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Online Reduced-Order Data-Enabled Predictive Control

Amin Vahidi-Moghaddam, Kaixiang Zhang, Xunyuan Yin, Vaibhav Srivastava, Zhaojian Li

TL;DR

An online DeePC framework designed for strongly nonlinear and/or time-varying systems is proposed, enabling the algorithm to update the Hankel matrix online by adding real-time informative signals, by exploiting the minimum non-zero singular value of the Hankel matrix.

Abstract

Data-enabled predictive control (DeePC) has garnered significant attention for its ability to achieve safe, data-driven optimal control without relying on explicit system models. Traditional DeePC methods use pre-collected input/output (I/O) data to construct Hankel matrices for online predictive control. However, in systems with evolving dynamics or insufficient pre-collected data, incorporating real-time data into the DeePC framework becomes crucial to enhance control performance. This paper proposes an online DeePC framework for time-varying systems (i.e., systems with evolving dynamics), enabling the algorithm to update the Hankel matrix online by adding real-time informative signals. By exploiting the minimum non-zero singular value of the Hankel matrix, the developed online DeePC selectively integrates informative data and effectively captures evolving system dynamics. Additionally, a numerical singular value decomposition technique is introduced to reduce the computational complexity for updating a reduced-order Hankel matrix. Simulation results on two cases, a linear time-varying system and the vehicle anti-rollover control, demonstrate the effectiveness of the proposed online reduced-order DeePC framework.

Online Reduced-Order Data-Enabled Predictive Control

TL;DR

An online DeePC framework designed for strongly nonlinear and/or time-varying systems is proposed, enabling the algorithm to update the Hankel matrix online by adding real-time informative signals, by exploiting the minimum non-zero singular value of the Hankel matrix.

Abstract

Data-enabled predictive control (DeePC) has garnered significant attention for its ability to achieve safe, data-driven optimal control without relying on explicit system models. Traditional DeePC methods use pre-collected input/output (I/O) data to construct Hankel matrices for online predictive control. However, in systems with evolving dynamics or insufficient pre-collected data, incorporating real-time data into the DeePC framework becomes crucial to enhance control performance. This paper proposes an online DeePC framework for time-varying systems (i.e., systems with evolving dynamics), enabling the algorithm to update the Hankel matrix online by adding real-time informative signals. By exploiting the minimum non-zero singular value of the Hankel matrix, the developed online DeePC selectively integrates informative data and effectively captures evolving system dynamics. Additionally, a numerical singular value decomposition technique is introduced to reduce the computational complexity for updating a reduced-order Hankel matrix. Simulation results on two cases, a linear time-varying system and the vehicle anti-rollover control, demonstrate the effectiveness of the proposed online reduced-order DeePC framework.
Paper Structure (9 sections, 2 theorems, 29 equations, 9 figures, 2 tables)

This paper contains 9 sections, 2 theorems, 29 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Statement
  3. Main Result
  4. Online Data-Enabled Predictive Control
  5. Online Reduced-Order Data-Enabled Predictive Control
  6. Simulation Results
  7. Linear Time-Varying System
  8. Vehicle Rollover Avoidance
  9. Conclusion

Key Result

Lemma 1

Consider the system system as a controllable LTI system with a pre-collected input/output (I/O) sequence $(u_{1:T}^{\mathrm{d}}, y_{1:T}^{\mathrm{d}})$ of length $T$. Providing a PE input sequence $u^{\mathrm{d}}_{1:T}$ of order $K+n$, any length-$K$ sequence $(u_{1:K}, y_{1:K})$ is an I/O trajector for some real vector $g \in \mathbb{R}^L$.

Figures (9)

  • Figure 1: Order of reduced-order mosaic-Hankel matrix for LTV system.
  • Figure 2: Comparison of control inputs for the LTV system.
  • Figure 3: Comparison of system outputs of the LTV system.
  • Figure 4: Order of reduced-order mosaic-Hankel matrix for vehicle rollover avoidance.
  • Figure 5: Control inputs for vehicle rollover avoidance.
  • ...and 4 more figures

Theorems & Definitions (8)

  • Definition 1: Hankel Matrix
  • Definition 2: Persistently Exciting
  • Lemma 1: Fundamental Lemma willems2005note
  • Remark 1: Rank of Hankel Matrix
  • Definition 3: Mosaic-Hankel Matrix
  • Lemma 2: Discontinuous Fundamental Lemma markovsky2022identifiability
  • Remark 2: Rank-1 Modifications
  • Remark 3: Comparison