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Disturbance feedback-based model predictive control in uncertain dynamic environments

Philipp Buschermöhle, Taouba Jouini, Torsten Lilge, Matthias A. Müller

TL;DR

The paper develops a robust MPC framework that handles uncertain, time-varying state constraints by parameterizing the control law with environment-dependent feedback from predicted future environment states. By using a convex policy of the form $u_{i|k} = c_{i|k} + \sum_{l=0}^{i} K_{(i,l)|k} o_{l|k}$ and constraining feasibility over predicted environment trajectories, the approach guarantees recursive feasibility and asymptotic convergence to a region around the origin. It introduces shrinking environment predictions and a terminal region to ensure feasibility and stability, with a worst-case cost yielding convergence to the origin and nominal costs yielding convergence to a forecast-dependent neighborhood. The simulation example with a three-vehicle platoon demonstrates constraint satisfaction under non-intersecting predicted constraint sets and aligns with the theoretical guarantees, highlighting practical applicability in uncertain dynamic environments.

Abstract

This paper presents a robust MPC scheme for linear systems subject to time-varying, uncertain constraints that arise from uncertain environments. The predicted input sequence is parameterized over future environment states to guarantee constraint satisfaction despite an imprecise environment prediction and unknown evolution of the future constraints. We provide theoretical guarantees for recursive feasibility and asymptotic convergence. Finally, a brief simulation example showcases our results.

Disturbance feedback-based model predictive control in uncertain dynamic environments

TL;DR

The paper develops a robust MPC framework that handles uncertain, time-varying state constraints by parameterizing the control law with environment-dependent feedback from predicted future environment states. By using a convex policy of the form and constraining feasibility over predicted environment trajectories, the approach guarantees recursive feasibility and asymptotic convergence to a region around the origin. It introduces shrinking environment predictions and a terminal region to ensure feasibility and stability, with a worst-case cost yielding convergence to the origin and nominal costs yielding convergence to a forecast-dependent neighborhood. The simulation example with a three-vehicle platoon demonstrates constraint satisfaction under non-intersecting predicted constraint sets and aligns with the theoretical guarantees, highlighting practical applicability in uncertain dynamic environments.

Abstract

This paper presents a robust MPC scheme for linear systems subject to time-varying, uncertain constraints that arise from uncertain environments. The predicted input sequence is parameterized over future environment states to guarantee constraint satisfaction despite an imprecise environment prediction and unknown evolution of the future constraints. We provide theoretical guarantees for recursive feasibility and asymptotic convergence. Finally, a brief simulation example showcases our results.
Paper Structure (8 sections, 4 theorems, 59 equations, 2 figures)

This paper contains 8 sections, 4 theorems, 59 equations, 2 figures.

Table of Contents

  1. Notation
  2. Preliminaries and setup
  3. Problem formulation
  4. Optimal control problem
  5. Main Results
  6. Simulation example
  7. Conclusion
  8. Proof of Lemma \ref{['lem:boundedK']}

Key Result

Proposition 6

(Shrinking environment prediction) Let Assumptions assum:containedPred and assum:termSetCont hold, then

Figures (2)

  • Figure 1: An example of the uncertain evolution of constraint sets predicted at time $k$ in existing literature (e.g. Liu19) and this paper. The intersection of the predicted constraint sets is depicted in gray.
  • Figure 2: Closed-loop simulation results for two different environment trajectories (A and B). The state trajectories are given in black and the actual constraint sets in blue and red, respectively. The terminal region is depicted in green.

Theorems & Definitions (8)

  • Remark 1
  • Remark 2
  • Proposition 6
  • Remark 7
  • Proposition 8
  • Lemma 13
  • Proposition 14
  • Remark 15