Hybrid automata

Verification of Digital and Hybrid Systems pp Cite as. A hybrid automaton is a formal model for a mixed discrete-continuous System.

W e classify hybrid automata acoording to what questions about their behavior can be answered algorithmically. The Classification reveals structure on mixed discrete-continuous State Spaces that was previously studied on purely discrete state Spaces only.

In particular, various classes of hybrid automata induce finitary trace equivalence or similarity, or bisimilarity relations on an uncountable State space, thus permitting the application of various model-checking techniques that were originally developed for finitestate Systems.

The Theory of Hybrid Automata

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Advertisement Hide. This process is experimental and the keywords may be updated as the learning algorithm improves. This is a preview of subscription content, log in to check access. Alur, C. Courcoubetis, T. Henzinger, and P. Hybrid automata: an algorithmic approach to the specification and verification of hybrid Systems.

Grossman, A.

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Nerode, A. Ravn, and H. Springer-Verlag, Google Scholar. Nicollin, A. Olivero, J. Sifakis, and S. An approach to the descrip-tion and analysis of hybrid Systems. Courcoubetis, N. Halbwachs, T. Henzinger, P.In automata theorya hybrid automaton plural: hybrid automata or hybrid automatons is a mathematical model for precisely describing systems in which digital computational processes interact with analog physical processes.

A hybrid automaton is a finite state machine with a finite set of continuous variables whose values are described by a set of ordinary differential equations. This combined specification of discrete and continuous behaviors enables dynamic systems that comprise both digital and analog components to be modeled and analyzed. In general, hybrid automata have been used to model and analyze a variety of embedded systems including vehicle control systems, air traffic control systems, mobile robotsand processes from systems biology.

So this is a labeled multidigraph. Hybrid automata come in several flavors: The Alur-Henzinger hybrid automaton is a popular model; it was developed primarily for algorithmic analysis of hybrid systems model checking. The HyTech model checking tool is based on this model. This model enables compositional modeling and analysis of hybrid systems. Another formalism which is useful to model implementations of hybrid automaton is the lazy linear hybrid automaton.

Given the expressiveness of hybrid automata it is not surprising that simple reachability questions are undecidable for general hybrid automata. In fact, a straightforward reduction from Counter machine to three variables hybrid automata two variables for storing counter values and one to restrict spending a unit-time per location proves the undecidablity of the reachability problem for hybrid automata.

A sub-class of hybrid automata are timed automata [2] where all of the variables grow with uniform rate i. Such restricted variables can act as timer variables, called clocks, and permit modeling of real-time systems. Other notable decidable subclasses include initialized rectangular hybrid automata [3]one-dimensional piecewise-constant derivatives PCD systems [4]priced timed automata [5]and constant-rate multi-mode systems [6].

From Wikipedia, the free encyclopedia.

hybrid automata

Journal of Computer and System Sciences. Optimal scheduling for constant-rate multi-mode systems. Categories : Automata computation Differential equations. Namespaces Article Talk. Views Read Edit View history.

Hybrid automaton

Help Learn to edit Community portal Recent changes Upload file. Download as PDF Printable version.The verification of continuous and hybrid systems is a challenging problem, and various approaches are currently being investigated to overcome the complexities of representing and computing with continuous sets of states.

Since verification problems are generally undecidable for such systems, experimental results are vital for evaluating and developing new ideas. The SpaceEx tool platform is designed to facilitate the implementation of algorithms related to reachability and safety verification. This document provides a brief overview of the capabilities of SpaceEx and the concepts behind SpaceEx State Space Explorer.

Examples and Tutorials. Introduction to SpaceEx This document provides a brief overview of the capabilities of SpaceEx and the concepts behind Plotting Options with SpaceEx. Friday, 3 August Wednesday, 9 March Bugfix Update: SpaceEx v0. Thursday, 9 July A bugfix update for SpaceEx is now available for download.

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A major bug has been fixed that could lead to wrong reachability results, so an update is strongly recommended. All contents released under GPL v.Often, the term "hybrid dynamical system" is used, to distinguish over hybrid systems such as those that combine neural nets and fuzzy logicor electrical and mechanical drivelines.

