DIFFERENTIAL PREDICATE TRANSITION PETRI NETS AND OBJECTS, AN AID FOR PROVING PROPERTIES IN HYBRID SYSTEMS E. Villani*, J. C. Pascal + , P. E. Miyagi*, R. Valette + * Escola Politécnica, University of São Paulo Av. Prof. Mello Moraes, 2231 CEP 05508-900 São Paulo, BRAZIL + Laboratoire d’Analyse et d’Architecture des Systèmes – LAAS / CNRS 7, Avenue du Colonel Roche, 31077 Tolouse Cedex 4 FRANCE e-mail: evillani@usp.br , jcp@laas.fr , pemiyagi@usp.br , robert@laas.fr Abstract: This paper introduces a new approach for the verification of behaviour properties in hybrid systems. By using Petri nets and object oriented concepts the proof of a system property is reduced from a complex proof involving the overall model to a set of simpler proofs involving the model of one or a few objects. Each local proof is made considering a set of hypotheses that should then be proven. Particularly, this paper considers the case of proving safety properties. Copyright © 2002 IFAC Keywords: Petri nets, object modelling techniques, differential equations. 1. INTRODUCTION The increasing employment of system integration and computer automation in industrial systems has lead to the need of dealing with more and more complex hybrid system (Antsaklis & Koutsoukos, 1998). (Here, the term “hybrid” indicates systems that involve both discrete and continuous dynamic) As result of this trend, both modelling and analysis of such systems cannot be easily addressed by the techniques defined for simple applications. Within the domain of system analysis, one of the most important aspects is the guarantee of the system reliability by the verification of behavioural properties. An example is proving that a forbidden state will never be reached. However, most of works already published can only be applied to special classes of hybrid systems. For the verification tool UPPAL (Amnell et al, 2000), the model must be reduced to a timed automata. Other approaches are based on linear hybrid automata, such as (Gueguen & Zaytoon, 2001) and the verification tool HyTech (Henzinger et al, 1997). Only a few approaches support non linear models, such as the verification tool Checkmate (Silva et al, 2001), which uses non linear hybrid automata but cannot easily deal with large-scale systems (Silva et al, 2001). The main problem of hybrid system analysis is the non-decidability issue, i.e., the non-guarantee that, with a finite number of steps the property can be proved. As it has been proven by (Alur et al, 1995), if continuous variables with different growing rates (different derivatives) are included in the model, then the reachability may become undecidable. Generally, this is the case of hybrid systems. In this context, the aim of this paper is to introduce a new approach for the hybrid system analysis. On the contrary of the cited works, Petri nets are used for modelling of the discrete part, and linear logic is used for its analysis, in order to deal with the discrete state explosion problem. For the continuous part, differential equation systems are adopted. The main innovative point of the proposed approach is that it uses the object-oriented concepts to decompose and analyse the system. By this way, an analysis problem, that would otherwise involve the overall model of the system, is decomposed into a set of simpler analysis problems involving the model of one or a few objects. Another important point of the approach is that it is not entirely automated. A more balanced solution is proposed where the user knowledge of the system is used in order to restrict the solution space and avoid the non-decidability (although no guarantee of a solution can be given).