Hybrid Automata

We present a formal verification of a control algorithm from the literature for a four-cylinder four-stroke engine in the cutoff mode. The controlled system is modeled, simulated and verified using CheckMate, a tool for formal verification of hybrid systems developed at Carnegie Mellon University. CheckMate automatically constructs a polyhedral-invariant hybrid automaton (PIHA) from a Matlab/Simulink model of the hybrid system and performs the verification using discrete model approximations. This case study illustrates how verification can be performed directly on a model of the hybrid system dynamics without first constructing an approximation to the continuous dynamics using timed automata or so-called linear hybrid automata models.

Petri nets (PNs) are widely used to model discrete event dynamic systems (computer systems, manu- facturing systems, communication systems, etc). Continuous Petri nets (in which the markings are real numbers and the transition firings are continuous) were defined more recently; such a PN may model a continuous system or approximate a discrete system. A hybrid Petri net can be obtained

This paper describes a methodology for the speci cation and analysis of distributed real-time systems using the toolset called PARAGON. PARAGON is based on the Communicating Shared R esources paradigm, which allows a real-time system to be modeled as a set of communicating processes that compete for shared resources. PARAGON supports both visual and textual languages for describing real-time systems. It o ers automatic analysis based on state space exploration as well as user-directed simulation. Our experience with using PARAGON in several case studies resulted in a methodology that includes design patterns and abstraction heuristics, as well as an overall process. This paper brie y overviews the communicating shared resource paradigm and its toolset PARAGON, including the textual and visual speci cation languages. The paper then describes our methodology with special emphasis on heuristics that can be used in PARAGON to reduce the state space. To illustrate the methodology, w e use examples from a real-life system case study.

Generation of pseudo-random binary sequences by one-dimensional cellular automata is surveyed using both uniform and hybrid automata. The updating function is a Boolean function that must satisfy criteria of resilience and nonlinearity for the sequence they generate to be secure for a stream cipher application.

This paper introduces iterative relaxation abstraction (IRA), a new method for reachability analysis of LHA that aims to improve scalability by combining the capabilities of current tools for analysis of low-dimensional LHA with the power of linear programming (LP) for large numbers of constraints and variables. IRA is inspired by the success of counterexample guided abstraction refinement (CEGAR) techniques in verification of discrete systems. On each iteration, a low-dimensional LHA called a relaxation abstraction is constructed using a subset of the continuous variables from the original LHA. Hybrid system reachability analysis then generates a regular language called the discrete path abstraction containing all possible counterexamples (paths to the bad locations) in the relaxation abstraction. If the discrete path abstraction is non-empty, a particular counterexample is selected and LP infeasibility analysis determines if the counterexample is spurious using the constraints along the path from the original high-dimensional LHA. If the counterexample is spurious, LP techniques identify an irreducible infeasible subset (IIS) of constraints from which the set of continuous variables is selected for the the construction of the next relaxation abstraction. IRA stops if the discrete path abstraction is empty or a legitimate counterexample is found. The effectiveness of the approach is illustrated with an example.

We present a hybrid, hierarchical architecture for mission control of autonomous underwater vehicles (AUVs). The architecture is model based and is designed with semiautomatic verification of safety and performance specifications as a primary capability in addition to the usual requirements such as real-time constraints, scheduling, shared-data integrity, etc. The architecture is realized using a commercially available graphical hybrid systems design and code generation tool. While the tool facilitates rapid redesign and deployment, it is crucial to include safety and performance verification into each step of the (re)design process. A formal model of the interacting hybrid automata in the design tool is outlined, and a tool is presented to automatically convert hybrid automata descriptions from the design tool into a format required by two hybrid verification tools. The application of this mission control architecture to a survey AUV is described and the procedures for verification outlined.

Hybrid automata model systems with both digital and analog components, such a s e m bedded control programs. Many v eri cation tasks for such programs can be expressed as reachability problems for hybrid automata. By improving on previous decidability and undecidability results, we identify a boundary between decidability and undecidability for the reachability problem of hybrid automata. On the positive side, we give an (optimal) PSPACE reachability algorithm for the case of initialized rectangular automata, where all analog variables follow independent trajectories within piecewise-linear envelopes and are reinitialized whenever the envelope changes. Our algorithm is based on the construction of a timed automaton that contains all reachability information about a given initialized rectangular automaton. The translation has practical signi cance for veri cation, because it guarantees the termination of symbolic procedures for the reachability analysis of initialized rectangular automata.

