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Distributionally Robust System Level Synthesis With Output Feedback Affine Control Policy

Yun Li, Jicheng Shi, Colin N. Jones, Neil Yorke-Smith, Tamas Keviczky

TL;DR

A novel SLS design using an output-feedback affine control policy is proposed and extended to a distributionally robust setting to improve system resilience by minimizing the cost function while ensuring constraint satisfaction against the worst-case uncertainty distribution.

Abstract

This paper studies the finite-horizon robust optimal control of constrained linear systems subject to model mismatch and additive stochastic disturbances. Utilizing the system level synthesis (SLS) parameterization, we propose a novel SLS design using an output-feedback affine control policy and extend it to a distributionally robust setting to improve system resilience by minimizing the cost function while ensuring constraint satisfaction against the worst-case uncertainty distribution. The scopes of model mismatch and stochastic disturbances are quantified using the 1-norm and a Wasserstein metric-based ambiguity set, respectively. For the closed-loop dynamics, we analyze the distributional shift between the predicted output-input response -- computed using nominal parameters and empirical disturbance samples -- and the actual closed-loop distribution, highlighting its dependence on model mismatch and SLS parameterization. Assuming convex and Lipschitz continuous cost functions and constraints, we derive a tractable reformulation of the distributionally robust SLS (DR-SLS) problem by leveraging tools from robust control and distributionally robust optimization (DRO). Numerical experiments validate the performance and robustness of the proposed approach.

Distributionally Robust System Level Synthesis With Output Feedback Affine Control Policy

TL;DR

A novel SLS design using an output-feedback affine control policy is proposed and extended to a distributionally robust setting to improve system resilience by minimizing the cost function while ensuring constraint satisfaction against the worst-case uncertainty distribution.

Abstract

This paper studies the finite-horizon robust optimal control of constrained linear systems subject to model mismatch and additive stochastic disturbances. Utilizing the system level synthesis (SLS) parameterization, we propose a novel SLS design using an output-feedback affine control policy and extend it to a distributionally robust setting to improve system resilience by minimizing the cost function while ensuring constraint satisfaction against the worst-case uncertainty distribution. The scopes of model mismatch and stochastic disturbances are quantified using the 1-norm and a Wasserstein metric-based ambiguity set, respectively. For the closed-loop dynamics, we analyze the distributional shift between the predicted output-input response -- computed using nominal parameters and empirical disturbance samples -- and the actual closed-loop distribution, highlighting its dependence on model mismatch and SLS parameterization. Assuming convex and Lipschitz continuous cost functions and constraints, we derive a tractable reformulation of the distributionally robust SLS (DR-SLS) problem by leveraging tools from robust control and distributionally robust optimization (DRO). Numerical experiments validate the performance and robustness of the proposed approach.

Paper Structure

This paper contains 11 sections, 53 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. System Level Synthesis With Output Feedback Affine Control Policy
  4. System Level Synthesis With Exact Model
  5. SLS Parameterization with Model Mismatch
  6. Distributionally Robust SLS Design and Tractable Reformulation
  7. Distributionally Robust SLS Formulation
  8. Characterization of Distribution Shift
  9. Tractable Reformulation
  10. Simulation Results
  11. Conclusion

Figures (3)

  • Figure 1: Output and input trajectories with N-SLS approach: (a) open-loop output prediction, (b) open-loop input prediction, (c) closed-loop output, (d) closed-loop input.
  • Figure 2: Output and input trajectories with DR-SLS approach: (a) open-loop output prediction, (b) open-loop input prediction, (c) closed-loop output, (d) closed-loop input.
  • Figure 3: Cost values and ratios of constraint violation of N-SLS and DR-SLS: (a) open-loop cost values, (b) closed-loop cost values, (c) ratios of constraint violation.