate the approach with a numerical example.

Data-Driven Predictive Control with Adaptive Disturbance Attenuation for Constrained Systems

TL;DR

The paper addresses data-driven design of constrained -type control for unknown linear time-invariant systems. It combines data-driven synthesis with moving-horizon MPC to enforce time-domain constraints while adaptively attenuating disturbances from to using forecasted energy bounds. The main contributions are an LMI-based synthesis yielding under Assumption 1, recursive feasibility and stability guarantees for online moving-horizon operation (Theorem 2), and a numerical example demonstrating constraint satisfaction and improved disturbance rejection relative to fixed-gain designs. This framework enables robust performance under noisy data and transient disturbances with practical computational feasibility.

Abstract

In this paper, we propose a novel data-driven predictive control approach for systems subject to time-domain constraints. The approach combines the strengths of H-infinity control for rejecting disturbances and MPC for handling constraints. In particular, the approach can dynamically adapt H-infinity disturbance attenuation performance depending on measured system state and forecasted disturbance level to satisfy constraints. We establish theoretical properties of the approach including robust guarantees of closed-loop stability, disturbance attenuation, constraint satisfaction under noisy data, as well as sufficient conditions for recursive feasibility, and illustrate the approach with a numerical example.
Paper Structure (6 sections, 42 equations, 2 figures, 2 tables)

This paper contains 6 sections, 42 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Problem Statement and Preliminaries
  3. Constrained $\mathcal{H}_{\infty}$ Control
  4. Moving-Horizon Control
  5. Numerical Example
  6. Conclusions

Figures (2)

  • Figure 1: Control input time history.
  • Figure 2: Disturbance attenuation level time history.