Almost-Sure Reachability in Stochastic Multi-Mode System

Fabio Somenzi; Behrouz Touri; Ashutosh Trivedi

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arXiv · 1610.05412

Almost-Sure Reachability in Stochastic Multi-Mode System

Fabio Somenzi·Behrouz Touri·Ashutosh Trivedi

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Abstract

A constant-rate multi-mode system is a hybrid system that can switch freely among a finite set of modes, and whose dynamics is specified by a finite number of real-valued variables with mode-dependent constant rates. We introduce and study a stochastic extension of a constant-rate multi-mode system where the dynamics is specified by mode-dependent compactly supported probability distributions over a set of constant rate vectors. Given a tolerance $\varepsilon > 0$, the almost-sure reachability problem for stochastic multi-mode systems is to decide the existence of a control strategy that steers the system almost-surely from an arbitrary start state to an $\varepsilon$-neighborhood of an arbitrary target state while staying inside a pre-specified safety set. We prove a necessary and sufficient condition to decide almost-sure reachability and, using this condition, we show that almost-sure reachability can be decided in polynomial time. Our algorithm can be used as a path-following algorithm in combination with any off-the-shelf path-planning algorithm to make a robot or an autonomous vehicle with noisy low-level controllers follow a given path with arbitrary precision.

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BibTeX RIS

Fabio Somenzi, Behrouz Touri, Ashutosh Trivedi. 2016-10-18. Almost-Sure Reachability in Stochastic Multi-Mode System. https://arxiv.org/abs/1610.05412

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