Cyber-physical systems (CPSs) integrate discrete computations with continuous physical processes and can be highly nonlinear and nondeterministic. Unlike the verification of CPS, which is difficult to handle, the falsification of CPS fulfills certain requirements from testing by seeking witness behavior of these systems and is easier to conduct. However, existing falsification techniques may fail to support the general complex CPS in practice because they usually focus on certain restricted classes of systems. In this article, we present a path-oriented, derivative-free approach to falsify safety properties in nonlinear and nondeterministic CPS. In our approach, we model the behavior of CPS by hybrid automata. Then, we enumerate candidate paths of hybrid automata (HA), transform the feasibility of candidate paths into optimization problems, and solve these optimization problems by our newly proposed classification model-based, derivative-free optimization algorithm. We also provide two novel pruning techniques to further improve the efficiency and efficacy of our approach: 1) a nested optimization structure with better model refinements for continuous search space pruning and 2) a hardly feasible path prefixes guided backtracking for discrete search space pruning. We implement our approach into a tool called PDF. Our experiments showed that PDF supported the safety falsification of CPS in all of our benchmarks, and it achieved success rates no lower than 95% in only seconds on 22/28 of the benchmarks.

Hybrid systems are widely used in safety-critical areas. Hybrid optimal control synthesis, which aims to generate an optimal sequence of control inputs for a given task, is one of the most important problems in the field. The classical Gradient-based methods are efficient but they require the system under control should be differentiable. Sampling-based methods have no such limitations, but the ability of existing ones to solve complex control missions is restricted.

Unlike standalone embedded devices, behaviors of a cyber-physical system (CPS) are highly dynamic. Many parameter values (e.g., those related to nature environment and third party black box functions) are unknown offline. Furthermore, distributed sub-CPSs may exchange data online. In this article, we first propose the concept of parametric hybrid automata (PHA) to describe such complex CPSs. As some PHA parameter values are unknown until runtime, conventional offline model checking is infeasible. Instead, we propose to carry out PHA model checking online, as a fault prediction mechanism. However, this usage is challenged by the high time cost of state reachability verification, which is the conventional focus of model checking. To address this challenge, we propose that the model checking shall focus on online scenario reachability validation instead. Furthermore, we propose a mechanism to compose/decompose scenarios. Our scenario reachability validation can exploit linear programming to achieve polynomial time cost. Evaluations on a state-of-the-art train control system show that our approach can cut online model checking time cost from over 1 h to within 200 ms.

Periodically online verification has been widely recognized as a practical and promising method to handle the non-deterministic and unpredictable behavior of dynamic CPS systems. However, it is a challenge to keep the online verification of CPS systems finishing quickly in time to give enough time for the running system to respond, if any error is detected. Nevertheless, the problems under verification for each cycle are highly similar to each other. Most of the differences are caused by run-time factors like changing of parameters' values or the reorganization of active components in the system. Under this investigation, this paper presents an incremental verification technique for online verification of CPS systems. A method is given to distinguish the differences between the problem under verification and the previous verified problem. Then, by reusing the problem space of the previous verified problem as a warm-start base, the modified part can be introduced into the base, which can be solved incrementally and efficiently. A set of case studies on a real-case train control system is presented in this paper to demonstrate the performance of the incremental online verification technique.