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Stochastic MPC with Online-optimized Policies and Closed-loop Guarantees

Marcell Bartos, Alexandre Didier, Jerome Sieber, Johannes Köhler, Melanie N. Zeilinger

TL;DR

The proposed stochastic model predictive control method for linear systems affected by additive Gaussian disturbances reduces conservatism and improved performance in terms of the achieved closed-loop cost is demonstrated in a numerical example.

Abstract

This paper proposes a stochastic model predictive control method for linear systems affected by additive Gaussian disturbances. Closed-loop satisfaction of probabilistic constraints and recursive feasibility of the underlying convex optimization problem is guaranteed. Optimization over feedback policies online increases performance and reduces conservatism compared to fixed-feedback approaches. The central mechanism is a finitely determined maximal admissible set for probabilistic constraints, together with the reconditioning of the predicted probabilistic constraints on the current knowledge at every time step. The proposed method's reduced conservatism and improved performance in terms of the achieved closed-loop cost is demonstrated in a numerical example.

Stochastic MPC with Online-optimized Policies and Closed-loop Guarantees

TL;DR

The proposed stochastic model predictive control method for linear systems affected by additive Gaussian disturbances reduces conservatism and improved performance in terms of the achieved closed-loop cost is demonstrated in a numerical example.

Abstract

This paper proposes a stochastic model predictive control method for linear systems affected by additive Gaussian disturbances. Closed-loop satisfaction of probabilistic constraints and recursive feasibility of the underlying convex optimization problem is guaranteed. Optimization over feedback policies online increases performance and reduces conservatism compared to fixed-feedback approaches. The central mechanism is a finitely determined maximal admissible set for probabilistic constraints, together with the reconditioning of the predicted probabilistic constraints on the current knowledge at every time step. The proposed method's reduced conservatism and improved performance in terms of the achieved closed-loop cost is demonstrated in a numerical example.

Paper Structure

This paper contains 21 sections, 131 equations, 2 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Setup and Preliminaries
  3. Notation
  4. Problem Setup
  5. System Level Parameterization
  6. Stochastic Optimal Control
  7. Probabilistic Constraints with Optimized Feedback
  8. Probabilistic Constraints with Terminal Controller
  9. Proposed Optimization Problem
  10. General Reconditioning Framework for SMPC
  11. Receding Horizon Control
  12. Proposed SMPC Scheme
  13. Closed-loop Analysis
  14. Numerical Example
  15. Conclusion
  16. ...and 6 more sections

Figures (2)

  • Figure 1: The evolution of the second state (velocity) over time using the proposed method (red) and IF-SMPC (blue). The thin lines correspond to 500 randomly picked disturbance sequence realizations (out of the $5\cdot 10^4$), the thick lines are the means, and the dashed lines show the empirical probability of constraint satisfaction (Case \ref{['case:velocity']}).
  • Figure 2: Closed-loop trajectories in the state space using the proposed method (red) and IF-SMPC (blue). The thin lines correspond to 500 randomly picked disturbance sequence realizations (out of the $5\cdot 10^4$), the thick lines are the means (Case \ref{['case:velocity']}).

Theorems & Definitions (9)

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