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Sample- and computationally efficient data-driven predictive control

Mohammad Alsalti, Manuel Barkey, Victor G. Lopez, Matthias A. Müller

TL;DR

This paper proposes an efficient data-driven predictive control (eDDPC) scheme which is both more sample efficient (requires less offline data) and computationally efficient (uses less decision variables) compared to existing schemes.

Abstract

Recently proposed data-driven predictive control schemes for LTI systems use non-parametric representations based on the image of a Hankel matrix of previously collected, persistently exciting, input-output data. Persistence of excitation necessitates that the data is sufficiently long and, hence, the computational complexity of the corresponding finite-horizon optimal control problem increases. In this paper, we propose an efficient data-driven predictive control (eDDPC) scheme which is both more sample efficient (requires less offline data) and computationally efficient (uses less decision variables) compared to existing schemes. This is done by leveraging an alternative data-based representation of the trajectories of LTI systems. We analytically and numerically compare the performance of this scheme to existing ones from the literature.

Sample- and computationally efficient data-driven predictive control

TL;DR

This paper proposes an efficient data-driven predictive control (eDDPC) scheme which is both more sample efficient (requires less offline data) and computationally efficient (uses less decision variables) compared to existing schemes.

Abstract

Recently proposed data-driven predictive control schemes for LTI systems use non-parametric representations based on the image of a Hankel matrix of previously collected, persistently exciting, input-output data. Persistence of excitation necessitates that the data is sufficiently long and, hence, the computational complexity of the corresponding finite-horizon optimal control problem increases. In this paper, we propose an efficient data-driven predictive control (eDDPC) scheme which is both more sample efficient (requires less offline data) and computationally efficient (uses less decision variables) compared to existing schemes. This is done by leveraging an alternative data-based representation of the trajectories of LTI systems. We analytically and numerically compare the performance of this scheme to existing ones from the literature.
Paper Structure (7 sections, 4 theorems, 11 equations, 2 tables, 2 algorithms)

This paper contains 7 sections, 4 theorems, 11 equations, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Efficient DDPC
  4. Overview of existing schemes
  5. Nominal eDDPC scheme
  6. Comparison to existing schemes
  7. Conclusions

Key Result

Lemma 1

Willems05 Let $w\in\mathscr{B}|_T$ with $\mathscr{B}\in\mathscr{L}_{m,n,\ell}^{q}$ controllable. Let $u\in(\mathbb{R}^m)^T$ be PE of order $L+n$, then $\textup{rank}(\mathscr{H}_L(w)) = mL+n$, and $\bar{w}\in\mathscr{B}|_L$ if and only if there exists $\alpha\in\mathbb{R}^{T-L+1}$ such that

Theorems & Definitions (10)

  • Definition 1
  • Lemma 1
  • Corollary 1
  • Theorem 1
  • proof
  • Definition 2
  • Lemma 2
  • proof
  • Remark 1
  • Remark 2