Dynamic analysis of Cyber-Physical Systems

With the recent advances in communication and computation technologies, integration of software into the sensing, actuation, and control is common. This has lead to a new branch of study called Cyber-Physical Systems (CPS). Avionics, automotives, power grid, medical devices, and robotics are a few examples of such systems. As these systems are part of critical infrastructure, it is very important to ensure that these systems function reliably without any failures. While testing improves confidence in these systems, it does not establish the absence of scenarios where the system fails. The focus of this thesis is on formal verification techniques for cyber-physical systems that prove the absence of errors in a given system. In particular, this thesis focuses on {\em dynamic analysis} techniques that bridge the gap between testing and verification. This thesis uses the framework of hybrid input output automata for modeling CPS. Formal verification of hybrid automata is undecidable in general. Because of the undecidability result, no algorithm is guaranteed to terminate for all models. This thesis focuses on developing heuristics for verification that exploit sample executions of the system. Moreover, the goal of the dynamic analysis techniques proposed in this thesis is to ensure that the techniques are sound, i.e., they always return the right answer, and they are relatively complete, i.e., the techniques terminate when the system satisfies certain special conditions. For undecidable problems, such theoretical guarantees are the strongest that can be expected out of any automatic procedure. This thesis focuses on safety properties, which require that nothing bad happens. In particular we consider invariant and temporal precedence properties; temporal precedence properties ensure that the temporal ordering of certain events in every execution satisfy a given specification. This thesis introduces the notion of a discrepancy function that aids in dynamic analysis of CPS. Informally, these discrepancy functions capture the convergence or divergence of continuous behaviors in CPS systems. In control theory, several proof certificates such as contraction metric and incremental stability have been proposed to capture the convergence and divergence of solutions of ordinary differential equations. This thesis establishes that discrepancy functions generalize such proof certificates. Further, this thesis also proposes a new technique to compute discrepancy functions for continuous systems with linear ODEs from sample executions. One of the main contributions of this thesis is a technique to compute an over-approximation of the set of reachable states using sample executions and discrepancy functions. Using the reachability computation technique, this thesis proposes a safety verification algorithm which is proved to be sound and relatively complete. This technique is implemented in a tool called, Compare-Execute-Check-Engine (C2E2) and experimental results show that it is scalable. To demonstrate the applicability of the algorithms presented, two challenging case studies are analyzed as a part of this thesis. The first case study is about an alerting mechanism in parallel aircraft landing. For performing this case study, the dynamic analysis presented for invariant verification is extended to handle temporal properties. The second case study is about verifying key specification of powertrain control system. New algorithms for computing discrepancy function were implemented in C2E2 for performing this case study. Both these case studies demonstrate that dynamic analysis technique gives promising results and can be applied to realistic CPS. For distributed CPS implementations, where message passing, and clocks skews between agents make formal verification difficult to scale, this thesis presents a dynamic analysis algorithm for inferring global predicates. Such global predicates include assertions about the physical state and the software state of all the agents involved in distributed CPS. This algorithm is applied to coordinated robotic maneuvers for inferring safety and detecting deadlock

Verification of Annotated Models from Executions

Simulations can help enhance confidence in system designs, but they provide almost no formal guarantees. In this paper, we present a simulation-based verification framework for embedded systems described by nonlinear, switched systems. In our framework, users are required to annotate the dynamics in each control mode of a switched system by something we call a “discrepancy function” that formally measures the nature trajectory convergence/divergence in the system. Discrepancy functions generalize other measures of trajectory convergence and divergence like Contraction Metrics and Incremental Lyapunov functions. Exploiting such annotations, we present a sound and relatively complete verification procedure for robustly safe/unsafe systems. We have built a tool based on the framework that is integrated into the popular Simulink/Stateflow modeling environment. Experiments with our prototype tool show that the approach (a) outperforms other verification tools on standard linear and nonlinear benchmarks, (b) scales reasonably to larger dimensional systems and to longer time horizons, and (c) applies to models with diverging trajectories and unknown parameters.National Science Foundation / NSF CNS 1016791Ope

Re-Thinking LiDAR-Stereo Fusion Frameworks (Student Abstract)

In this paper, we present a 2-step framework for high-precision dense depth perception from stereo RGB images and sparse LiDAR input. In the first step, we train a deep neural network to predict dense depth map from the left image and sparse LiDAR data, in a novel self-supervised manner. Then in the second step, we compute a disparity map from the predicted depths, and refining the disparity map by making sure that for every pixel in the left, its match in the right image, according to the final disparity, is the local optimum

ARCH-COMP22 category report: Continuous and hybrid systems with nonlinear dynamics

We present the results of a friendly competition for formal verification of continuous and hybrid systems with nonlinear continuous dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2022. This year, 6 tools Ariadne, CORA, DynIbex, JuliaReach, Kaa and KeYmaera X (in alphabetic order) participated. These tools are applied to solve reachability analysis problems on six benchmark problems, two of them featuring hybrid dynamics. We do not rank the tools based on the results, but show the current status and discover the potential advantages of different tools

ARCH-COMP21 Category Report: Continuous and Hybrid Systems with Nonlinear Dynamics

We present the results of a friendly competition for formal verification of continuous and hybrid systems with nonlinear continuous dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2021. This year, 5 tools Ariadne, CORA, DynIbex, JuliaReach and Kaa (in alphabetic order) participated. These tools are applied to solve reachability analysis problems on five benchmark problems, two of them featuring hybrid dynamics. We do not rank the tools based on the results, but show the current status and discover the potential advantages of different tool