Verifying Hybrid Systems Involving Transcendental Functions

Abstract. We explore uses of a link we have constructed between the KeYmaera hybrid systems theorem prover and the MetiTarski proof en-gine for problems involving special functions such as sin, cos, exp, etc. Transcendental functions arise in the specification of hybrid systems and often occur in the solutions of the differential equations that govern how the states of hybrid systems evolve over time. To date, formulas ex-changed between KeYmaera and external tools have involved polynomi-als over the reals, but not transcendental functions, chiefly because of the lack of tools capable of proving such goals.

A Rewriting-Logic-Based Technique for Modeling Thermal Systems

This paper presents a rewriting-logic-based modeling and analysis technique for physical systems, with focus on thermal systems. The contributions of this paper can be summarized as follows: (i) providing a framework for modeling and executing physical systems, where both the physical components and their physical interactions are treated as first-class citizens; (ii) showing how heat transfer problems in thermal systems can be modeled in Real-Time Maude; (iii) giving the implementation in Real-Time Maude of a basic numerical technique for executing continuous behaviors in object-oriented hybrid systems; and (iv) illustrating these techniques with a set of incremental case studies using realistic physical parameters, with examples of simulation and model checking analyses.Comment: In Proceedings RTRTS 2010, arXiv:1009.398

Про нестійкість фазових орбіт одного класу гібридних автоматів

Розглядається загальна модель неперервно-дискретних систем – стохастичний гібридний автомат. Для цієї моделі доводяться теореми про нестійкість тривіальних фазових орбіт. У першій теоремі про нестійкість робиться припущення про існування спільної функції Ляпунова, у другій теоремі про нестійкість ця умова усунена.Рассматривается общая модель непрерывно-дискретных систем – стохастический гибридный автомат. Для этой модели доказываются теоремы о неустойчивости тривиальных фазовых орбит. В первой теореме о неустойчивости делается предположение о существовании общей функции Ляпунова, во второй теореме о неустойчивости это условие устранено.In this paper, the common model of continuously-discontinuous systems, stochastic switched hybrid system, in particular, is considered. For this model, the theorems regarding instability of trivial phase orbit were proved. In the first theorem regarding instability, an assumption about existing of a common Liapunov’s function was made, in the second theorem, this condition was eliminated

A Taylor Function Calculus for Hybrid System Analysis: Validation in Coq

International audienceWe present a framework for the verification of the numerical algorithms used in Ariadne, a tool for analysis of nonlinear hybrid system. In particular, in Ariadne, smooth functions are approximated by Taylor models based on sparse polynomials. We use the Coq theorem prover for developing Taylor models as sparse polynomials with floating-point coefficients. This development is based on the formalisation of an abstract data type of basic floating-point arithmetic . We show how to devise a type of continuous function models and thereby parametrise the framework with respect to the used approximation, which will allow us to plug in alternatives to Taylor models