Relational Differential Dynamic Logic

International audienceIn the field of quality assurance of hybrid systems (that combine continuous physical dynamics and discrete digital control), Platzer's differential dynamic logic (dL) is widely recognized as a deductive verification method with solid mathematical foundations and sophisticated tool support. Motivated by benchmarks provided by our industry partner , we study a relational extension of dL, aiming to formally prove statements such as "an earlier deployment of the emergency brake decreases the collision speed." A main technical challenge here is to relate two states of two dynamics at different time points. Our main contribution is a theory of suitable relational differential invariants (a relational extension of differential invariants that are central proof methods in dL), and a derived technique of time stretching. The latter features particularly high applicability, since the user does not have to synthesize a relational differential invariant out of the air. We derive new inference rules for dL from these notions, and demonstrate their use over a couple of automotive case studies

Verifying safety properties of a nonlinear control by interactive theorem proving with the Prototype Verification System

Interactive, or computer-assisted, theorem proving is the verification of statements in a formal system, where the proof is developed by a logician who chooses the appropriate inference steps, in turn executed by an automatic theorem prover. In this paper, interactive theorem proving is used to verify safety properties of a nonlinear (hybrid) control system

HyPLC: Hybrid Programmable Logic Controller Program Translation for Verification

Programmable Logic Controllers (PLCs) provide a prominent choice of implementation platform for safety-critical industrial control systems. Formal verification provides ways of establishing correctness guarantees, which can be quite important for such safety-critical applications. But since PLC code does not include an analytic model of the system plant, their verification is limited to discrete properties. In this paper, we, thus, start the other way around with hybrid programs that include continuous plant models in addition to discrete control algorithms. Even deep correctness properties of hybrid programs can be formally verified in the theorem prover KeYmaera X that implements differential dynamic logic, dL, for hybrid programs. After verifying the hybrid program, we now present an approach for translating hybrid programs into PLC code. The new tool, HyPLC, implements this translation of discrete control code of verified hybrid program models to PLC controller code and, vice versa, the translation of existing PLC code into the discrete control actions for a hybrid program given an additional input of the continuous dynamics of the system to be verified. This approach allows for the generation of real controller code while preserving, by compilation, the correctness of a valid and verified hybrid program. PLCs are common cyber-physical interfaces for safety-critical industrial control applications, and HyPLC serves as a pragmatic tool for bridging formal verification of complex cyber-physical systems at the algorithmic level of hybrid programs with the execution layer of concrete PLC implementations.Comment: 13 pages, 9 figures. ICCPS 201

On Provably Correct Decision-Making for Automated Driving

The introduction of driving automation in road vehicles can potentially reduce road traffic crashes and significantly improve road safety. Automation in road vehicles also brings several other benefits such as the possibility to provide independent mobility for people who cannot and/or should not drive. Many different hardware and software components (e.g. sensing, decision-making, actuation, and control) interact to solve the autonomous driving task. Correctness of such automated driving systems is crucial as incorrect behaviour may have catastrophic consequences. Autonomous vehicles operate in complex and dynamic environments, which requires decision-making and planning at different levels. The aim of such decision-making components in these systems is to make safe decisions at all times. The challenge of safety verification of these systems is crucial for the commercial deployment of full autonomy in vehicles. Testing for safety is expensive, impractical, and can never guarantee the absence of errors. In contrast, formal methods, which are techniques that use rigorous mathematical models to build hardware and software systems can provide a mathematical proof of the correctness of the system. The focus of this thesis is to address some of the challenges in the safety verification of decision-making in automated driving systems. A central question here is how to establish formal verification as an efficient tool for automated driving software development.A key finding is the need for an integrated formal approach to prove correctness and to provide a complete safety argument. This thesis provides insights into how three different formal verification approaches, namely supervisory control theory, model checking, and deductive verification differ in their application to automated driving and identifies the challenges associated with each method. It identifies the need for the introduction of more rigour in the requirement refinement process and presents one possible solution by using a formal model-based safety analysis approach. To address challenges in the manual modelling process, a possible solution by automatically learning formal models directly from code is proposed

Enclosing the behavior of a hybrid automaton up to and beyond a Zeno point

Even simple hybrid automata like the classic bouncing ball can exhibit Zeno behavior. The existence of this type of behavior has so far forced a large class of simulators to either ignore some events or risk looping indefinitely. This in turn forces modelers to either insert ad-hoc restrictions to circumvent Zeno behavior or to abandon hybrid automata. To address this problem, we take a fresh look at event detection and localization. A key insight that emerges from this investigation is that an enclosure for a given time interval can be valid independent of the occurrence of a given event. Such an event can then even occur an unbounded number of times. This insight makes it possible to handle some types of Zeno behavior. If the post-Zeno state is defined explicitly in the given model of the hybrid automaton, the computed enclosure covers the corresponding trajectory that starts from the Zeno point through a restarted evolution

On Optimization-Based Falsification of Cyber-Physical Systems

In what is commonly referred to as cyber-physical systems (CPSs), computational and physical resources are closely interconnected. An example is the closed-loop behavior of perception, planning, and control algorithms, executing on a computer and interacting with a physical environment. Many CPSs are safety-critical, and it is thus important to guarantee that they behave according to given specifications that define the correct behavior. CPS models typically include differential equations, state machines, and code written in general-purpose programming languages. This heterogeneity makes it generally not feasible to use analytical methods to evaluate the system’s correctness. Instead, model-based testing of a simulation of the system is more viable. Optimization-based falsification is an approach to, using a simulation model, automatically check for the existence of input signals that make the CPS violate given specifications. Quantitative semantics estimate how far the specification is from being violated for a given scenario. The decision variables in the optimization problems are parameters that determine the type and shape of generated input signals. This thesis contributes to the increased efficiency of optimization-based falsification in four ways. (i) A method for using multiple quantitative semantics during optimization-based falsification. (ii) A direct search approach, called line-search falsification that prioritizes extreme values, which are known to often falsify specifications, and has a good balance between exploration and exploitation of the parameter space. (iii) An adaptation of Bayesian optimization that allows for injecting prior knowledge and uses a special acquisition function for finding falsifying points rather than the global minima. (iv) An investigation of different input signal parameterizations and their coverability of the space and time and frequency domains. The proposed methods have been implemented and evaluated on standard falsification benchmark problems. Based on these empirical studies, we show the efficiency of the proposed methods. Taken together, the proposed methods are important contributions to the falsification of CPSs and in enabling a more efficient falsification process