REACHABILITY COMPUTATION FOR UNCERTAIN PLANAR AFFINE SYSTEMS USING LINEAR ABSTRACTIONS

This report presents results of a friendly competition for formal verification of continuous and hybrid systems with piecewise constant dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2018. In this second edition, five tools have been applied to solve five different benchmark problems in the category for piecewise constant dynamics: BACH, Lyse, PHAVer, PHAVer-lite, and VeriSiMPL. Compared to last year, a new tool has participated (PHAVer-lite) and a benchmark has been made more complex (Dutch Railway Network). The result is a snapshot of the current landscape of tools and the types of benchmarks they are particularly suited for. Due to the diversity of problems, we are not ranking tools, yet the presented results probably provide the most complete assessment of tools for the safety verification of continuous and hybrid systems with piecewise constant dynamics up to this date.

This report presents results of a friendly competition for formal verification of continuous and hybrid systems with linear continuous dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2017. In its first edition, three tools have been applied to solve three different benchmark problems in the category ofbounded model checking of hybrid systems with piecewise constant dynamics (in alphabetical order): BACH, HyDRA, and XSpeed. The result is a snapshot of the current landscape of tools and the types of benchmarks they are particularly suited for. Due to the diversity of problems, we are not ranking tools and we also welcome more tools to join in this friendly competition in the future event.

Hybrid systems combining discrete and continuous dynamics arise as mathematical models of various artificial and natural systems, and as an approximation to complex continuous systems. Reachability analysis has been the principal research question in the verification of hybrid systems, even though it is a wellknown result that most non-trivial subclasses of hybrid systems reachability and most verification problems are undecidable [1]. Nonetheless, various decidable subclasses have been identified, including polygonal hybrid systems (SPDIs) [2]. SPDIs can be used, for instance, in the analysis of approximations of non-linear differential equations in two-dimensions.KeywordsModel CheckHybrid SystemPhase PortraitHybrid AutomatonReachability AnalysisThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A methodology for safety verification of continuous and hybrid systems using barrier certificates has been proposed recently. Conditions that must be satisfied by a barrier certificate can be formulated as a convex program, and the feasibility of the program implies system safety in the sense that there is no trajectory starting from a given set of initial states that reaches a given unsafe region. The dual of this problem, i.e., the reachability problem, concerns proving the existence of a trajectory starting from the initial set that reaches another given set. Using insights from the linear programming duality appearing in the discrete shortest path problem, we show in this paper that reachability of continuous systems can also be verified through convex programming. Several convex programs for verifying safety and reachability, as well as other temporal properties such as eventuality, avoidance, and their combinations, are formulated. Some examples are provided to illustrate the application of the proposed methods. Finally, we exploit the convexity of our methods to derive a converse theorem for safety verification using barrier certificates.

Hybrid systems are characterized by a composition of discrete and continuous dynamics.In particular, the system has a continuous evolution and occasional jumps.The jumps are caused either by controllable, uncontrollable external events or by its continuous evolution.The continuous evolution and these jumps in control loops are the origins from the most stringent real-time demands.With the necessity to launch more satellites, Brazilian National Institute for Space Research (INPE) has been carrying out research on modeling and verifying hybrid systems, of which its main focus is to obtain a better balance between dependability, schedule, and cost.We are attempting to use Object Management Group (OMG) specifications to model discrete events.We are focusing mainly in Modelica (with some degree of Scicoslab) to model continuous dynamics.Another concern addressed by this, INPE, research is to be independent from commercial tools, establishing itself on open source software.This paper presents an approach to implement Model-Driven Architecture in hybrid systems based on vendor neutral specifications.It shows how the models are defined, traced and used, as well as a set of tools for this.SysML (Systems Modeling Language), and MARTE (Modeling and Analysis of Real-Time Embedded Systems) allowed us to define a Computation Independent Model focused mainly on high-level structure and behavior (state oriented).At the end, a case study is presented (inverted pendulum).From this case study, we have concluded that the proposed approach can complement uncovered topics in current research applied to hybrid systems development and maintenance.

An Experimental Batch Plant as a Test Case for the Verification of Hybrid Systems

Hybrid systems are characterized by combining discrete and continuous behaviors. Verification of hybrid systems is, in general, a diffcult task due to the potential complexity of the continuous dynamics. Currently, there are different formalisms and tools which are able to analyze specific types of hybrid systems, model checking being one of the most used approaches. In this paper, we describe an extension of Java PathFinder in order to analyze hybrid systems. We apply a general methodology which has been successfully used to extend Spin. This methodology is non-intrusive, and uses external libraries, such as the Parma Polyhedra Library, to abstract the continuous behavior of the hybrid system.