In this paper we present pddl+, a planning domain description language for modelling mixed discrete-continuous planning domains. We describe the syntax and modelling style of pddl+, showing that the language makes convenient the modelling of complex time-dependent effects. We provide a formal semantics for pddl+ by mapping planning instances into constructs of hybrid automata. Using the syntax of HAs as our semantic model we construct a semantic mapping to labelled transition systems to complete the formal interpretation of pddl+ planning instances. An advantage of building a mapping from pddl+ to HA theory is that it forms a bridge between the Planning and Real Time Systems research communities. One consequence is that we can expect to make use of some of the theoretical properties of HAs. For example, for a restricted class of HAs the Reachability problem (which is equivalent to Plan Existence) is decidable. pddl+ provides an alternative to the continuous durative action model of pddl2.1, adding a more flexible and robust model of time-dependent behaviour.

This paper explores the application of rewriting logic to the executable formal modeling of real-time and hybrid systems. We give general techniques by which such systems can be specified as ordinary rewrite theories, and show that a wide range of real-time and hybrid system models, including object-oriented systems, timed automata [3], hybrid automata [2], timed and phase transition systems , and timed extensions of Petri nets , can indeed be expressed in rewriting logic quite naturally and directly. Since rewriting logic is executable and is supported by several language implementations, our approach complements property-oriented methods and tools less well suited for execution purposes, and can be used as the basis for symbolic simulation and formal analysis of real-time and hybrid systems . The relationships with the timed rewriting logic approach of Kosiuczenko and Wirsing are also studied.

In this paper, we study the verification of dense time properties by discrete time analysis. Interval Duration Logic, (IDL), is a highly expressive dense time logic for specifying properties of real-time systems. Validity checking of IDL formulae is in general undecidable. A corresponding discrete-time logic QDDC has decidable validity. In this paper, we consider a reduction of IDL validity question to QDDC validity using notions of digitization. A new notion of Strong Closure under Inverse Digitization, SCID, is proposed. For all SCID formulae, the dense and the discrete-time validity coincide. Moreover, SCID has good algebraic properties which can be used to conveniently prove that many IDL formulae are SCID. We also give some approximation techniques to strengthen/weaken formulae to SCID form. For SCID formulae, the validity of dense-time IDL formulae can be checked using the validity checker for discrete-time logic QDDC.

A {\em hybrid automaton\/} consists of a finite automaton interacting with a dynamical system. Hybrid automata are used to model embedded controllers and other systems that consist of interacting discrete and continuous components. A hybrid automaton is {\em rectangular\/} if each of its continuous variables~$x$ satisfies a nondeterministic differential equation of the form $a\le\frac{dx}{dt}\le b$, where $a$ and~$b$ are rational constants. Rectangular hybrid automata are particularly useful for the analysis of communication protocols in which local clocks have bounded drift, and for the conservative approximation of systems with more complex continuous behavior. We examine several verification problems on the class of rectangular hybrid automata, including reachability, temporal logic model checking, and controller synthesis. Both dense-time and discrete-time models are considered. We identify subclasses of rectangular hybrid automata for which these problems are decidable and give...

We define five increasingly comprehensive classes of infinite-state systems, called STS1-STS5, whose state spaces have finitary structure. For four of these classes, we provide examples from hybrid systems. STS1 These are the systems with finite bisimilarity quotients. They can be analyzed symbolically by iteratively applying predecessor and boolean operations on state sets, starting from a finite number of observable state sets. Any such iteration is guaranteed to terminate in that only a finite number of state sets can be generated. This enables model checking of the µ-calculus.

