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Approximate Robust Control of Uncertain Dynamical Systems

Edouard Leurent, Yann Blanco, Denis Efimov, Odalric-Ambrym Maillard

TL;DR

This work tackles robust control for large-scale nonlinear systems under uncertain dynamics by introducing two tractable approaches. The first uses sampling-based optimistic planning in finite ambiguity and action spaces to approximate the robust objective with regret guarantees. The second uses interval predictors to form a conservative, lower-bounded surrogate objective for continuous ambiguity, enabling interval-based policy evaluation and search. Together, these methods enable safe, scalable planning in applications such as autonomous driving, where systems must perform reliably across a range of possible behaviors and dynamics.

Abstract

This work studies the design of safe control policies for large-scale non-linear systems operating in uncertain environments. In such a case, the robust control framework is a principled approach to safety that aims to maximize the worst-case performance of a system. However, the resulting optimization problem is generally intractable for non-linear systems with continuous states. To overcome this issue, we introduce two tractable methods that are based either on sampling or on a conservative approximation of the robust objective. The proposed approaches are applied to the problem of autonomous driving.

Approximate Robust Control of Uncertain Dynamical Systems

TL;DR

This work tackles robust control for large-scale nonlinear systems under uncertain dynamics by introducing two tractable approaches. The first uses sampling-based optimistic planning in finite ambiguity and action spaces to approximate the robust objective with regret guarantees. The second uses interval predictors to form a conservative, lower-bounded surrogate objective for continuous ambiguity, enabling interval-based policy evaluation and search. Together, these methods enable safe, scalable planning in applications such as autonomous driving, where systems must perform reliably across a range of possible behaviors and dynamics.

Abstract

This work studies the design of safe control policies for large-scale non-linear systems operating in uncertain environments. In such a case, the robust control framework is a principled approach to safety that aims to maximize the worst-case performance of a system. However, the resulting optimization problem is generally intractable for non-linear systems with continuous states. To overcome this issue, we introduce two tractable methods that are based either on sampling or on a conservative approximation of the robust objective. The proposed approaches are applied to the problem of autonomous driving.

Paper Structure

This paper contains 24 sections, 2 theorems, 35 equations, 2 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Sampling-based planning
  3. Definition
  4. Interval predictors
  5. Definition
  6. Definition
  7. Definition
  8. Experiments
  9. Conclusion
  10. Detailed proofs
  11. Lemma \ref{['lemma:uvb']}
  12. Theorem \ref{['theorem:drop-regret']}
  13. Property \ref{['prop:lower-bound']}
  14. Environment dynamics
  15. Kinematics
  16. ...and 9 more sections

Key Result

Lemma 1

The robust values, u-values and b-values exhibit similar properties as the optimal values, u-values and b-values, that is: for all $0 < t < n$ and $i\in\mathcal{T}_n$,

Figures (2)

  • Figure 3: From left to right: two simple models and corresponding u-values with optimal sequences in blue; the naive version of the robust values returns sub-optimal paths in red; our robust u-value properly recovers the robust policy in green.
  • Figure 4: The https://github.com/eleurent/highway-env environment. The ego-vehicle (green) is approaching a roundabout with flowing traffic (yellow).

Theorems & Definitions (9)

  • Remark 1: On the ordering of min and max
  • Lemma 1: Robust values ordering
  • proof
  • Theorem 1: Regret bound
  • proof
  • proof
  • proof
  • proof
  • proof