Distributionally Robust Strategy Synthesis for Switched Stochastic Systems

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Abstract

We present a novel framework for formal control of uncertain discrete-time switched stochastic systems against probabilistic reach-avoid specifications. In particular, we consider stochastic systems with additive noise, whose distribution lies in an ambiguity set of distributions that are ε−close to a nominal one according to the Wasserstein distance. For this class of systems we derive control synthesis algorithms that are robust against all these distributions and maximize the probability of satisfying a reach-avoid specification, defined as the probability of reaching a goal region while being safe. The framework we present first learns an abstraction of a switched stochastic system as a robust Markov decision process (robust MDP) by accounting for both the stochasticity of the system and the uncertainty in the noise distribution. Then, it synthesizes a strategy on the resulting robust MDP that maximizes the probability of satisfying the property and is robust to all uncertainty in the system. This strategy is then refined into a switching strategy for the original stochastic system. By exploiting tools from optimal transport and stochastic programming, we show that synthesizing such a strategy reduces to solving a set of linear programs, thus guaranteeing efficiency. We experimentally validate the efficacy of our framework on various case studies, including both linear and non-linear switched stochastic systems. Our results represent the first formal approach for control synthesis of stochastic systems with uncertain noise distribution.

Original languageEnglish
Title of host publicationProceedings of the 26th ACM International Conference on Hybrid Systems, HSCC 2023
Subtitle of host publicationComputation and Control, Part of CPS-IoT Week
PublisherAssociation for Computing Machinery (ACM)
Number of pages10
ISBN (Electronic)979-8-4007-0033-0
DOIs
Publication statusPublished - 2023
Event26th ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2023, Part of CPS-IoT Week 2023 - San Antonio, United States
Duration: 10 May 202312 May 2023

Conference

Conference26th ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2023, Part of CPS-IoT Week 2023
Country/TerritoryUnited States
CitySan Antonio
Period10/05/2312/05/23

Keywords

  • Formal synthesis
  • Safe autonomy
  • Switched stochastic systems
  • Uncertain Markov decision processes
  • Wasserstein distance

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