Efficient strategy synthesis for switched stochastic systems with distributional uncertainty

Ibon Gracia*, Dimitris Boskos, Morteza Lahijanian, Luca Laurenti, Manuel Mazo

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We introduce a framework for the control of discrete-time switched stochastic systems with uncertain distributions. In particular, we consider stochastic dynamics with additive noise whose distribution lies in an ambiguity set of distributions that are ɛ−close, in the Wasserstein distance sense, to a nominal one. We propose algorithms for the efficient synthesis of distributionally robust control strategies that maximize the satisfaction probability of reach-avoid specifications with either a given or an arbitrary (not specified) time horizon, i.e., unbounded-time reachability. The framework consists of two main steps: finite abstraction and control synthesis. First, we construct a finite abstraction of the switched stochastic system as a robust Markov decision process (robust MDP) that encompasses both the stochasticity of the system and the uncertainty in the noise distribution. Then, we synthesize a strategy that is robust to the distributional uncertainty on the resulting robust MDP. We employ techniques from optimal transport and stochastic programming to reduce the strategy synthesis problem to a set of linear programs, and propose a tailored and efficient algorithm to solve them. The resulting strategies are correctly refined into switching strategies for the original stochastic system. We illustrate the efficacy of our framework on various case studies comprising both linear and non-linear switched stochastic systems.
Original languageEnglish
Article number101554
Number of pages22
JournalNonlinear Analysis: Hybrid Systems
Volume55
DOIs
Publication statusPublished - 2025

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

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

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