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Data-Enabled Predictive Iterative Control

Kai Zhang, Riccardo Zuliani, Efe C. Balta, John Lygeros

TL;DR

This work addresses data-driven control for iterative LTI systems without a parametric model, while enforcing convex input/output constraints and convergence to the infinite-horizon optimum. The approach combines a nominal DeePRC controller with a tube-based safe exploration and a left-kernel disturbance design to safely extend the prediction horizon, plus an end-to-end formulation that integrates disturbance design into planning. Key contributions include a data-driven io convex safe set, recursive feasibility and convergence guarantees, a rank-augmenting exploration strategy, and a tractable end-to-end MIQP formulation; together, these yield sample-efficient, safe iterative control with improved long-horizon performance. The results demonstrate how exploration enriches history to enlarge horizon and speed up convergence, with practical implications for autonomous systems and robotics where repeated tasks are common.

Abstract

This work introduces the Data-Enabled Predictive iteRative Control (DeePRC) algorithm, a direct data-driven approach for iterative LTI systems. The DeePRC learns from previous iterations to improve its performance and achieves the optimal cost. By utilizing a tube-based variation of the DeePRC scheme, we propose a two-stage approach that enables safe active exploration using a left-kernel-based input disturbance design. This method generates informative trajectories to enrich the historical data, which extends the maximum achievable prediction horizon and leads to faster iteration convergence. In addition, we present an end-to-end formulation of the two-stage approach, integrating the disturbance design procedure into the planning phase. We showcase the effectiveness of the proposed algorithms on a numerical experiment.

Data-Enabled Predictive Iterative Control

TL;DR

This work addresses data-driven control for iterative LTI systems without a parametric model, while enforcing convex input/output constraints and convergence to the infinite-horizon optimum. The approach combines a nominal DeePRC controller with a tube-based safe exploration and a left-kernel disturbance design to safely extend the prediction horizon, plus an end-to-end formulation that integrates disturbance design into planning. Key contributions include a data-driven io convex safe set, recursive feasibility and convergence guarantees, a rank-augmenting exploration strategy, and a tractable end-to-end MIQP formulation; together, these yield sample-efficient, safe iterative control with improved long-horizon performance. The results demonstrate how exploration enriches history to enlarge horizon and speed up convergence, with practical implications for autonomous systems and robotics where repeated tasks are common.

Abstract

This work introduces the Data-Enabled Predictive iteRative Control (DeePRC) algorithm, a direct data-driven approach for iterative LTI systems. The DeePRC learns from previous iterations to improve its performance and achieves the optimal cost. By utilizing a tube-based variation of the DeePRC scheme, we propose a two-stage approach that enables safe active exploration using a left-kernel-based input disturbance design. This method generates informative trajectories to enrich the historical data, which extends the maximum achievable prediction horizon and leads to faster iteration convergence. In addition, we present an end-to-end formulation of the two-stage approach, integrating the disturbance design procedure into the planning phase. We showcase the effectiveness of the proposed algorithms on a numerical experiment.
Paper Structure (18 sections, 7 theorems, 28 equations, 1 figure, 1 table, 1 algorithm)

This paper contains 18 sections, 7 theorems, 28 equations, 1 figure, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Setting
  4. Review of DeePC
  5. Nominal DeePRC
  6. Input/Output Convex Safe Set
  7. The Nominal DeePRC Algorithm
  8. Hankel Matrix Update
  9. Safe and Active Exploration
  10. Safe Exploration: Tube DeePRC
  11. Active Exploration: LKB Input Disturbance Design
  12. An End-to-End Formulation
  13. Properties and Guarantees
  14. Closed-Loop Properties
  15. Recursive Feasibility of the End-to-End Formulation
  16. ...and 3 more sections

Key Result

Lemma 1

Consider a length $T$ input/output trajectory $\{u^{\rm d}, y^{\rm d}\}$ of system eq:ABCD. The image of $\mathscr{H}_{L}(u^{\rm d},y^{\rm d}):= {\rm col}(\mathscr{H}_{L}(u^{\rm d}), \mathscr{H}_{L}(y^{\rm d}))$ is the span of all length $L$ trajectories of the system if and only if

Figures (1)

  • Figure 1: Evolution of the rank of the Hankel matrix.

Theorems & Definitions (11)

  • Lemma 1: markovsky_identifiability_2023
  • Theorem 2
  • proof
  • Proposition 3
  • proof
  • Corollary 4
  • Proposition 5
  • proof
  • Proposition 6
  • Theorem 7
  • ...and 1 more