A dynamic game approach to distributionally robust safety specifications for stochastic systems

A dynamic game approach to distributionally robust safety specifications for stochastic systems This paper presents a new safety specification method that is robust against errors in the probability distribution of disturbances. Our proposed distributionally robust safe policy maximizes the probability of a system remaining in a desired set for all times, subject to the worst possible disturbance distribution in an ambiguity set. We propose a dynamic game formulation of constructing such policies and identify conditions under which a non-randomized Markov policy is optimal. Based on this existence result, we develop a practical design approach to safety-oriented stochastic controllers with limited information about disturbance distributions. However, an associated Bellman equation involves infinite-dimensional minimax optimization problems since the disturbance distribution may have a continuous density. To alleviate computational issues, we propose a duality-based reformulation method that converts the infinite-dimensional minimax problem into a semi-infinite program that can be solved using existing convergent algorithms. We prove that there is no duality gap, and that this approach thus preserves optimality. The results of numerical tests confirm that the proposed method is robust against distributional errors in disturbances, while a standard stochastic safety verification tool is not. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Automatica Elsevier

A dynamic game approach to distributionally robust safety specifications for stochastic systems

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Publisher
Elsevier
Copyright
Copyright © 2018 Elsevier Ltd
ISSN
0005-1098
D.O.I.
10.1016/j.automatica.2018.04.022
Publisher site
See Article on Publisher Site

Abstract

This paper presents a new safety specification method that is robust against errors in the probability distribution of disturbances. Our proposed distributionally robust safe policy maximizes the probability of a system remaining in a desired set for all times, subject to the worst possible disturbance distribution in an ambiguity set. We propose a dynamic game formulation of constructing such policies and identify conditions under which a non-randomized Markov policy is optimal. Based on this existence result, we develop a practical design approach to safety-oriented stochastic controllers with limited information about disturbance distributions. However, an associated Bellman equation involves infinite-dimensional minimax optimization problems since the disturbance distribution may have a continuous density. To alleviate computational issues, we propose a duality-based reformulation method that converts the infinite-dimensional minimax problem into a semi-infinite program that can be solved using existing convergent algorithms. We prove that there is no duality gap, and that this approach thus preserves optimality. The results of numerical tests confirm that the proposed method is robust against distributional errors in disturbances, while a standard stochastic safety verification tool is not.

Journal

AutomaticaElsevier

Published: Aug 1, 2018

References

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