A Framework for Safe Probabilistic Invariance Verification of Stochastic Dynamical Systems
CoRR(2024)
摘要
Ensuring safety through set invariance has proven to be a valuable method in
various robotics and control applications. This paper introduces a
comprehensive framework for the safe probabilistic invariance verification of
both discrete- and continuous-time stochastic dynamical systems over an
infinite time horizon. The objective is to ascertain the lower and upper bounds
of the liveness probability for a given safe set and set of initial states.
This probability signifies the likelihood of the system remaining within the
safe set indefinitely, starting from the set of initial states. To address this
problem, we propose optimizations for verifying safe probabilistic invariance
in discrete-time and continuous-time stochastic dynamical systems. These
optimizations adapt classical stochastic barrier certificates, which are based
on Doob's non-negative supermartingale inequality, and the equations described
in [29],[31], which can precisely define the probability of reaching a target
set while avoiding unsafe states. Finally, we demonstrate the effectiveness of
these optimizations through several examples using semi-definite programming
tools.
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