Many natural systems exhibit a hybrid behavior characterized by a set of continuous laws which are switched by discrete events. Such behaviors can be described in a very natural way by a class of automata called hybrid automata. Their evolution are represented by both dynamical systems on dense domains and discrete transitions. Once a real system is modeled in a such framework, one may want to analyze it by applying automatic techniques, such as Model Checking or Abstract Interpretation. Unfortunately, the discrete/continuous evolutions not only provide hybrid automata of great flexibility, but they are also at the root of many undecidability phenomena. This paper addresses issues regarding the decidability of the reachability problem for hybrid automata (i.e., "can the system reach a state a from a state b ?") by proposing an "inaccurate" semantics. In particular, after observing that dense sets are often abstractions of real world domains, we suggest, especially in the context of biological simulation, to avoid the ability of distinguishing between values whose distance is less than a fixed . On the ground of the above considerations, we propose a new semantics for first-order formulae which guarantees the decidability of reachability. We conclude providing a paradigmatic biological example showing that the new semantics mimics the real world behavior better than the precise one.

A notion of diagnosability for hybrid systems is defined, which generalizes the notion of observability. We verify diagnosability properties on a timed automaton abstraction of the original hybrid system. We propose a procedure to check diagnosability, and show that the complexity of the verification problem is in PTIME for the system class of our abstraction, namely for a subclass of timed automata: the durational graphs. We apply our procedure to an electromagnetic valve system for camless engines.

We propose a new biological framework based on the Lynch et al. theory of Hybrid I/O Automata (HIOAs) for modeling and simulating excitable tissue. Within this framework, we view an excitable tissue as a composition of two main kinds of component: a diffusion medium and a collection of cells, both modeled as an HIOA. This approach yields a notion of decomposition that allows us to describe a tissue as the parallel composition of several interacting tissues, a property that could be exploited to parallelize, and hence improve, the efficiency of the simulation process.

A method of analysing diagnosability of discrete time hybrid systems (DTHS), which are similar to the simple n-rate timed automata [R. Alur, C. Courcoubetis, T.A. Henzinger, P. Ho, Hybrid automata: an algorithmic approach to the specification and verification of hybrid systems, in: Hybrid Systems, LNCS 736, Springer Verlag, 1993, pp. 209-229], has been proposed. A state based fault modeling formalism is used. The properties of the DTHS model, under measurement limitations due to inadequacy or non-availability of sensors, are discussed. A definition of diagnosability for DTHS models has been adopted from the one proposed in [M. Sampath, R. Sengupta, S. Lafortune, K. Sinnamohideen, D. Teneketzis, Diagnosability of discrete-event systems, IEEE Transactions on Automatic Control 40 (9) (1995) 1555-1575] for discreteevent system (DES) models. Based on the measurement limited DTHS models, an algorithm for construction of a diagnoser is presented. It is next demonstrated through an example of a chemical reaction chamber that the diagnosability condition (over the diagnoser), which has been shown to be necessary and sufficient for DES diagnosability, fails to hold for many systems. This is so because the abstraction employed in DES modeling obliterates an important feature of the transitions namely fairness. Exploiting the explicit continuous dynamics of the DTHS models, the fairness of transitions is identified and used to demonstrate diagnosability. The diagnosability condition over the diagnoser is suitably modified to encompass the situations typified by the example.

The modeling and analysis of hybrid systems is a recent and challenging research area which is actually dominated by two main lines: a functional analysis based on the description of the system in terms of discrete state (hybrid) automata (whose goal is to ascertain for conformity and reachability properties), and a stochastic analysis (whose aim is to provide performance and dependability measures). This paper investigates a unifying view between formal methods and stochastic methods by proposing an analysis methodology of hybrid systems based on Fluid Petri Nets (FPN). It is shown that the same FPN model can be fed to a functional analyser for model checking as well as to a stochastic analyser for performance evaluation. We illustrate our approach and show its usefulness by applying it to a "real world" hybrid system: the temperature control system of a co-generative plant.

The use of formal methods, techniques and tools may generally guarantee a systems ’ safe operation. Such a process includes system modeling with a mathematical model, which is an approximation of the physical system, and is used to make easier the next step of analysis. Formal analysis of hybrid systems, which involve mixed continuous-valued and discrete dynamics, is concerned with verifying whether a hybrid system satisfies a desired specification, like avoiding an unsafe region of the state space. In this paper, we examine the general impact of hybrid automata on modeling and analyzing hybrid systems and we discuss in particular some advantages that arise when exploiting them in the context of particular methods for verifying the reachability of states in common paradigms that have already being investigated with other classical methods. Finally, we use two case studies concerning different classes of hybrid automata to demonstrate the applicability and the efficiency of exploitin...

This paper shows how multiagent systems can be modeled by a combination of UML statecharts and hybrid automata. This allows formal system specification on different levels of abstraction on the one hand, and expressing real-time system behavior with continuous variables on the other hand. It is shown how multi-robot systems can be modeled by hybrid and hierarchical state machines and how model checking techniques for hybrid automata can be applied. An enhanced synchronization concept is introduced that allows synchronization taking time and avoids state explosion to a certain extent. This research is supported by the grants Fu 263/8 and Sto 421/2 from the German research foundation DFG within the special priority program 1125 on Cooperating Teams of Mobile Robots in Dynamic Environments.

Autonomous navigation in urban environments inevitably leads to having to switch between various, sometimes conflicting control tasks. Sting Racing, a collaboration between Georgia Tech and SAIC, has developed a modular control architecture for this purpose and this paper describes the operation and definition of this architecture through so-called nested hybrid automata. We show how to map the requirements associated with the DARPA Urban Grand Challenge onto these nested automata and illustrate their operation through a number of experimental results.

We relate two di erent approaches for the speci cation and veri cation of hybrid systems. The rst one is logic-based and uses the framework of the Calculus of Durations (CoD), the second one is automatabased and uses algorithmic analysis techniques for hybrid automata. Fragments of CoD have been identi ed in 13, 19] for the description of control systems and their requirements. We mainly show that the problem of verifying that a CoD control design satis es a CoD requirement is decidable. This is proved by reducing this veri cation problem to the reachability problem for a subclass of linear hybrid automata where this problem is decidable.

Embedded control systems typically comprise continuous control laws combined with discrete mode logic. These systems are modeled using a hybrid automaton formalism, which is obtained by combining the discrete transition system formalism with continuous dynamical systems. This paper develops automated analysis techniques for asserting correctness of hybrid system designs. Our approach is based on symbolic representation of the state space of the system using mathematical formulas in an appropriate logic. Such formulas are manipulated using symbolic theorem proving techniques.

We propose a new biological framework based on the Lynch et al. theory of Hybrid I/O Automata (HIOAs) for modeling and simulating excitable tissue. Within this framework, we view an excitable tissue as a composition of two main kinds of component: a diffusion medium and a collection of cells, both modeled as an HIOA. This approach yields a notion of decomposition that allows us to describe a tissue as the parallel composition of several interacting tissues, a property that could be exploited to parallelize, and hence improve, the efficiency of the simulation process.

Cement milling circuits are controlled by linear quadratic strategies with the purpose of retaining the circuit stability. Generally, the controlled variables of milling circuits present discontinuities over the range of values they take during the plant operation. The design of linear quadratic control algorithms is based on linear approximations of the nonlinear differential equations that hold over the continuous time ranges of the controlled variables. These approximations make the practical implementation of these algorithms less effective than expected and for this reason there is the need to verify the range of the variable values over which the algorithms can retain the circuit stability before commissioning them. In this paper, an alternative model to that of the nonlinear differential equations is developed for the verification of the milling circuit stability. The model is based on the rectangular hybrid automata formalism. This formalism provides a more systematic and formal way of modeling the plant operation over different ranges of variables presenting discontinuities and does not require to develop informal textual description of the conditions under which different sets of differential equations model the plant operation within the different continuous ranges of the variables. In order to use this model for verifying the circuit stability, the requirements for the circuit stability are expressed in the form of a logical proposition of the ranges of the values within which certain variables of the cement milling circuit must remain. The circuit stability is verified by finding whether the states that are defined by the logical proposition are included in the state space of the automaton. There are, however, cases in which existing algorithms that search into the state space either do not terminate or take very long times in identifying the existence or not of the desired state. After the elapse of a significant portion of time the analyst does not know whether this long time is due to algorithm termination problem or to the very large number of remaining computations. In this paper, a new algorithm was developed which does not search into the state space of the automaton as most of the other algorithms do, but computes the number of automaton iterations required for reaching a state. If this is a finite number one can conclude that the desired state is reachable. This algorithm was used in verifying the circuit stability.