A hybrid system has the benefit of encompassing a larger class of systems within its structure, allowing for more flexibility in modeling dynamic phenomena. In general, the state of a hybrid system is defined by the values of the continuous variables and a discrete mode.

The state changes either continuously, according to a flow condition, or discretely according to a control graph. Continuous flow is permitted as long as so-called invariants hold, while discrete transitions can occur as soon as given jump conditions are satisfied. Discrete transitions may be associated with events.

Hybrid systems have been used to model several cyber-physical systems, including physical systems with impactlogic-dynamic controllersand even Internet congestion. A canonical example of a hybrid system is the bouncing balla physical system with impact.

Here, the ball thought of as a point-mass is dropped from an initial height and bounces off the ground, dissipating its energy with each bounce. The ball exhibits continuous dynamics between each bounce; however, as the ball impacts the ground, its velocity undergoes a discrete change modeled after an inelastic collision. A mathematical description of the bouncing ball follows. A hybrid system describing the ball is as follows:. These equations state that when the ball is above ground, it is being drawn to the ground by gravity.

Effectively, this describes the nature of the inelastic collision. The bouncing ball is an especially interesting hybrid system, as it exhibits Zeno behavior.

Zeno behavior has a strict mathematical definition, but can be described informally as the system making an infinite number of jumps in a finite amount of time. In this example, each time the ball bounces it loses energy, making the subsequent jumps impacts with the ground closer and closer together in time. It is noteworthy that the dynamical model is complete if and only if one adds the contact force between the ground and the ball. Indeed, without forces, one cannot properly define the bouncing ball and the model is, from a mechanical point of view, meaningless.

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The simplest contact model that represents the interactions between the ball and the ground, is the complementarity relation between the force and the distance the gap between the ball and the ground.

One also notices from basic convex analysis that the complementarity relation can equivalently be rewritten as the inclusion into a normal cone, so that the bouncing ball dynamics is a differential inclusion into a normal cone to a convex set.

See also the other references on non-smooth mechanics.

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There are approaches to automatically proving properties of hybrid systems e. Common techniques for proving safety of hybrid systems are computation of reachable sets, abstraction refinementand barrier certificates.

Most verification tasks are undecidable, [1] making general verification algorithms impossible. Instead, the tools are analyzed for their capabilities on benchmark problems. A possible theoretical characterization of this is algorithms that succeed with hybrid systems verification in all robust cases [2] implying that many problems for hybrid systems, while undecidable, are at least quasi-decidable. Two basic hybrid system modeling approaches can be classified, an implicit and an explicit one.

The explicit approach is often represented by a hybrid automatona hybrid program or a hybrid Petri net. The implicit approach is often represented by guarded equations to result in systems of differential algebraic equations DAEs where the active equations may change, for example by means of a hybrid bond graph.

As a unified simulation approach for hybrid system analysis, there is a method based on DEVS formalism in which integrators for differential equations are quantized into atomic DEVS models. These methods generate traces of system behaviors in discrete event system manner which are different from discrete time systems. From Wikipedia, the free encyclopedia.

Henzinger, Peter W. Categories : Systems theory Differential equations Dynamical systems Control theory. Namespaces Article Talk.Such a system can be formalized by a hybrid automaton which equipped with finitely many discrete states and continuous variables. A state of a hybrid automaton can be denoted by a discrete state along with a valuation of the variables. The reachability problem on hybrid automata can be defined as follows.

For example, in safety verification, we want to check whether an unsafe state is reachable by the system. Since the reachability problem on hybrid automata is not decidablethe tool computes an over-approximation for a reachable state set.

If a given state is not included then it is absolutely unreachable. The over-approximation set is represented as a finite set of Taylor models. Besides chaotic and stiff continuous dynamics defined by non-linear ODEs, the following difficulties still exist in all reachability computation problems for non-linear systems. Working on 1 and 2 allows us to verify more general properties. Only a combination of them gives a challenge.

Notice that computing reachable set over-approximations from a tiny initial set is often easy even on large scale systems, especially the initial values of some variables take single values. