Efficient Strategy Synthesis for Switched Stochastic Systems with Distributional Uncertainty
arxiv(2022)
摘要
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 ε-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.
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