Multilevel Monte Carlo Method for Statistical Model Checking of Hybrid Systems

Abstract

Abstract. We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo method (MLMC) and work on a sequence of discrete-time stochastic processes whose executions approximate and converge weakly to that of the original continuous-time stochastic hybrid system with respect to satisfaction of the property of interest. With focus on bounded-horizon reachability, we recast the model checking problem as the computation of the distribution of the exit time, which is in turn formulated as the expectation of an indicator function. This latter computation involves estimating discontinuous functionals, which reduces the bound on the convergence rate of the Monte Carlo algorithm. We propose a smoothing step with tunable precision and formally quantify the error of the MLMC approach in the mean-square sense, which is composed of smoothing error, bias, and variance. We formulate a general adaptive algorithm which balances these error terms. Finally, we describe an application of our technique to verify a model of thermostatically controlled loads.

ARCH-COMP18 Category Report: Stochastic Modelling

“…The closed-loop model fits into the framework of discrete-time hybrid systems, which has six continuous states, two discrete modes, and nonlinear vector fields in each mode. Although statistical techniques such as multilevel Monte Carlo method [17] can be used to verify properties of the continuous-time dynamics presented in [20], we transform the model into discrete-time polynomial dynamics and use barrier certificates [27] for the verification task.…”

“…Problem 2.5.1. Let φ be a given LTL formula and let the robot evolve according to dynamics (16), with observation dynamics (17), and using a Bayesian filter defined by (18).…”