The cell cycle is a complex biological system frequently investigated from a mathematical perspective. In fact, over the past years a huge number of deterministic mathematical models describing the dynamics and the regulation of this process have been proposed. A crucial point concerning the cell cycle modeling is the combination of continuous and discrete dynamics in order to obtain results which are coherent with the biological context.

The modelling of gene regulatory networks (GRNs) has classically been addressed through very different approaches. Among others, extensions of Thomas's asynchronous Boolean approach have been proposed, to better fit the dynamics of biological systems: genes may reach different discrete expression levels, depending on the states of other genes, called the regulators: thus, activations and inhibitions are triggered conditionally on the proper expression levels of these regulators. In contrast, some fine-grained propositions have focused on the molecular level as modelling the evolution of biological compound concentrations through differential equation systems. Both approaches are limited. The first one leads to an oversimplification of the system, whereas the second is incapable to tackle large GRNs. In this context, hybrid paradigms, that mix discrete and continuous features underlying distinct biological properties, achieve significant advances for investigating biological properties. One of these hybrid formalisms proposes to focus, within a GRN abstraction, on the time delay to pass from a gene expression level to the next. Until now, no research work has been carried out, which attempts to benefit from the modelling of a GRN by differential equations, converting it into a multi-valued logical formalism of Thomas, with the aim of performing biological applications.

Power electronic circuits are networks composed of electronic components and semiconductor devices. Usually, the analysis of power electronic circuits is performed by numerical simulation. For evaluating the effect of different initial conditions or parametric variation over the circuit operation it is necessarv to perform exhaustive simulations and tests. However, even by doing this, there is no guarantees of the full correctness of the results, because it will be necessary to simulate the system for an infinite number of operating conditions. The goal of this paper is to use formal methods to study power electronic circuits. This is made by introducing a procedure to obtain hybrid automata from a power circuit, introducing the possibility to model time varying sources in the circuits components, and implementing formal verification and controller redesign procedures. We use the formalism of hybrid automata to represent the behavior of circuits because they can capture naturally a wide range of circuit behavior and, moreover, provide a framework suitable for the verification problems we work.

Physical systems can fail. For this reason the problem of identifying and reacting to faults has received a large attention in the control and computer science communities. In this paper we study the fault diagnosis problem for hybrid systems from a game-theoretical point of view. A hybrid system is a system mixing continuous and discrete behaviours that cannot be faithfully modeled neither by using a formalism with continuous dynamics only nor by a formalism including only discrete dynamics. We use the well known framework of hybrid automata for modeling hybrid systems, and we define a Fault Diagnosis Game on them, using two players: the environment and the diagnoser. The environment controls the evolution of the system and chooses whether and when a fault occurs. The diagnoser observes the external behaviour of the system and announces whether a fault has occurred or not. Existence of a winning strategy for the diagnoser implies that faults can be detected correctly, while computing such a winning strategy corresponds to implement a diagnoser for the system. We will show how to determine the existence of a winning strategy, and how to compute it, for some decidable classes of hybrid automata like o-minimal hybrid automata.

Combining discrete state-machines with continuous behavior, hybrid systems are a well-established mathematical model for discrete systems acting in a continuous environment. As a priori infinite state systems, their computational properties are undecidable in the general model and the main line of research concentrates on model checking of finite abstractions of restricted subclasses of the general model. In our work, we use deductive methods, falling back upon the general-purpose theorem prover PVS. To do so we extend the classical approach for the verification of state-based programs by developing an inductive proof method to deal with the parallel composition of hybrid systems. The methods cover shared variable communication, label-synchronization, and especially the common continuous activities in the parallel composition of hybrid automata. Besides hybrid systems and their parallel composition, we formalized their operational step semantics and a number of proof-rules within PV...

