Linear Hybrid System Falsification Through Local Search ⋆ Houssam Abbas and Georgios Fainekos Arizona State University, Tempe, AZ, USA, {hyabbas,fainekos}@asu.edu Abstract. In this paper, we address the problem of local search for the falsification of hybrid automata with affine dynamics. Namely, given a sequence of locations and a maximum simulation time, we return the trajectory that comes closest to the unsafe set. This problem is formu- lated as a differentiable optimization problem and solved. The purpose of developing such a local search method is to combine it with high level stochastic optimization algorithms in order to falsify hybrid systems with complex discrete dynamics and high dimensional continuous spaces. Ex- perimental results indicate that the local search procedure improves upon the results of pure stochastic optimization algorithms. Keywords: Model Validation and Analysis; Robustness; Simulation; Hybrid systems 1 Introduction Despite the recent advances in the computation of reachable sets in medium to large-sized linear systems (about 500 continuous variables) [1], the verification of hybrid systems through the computation of the reachable state space remains a challenging problem [2]. To overcome this difficult problem, many researchers have looked into testing methodologies as an alternative. Testing methodolo- gies can be coarsely divided into two categories: robust testing (e.g. [3, 4] and systematic/randomized testing [5, 6]. Along the lines of randomized testing, we investigated the application of Monte Carlo techniques [7] to the temporal logic falsification problem of hybrid systems. In detail, utilizing the robustness of temporal logic specifications [8] as a cost function, we managed to convert a decision problem, i.e., does there exist a trajectory that falsifies the system, into an optimization problem, i.e., what is the trajectory with the minimum robustness value? The resulting optimiza- tion problem is highly nonlinear and, in general, without any obvious structure. Therefore, we treated the model of the hybrid system as a black box, and the cost function was minimized using Simulated Annealing (SA). ⋆ This work was partially supported by a grant from the NSF Industry/University Cooperative Research Center (I/UCRC) on Embedded Systems at Arizona State University and NSF award CNS-1017074.