In this paper we propose a testing based method for safety/reachability analysis of stochastic hybrid systems. Testing based methods are characterized by analysis based on the execution traces of the system or the simulation thereof. Testing based method is very appealing because of the simplicity of its execution, the possibility of having a partial verification, and its highly parallel structure. The key idea in this paper is the construction of a robust neighborhood consisting of states that have the same probabilistic safety/reachability properties. We construct the robust neighborhood using the level sets of a stochastic bisimulation function. We also show how to construct stochastic bisimulation functions for systems whose continuous dynamics is stable and linear. As a case example, we consider the problem of conflict detection of aircraft flight, and show that we can infer some robust probabilistic safety property by using the algorithm that we present in this paper.

We present an algorithm for falsifying safety properties of hybrid systems, i.e., for finding a trajectory to an unsafe state. The approach is to approximate how close a point is to being an initial point of an error trajectory using a real-valued quality function, and then to use numerical optimisation to search for an optimum of this function. The function is computed by running simulations, where information coming from abstractions computed by a verification algorithm is exploited to determine whether a simulation looks promising and should be continued or cancelled. This information becomes more reliable as the abstraction becomes more refined. We thus interleave falsification and verification attempts.

1.10 Termination criterion using disparity...................... 38

Abstract. This paper develops a novel computational method for the falsification of safety properties specified by syntactically safe linear temporal logic (LTL) formulas φ for hybrid systems with general nonlinear dynamics and input controls. The method is based on an effective combination of robot motion planning and model checking. Experiments on a hybrid robotic system benchmark with nonlinear dynamics show significant speedup over related work. The experiments also indicate significant speedup when using minimized DFA instead of non-minimized NFA, as obtained by standard tools, for representing the violating prefixes of φ. 1

Abstract — In this paper, we describe a simulation-based approach to the verification of high dimensional nonlinear systems subject to disturbances and uncertainty in the initial conditions. Standard simulation can only sample finitely many initial states and disturbance signals and cannot verify correctness in an exhaustive manner. The alternative approach of computing all the reachable states of the system using set-based simulation, can provide, in principle, correctness proofs but is computationally expensive especially for high dimensional and nonlinear systems. In this paper we propose an approach that provides a good compromise between set-based computation and simulation by combining guided random exploration of the state space together with sensitivity analysis. The exploration technique is used to choose input signals that guarantee good coverage of the reachable set, while sensitivity information is used to create neighborhoods around explored behaviors that cover the trajectories generated by neighboring input signals. I.

This paper deals with the robust Metric Temporal Logic (MTL) testing and verification of linear systems with parametric uncertainties. This is a very general class of systems that includes not only Linear Time Invariant (LTI) systems with unknown constant parameters, but also Linear Time Varying (LTV) systems and certain classes of nonlinear systems through abstraction. The two main tools for the solution of this problem are the approximate bisimulation relations and a notion of robustness for temporal logic formulas.

1.2 Modeling with timed and hybrid automata................... 3

Copyright c ○ July 2009 by the author(s)