This paper introduces a method and tool-support for the automatic analysis and verification of hybrid and embedded control systems, whose continuous dynamics are often modelled using MATLAB/Simulink. The method is based upon converting system models into the uniform input language of our efficient multi-domain constraint solving library, ABSOLVER, which is then used for subsequent analysis. Basically, ABSOLVER is an extensible SMT-solver which addresses mixed Boolean and (nonlinear) arithmetic constraint problems as they appear in the design of hybrid control systems. It allows the integration and semantic connection of various domain specific solvers via a logical circuit, such that almost arbitrary multi-domain constraint problems can be formulated and solved. Its design has been tailored for extensibility, and thus facilitates the reuse of expert knowledge, in that the most appropriate solver for a given task can be integrated and used. As such the only constraint over the problem domain is the capability of the employed solvers. Our approach to systems verification has been validated in an industrial case study using the model of a car's steering control system. However, additional benchmarks show that other hard instances of problems could also be solved by ABSOLVER in respectable time, and that for some instances, ABSOLVER's approach was the only means of solving a problem at all.

Intelligent environments can be described as hybrid systems, which combine continuous dynamics, modelling the behaviour of physical components, and discrete dynamics, modelling the software components that control the evolution of the physical variables. The growing boom in intelligent environments makes the construction of complex discrete components necessary, which may require the use of more sophisticated concurrent languages. Hy-tccp is a concurrent language for modelling hybrid systems with high-level notations that facilitate the description of computational systems, abstracting away from the implementation details. In this paper, we present an operational semantics based on hybrid automata for Hy-tccp which is a theoretical basis for the analysis and verification of hybrid systems like intelligent environment.

Verifying properties of hybrid systems can be highly complex. To reduce the effort required to produce a correct proof, the use of mechanical verification techniques is promising. Recently, we extended a mechanical verification system, originally developed to reason about deterministic real-time automata, to verify properties of hybrid systems. To evaluate our approach, we applied our extended proof system to a solution, based on the Lynch-Vaandrager timed automata model, of the Steam Boiler Controller problem, a hybrid systems benchmark. This paper reviews our mechanical verification system, which builds on SRI's Prototype Verification System (PVS), and describes the features we added to handle hybrid systems. It also discusses some errors we detected in applying our system to the benchmark problem. We conclude with a summary of insights we acquired in using our system to specify and verify hybrid systems.

Safety verification and reachability analysis for hybrid systems

This report presents the results of a friendly competition for formal verification and policy synthesis of stochastic models. It also introduces new benchmarks within this category, and recommends next steps for this category towards next year’s edition of the competition. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in Spring 2019.

Reachability analysis has recently proved to be a useful technique for analysing the behaviour of under-specified biological models. In this paper, we propose a method exploiting the eigenstructure of a linear continuous system to efficiently estimate a bounded interval containing the time at which the system can reach a target set from an initial set. Then this estimation can be directly integrated in an existing algorithm for hybrid systems with linear continuous dynamics, to speed up reachability computations. Furthermore, it can also be used to improve time-efficiency of the hybridization technique that is based on a piecewise-linear approximation of non-linear continuous dynamics. The proposed method is illustrated on a number of examples including a biological model.

A Tool for Modular Modelling and Verification of Hybrid Systems

Hybrid systems are networks of interacting digital devices and continuous plants reacting to a changing environment. Our multiple agent hybrid control architecture ([KN93b], [KN93c]) is based on the notion of hybrid system state. The latter incorporates evolution models using differential or difference equations, logic constraints, and geometric constraints. The set of hybrid states of a hybrid system can be construed in a variety of ways as a differentiable (or a C ∞) manifold which we have called the carrier manifold ([KNRG95]). We have suggested that for control problems the coordinates of points of the carrier manifolds should be selected to incorporate all information about system state, control state, and environment needed to choose new values of control parameters.This paper provides an outline of our ongoing work which expresses a wide class of control problems as relaxed, or convexified, calculus of variations problems on carrier manifolds. Weierstrass pointed out that many calculus of variations problems with time as an independent variable can be rewritten as parametric problems, that is, as problems where time is not an explicit variable, by moving to a larger manifold where time is an extra variable, x n+1=t, with the extra constraint x n+1=1. Then Finsler (1918) pointed out that each such parametric calculus of variations problem induces a metric ground form ds 2 associated with the manifold. We reduce a wide class of optimal control problems to calculating the Cartan affine connection associated with the Finsler metric ground form induced by the corresponding convexified calculus of variations problem. For any prescribed ε of deviation from the variational minimum, we then use chatterings of control flows on the manifold to approximate to a connection and use this to compute a finite state control program which enforces ε-optimal behavior. Thus we find that Finsler manifolds and their associated differential geometry and control flows form a computational basis for extraction and verification of hybrid systems and intelligent control systems in general. We remark that other connections, not arising from metrics, can be usefully employed in control too.Here we discuss only the simplest problem of the calculus of variations and optimal control: find an “optimal” path x(t) among admissible paths on the manifold M extending from initial point x(t 0 )=x0 to endpoint x(t 1 )=x1 with a given end direction. x(t 1 )=y 1. The theory of Finsler manifolds is not familiar to most electrical engineers and certainly not to computer scientists. The goal of this paper is to give some historical background and a brief description of how one interprets connections as optimal controls and extraction of finite state control programs as extraction of approximations to connections. One can also unwind and use connections similarly for non-parametric problems. A book length mathematical treatment is in preparation.KeywordsHybrid SystemTangent SpaceTangent VectorParallel TransportFinsler SpaceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.