Almost-Sure Reachability in Stochastic Multi-Mode System release_sct4avz47zajjdml3mbwm6jyyq

by Fabio Somenzi and Behrouz Touri and Ashutosh Trivedi

Released as a article .

2016  

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 ε > 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 ε-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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Type  article
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Date   2016-10-18
Version   v1
Language   en ?
arXiv  1610.05412v1
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