We propose an improved symbolic algorithm for the verification of linear hybrid automata with large discrete state spaces (where an explicit representation of discrete states is difficult). Here both the discrete part and the continuous part of the hybrid state space are represented by one symbolic representation called LinAIGs. LinAIGs represent (possibly non-convex) polyhedra extended by Boolean variables. Key components of our method for state space traversal are redundancy elimination and constraint minimization: redundancy elimination eliminates so-called redundant linear constraints from LinAIG representations by a suitable exploitation of the capabilities of SMT (Satisfiability Modulo Theories) solvers. Constraint minimization optimizes polyhedra by exploiting the fact that states already reached in previous steps can be interpreted as ''don't cares'' in the current step. Experimental results (including comparisons to the state-of-the-art model checkers PHAVer and RED) demonstrate the advantages of our approach.

Hybrid automata is a powerful framework for representing the dynamics of rigid-body mechanical systems. Thus far however, work has mainly focused on examples with only single points of contact. Consider for instance, the ubiquitous bouncing-ball example. The case of multiple contacts is much more complex. An event at one contact can affect the other contacts even when there is no apparent transmission mechanism. In this paper, we present a general hybrid automaton for systems consisting of multiple rigid-bodies with convex differentiable surfaces. The hybrid automaton assumes that Newton's impact law (restitution) and Coulomb friction are acting at the points of contact. Multiple contacts are addressed by introducing computational nodes which can be considered as the well-known mythical modes in the discontinuous systems' literature. These nodes consist of non-dynamical discrete states and reset operations which find valid combinations of contact forces. In this manner, they will guide the executions of the hybrid automaton to the relevant hybrid discrete locations.

We propose a computational-oriented perspective within the study of discontinuous chaotic systems, and provide insights into the modelling, control and simulation of chaotic systems with switching dynamics. In particular, the Lorenz system in its piecewise-linear version is studied. This system is reinterpreted within the hybrid-automaton framework, and what is referred to as the Lorenz hybrid automaton is established. Furthermore, a discontinuous control which eliminates the chaotic behaviour and steers the trajectories to a desired equilibrium is proposed. An integral characteristic of the modelling framework is that the controlled system, exhibiting three discontinuity surfaces, is reduced to the composition of several Lorenz hybrid automata. The approach proposed here is especially useful in order to specify the transitions between the different system operation modes, which becomes a crucial problem due to the existence of multiple switching surfaces.

We show how to automatically learn the class of Hybrid Automata called Cycle-Linear Hybrid Automata (CLHA) in order to model the behavior of excitable cells. Such cells, whose main purpose is to amplify and propagate an electrical signal known as the action potential (AP), serve as the "biologic transistors" of living organisms. The learning algorithm we propose comprises the following three phases: (1) Geometric analysis of the APs in the training set is used to identify, for each AP, the modes and switching logic of the corresponding Linear Hybrid Automata.

The optimal control of switched linear autonomous systems with quadratic performance index over infinite time horizon is considered. The decision variables are the switching times and the mode sequence, under the following constraints: the mode sequence has finite length; an automaton restricts the possible switches within adjacent locations, with a cost associated to each switch; the time interval between two consecutive switches is greater than a fixed quantity. A state-feedback solution is computed off-line through a numerical procedure. The method is extended to the case of infinite number of switches.

Given a hybrid automaton and a desired precision, we aim at constructing an approximate abstraction by means of a timed automaton, whose discrete state trajectories approximate the discrete state trajectories of the original system, with the desired precision on switching times. We show that using the Euclidian metric on reals it is not always possible to construct a timed automaton that is close to a hybrid automaton with finite precision. For this reason, we motivate and introduce relative metrics on reachability time, external language and simulation relation to quantify the precision of our abstraction. Our main result is to propose a novel algorithm to construct a timed automaton that is an approximate timed abstraction of a hybrid automaton with desired precision, and study its convergence properties. For an extended version of this paper refer to .

In formally analyzing and developing industrial sized systems we are often confronted with the problem of expressing re- altime properties. Especially in safety critical applications as, for example, in embedded systems or in control software these properties are crucial for the fight functioning of the systems. There are numerous suitable approaches that allow us to spec- ify realtime properties: MTL, TLA or VSE-SL to name a few, and also there are various tools available to formally develop such systems. But in most cases the approaches are trimmed for their own highly specialized application area. We try to overcome this restriction by exploiting the advantages of a (fairly general) formal development tool like VSEolI and the rather specialized Hybrid Automata by combining these two approaches.

