Global Almost-Sure Reachability in Stochastic Constant-Rate Multi-Mode Systems

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 modedependent constant rates. We introduce and study a stochastic extension of a constant-rate multimode 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. *

Capturing Dynamicity and Uncertainty in Security and Trust via Situational Patterns

“…It allows the developer to describe the likelihood of evaluating the condition of strategy selection to true. Using formal approach, [38] presents stochastic multi-mode systems (SMMS) that approximate the action of a moving vehicle, so it satisfies almost-sure reachability, which is the movement within a certain safety corridor. As for uncontrollable entities, [6] introduced a proactive adaptation to capture possible dangerous situations using prediction over historical data (i.e., fire prediction).…”