Independent Dynamics Hybrid Automata (IDA) describe a new class of hybrid automata that extends decidable O-minimal automata by further allowing identity resets. We define the conditions under which reachability is decidable over IDA. These conditions involve the satisfiability of first-order formulæ that limit the interval of time we need to consider to study reachability. In order to prove the decidability of reachability we mainly exploit the decidability of the first-order formulæ which define IDA. IDA are useful in the ...

In this paper we introduce the problem of reach- ability analysis of hybrid automata to decide safety properties. Then we describe ARIADNE, an in-progress open environment to design algorithms for computing with hybrid automata. We show that ARIADNE relies on a rigorous computable analysis theory to represent geometric objects, in order to achieve provable approximation bounds along the computations. The proposed tool differs from existing ones because it relies on a sound theoretical basis for the semantics of operators in continuous space and time, making available exact and approx- imate, but error-bounded operations on geometric points and sets. Currently the geometry module is substantially completed, and work is in progress on the evaluation module. As a first application, we will use ARIADNE to compute the reachable sets of a challenging collection of benchmarks whose safety properties have practical interest.

In this article, we propose a refinement of the modeling of genetic regulatory networks based on the approach of René Thomas. The notion of delays of activation/inhibition are added in order to specify which variable is faster affected by a change of its regulators. The formalism of linear hybrid automata is well suited to allow such refinement. We then use HyTech for two purposes: (1) to find automatically all paths from a specified initial state to another one and (2) to synthesize constraints on the delay parameters in order to follow any specific path.

In this paper we tackle the decidability of marking reachability for a hybrid formalism based on Petri nets. The model we consider is the untimed version of First–Order Hybrid Petri Nets: it combines a discrete Petri net and a continuous Petri net, the latter being a fluid version of a usual discrete Petri net. It is suggested that the decidability results should be pursued exploiting a hierarchy of models as it has been done in the framework of Hybrid Automata. In this paper we define the class of Single–Rate Hybrid Petri Nets: the continuous dynamics of these nets is such that the vector of the marking derivatives of the continuous places is constant but for a scalar factor. This class of nets can be seen as the counterpart of timed automata with skewed clocks. We prove that the reachability problem for this class can be reduced to the reachability problem of an equivalent discrete net and thus it is decidable. 1

The use of formal methods, techniques and tools may generally guarantee a systems’ safe operation. Such a process includes system modeling with a mathematical model, which is an approximation of the physical system, and is used to make easier the next step of analysis. Formal analysis of hybrid systems, which involve mixed continuous-valued and discrete dynamics, is concerned with verifying whether a hybrid system satisfies a desired specification, like avoiding an unsafe region of the state space. In this paper, we examine the general impact of hybrid automata on modeling and analyzing hybrid systems and we discuss in particular some advantages that arise when exploiting them in the context of particular methods for verifying the reachability of states in common paradigms that have already being investigated with other classical methods. Finally, we use two case studies concerning different classes of hybrid automata to demonstrate the applicability and the efficiency of exploiting...

A Petri net-based design inference network (PNDN) architecture is presented in this paper. The network models the logical behaviour of any design artefact developed by designers at the conceptual design level by representing the subfunctions and their inter-relationships to perform a required overall function. The theoretical framework in developing the PNDN is based on the improved theory of Petri nets and hybrid automata. The theoretical PNDN architecture was implemented in a C++ based software called the design network simulator (DNS). The logical behaviour of a design artefact is modelled through the token flow within the PNDN. The token flow model is developed both for deterministic and nondeterministic PNDN, which involves uncertainties. In this paper we present the mathematical formalism of the deterministic token flow through the PNDN. We also provide a conceptual design example in order to explain the application of our theoretical architecture for structuring the PNDN.

Unified Modeling Language is proposed as an effective framework for constructing simulation models of hybrid manufacturing systems. The plant processes jobs through a network of machines and buffers. Machines are represented as hybrid automata in which continuous time dependent operating conditions are modeled through ordinary differential equations. Machines are connected through buffers. Modularity, versatility and maintenance of the model are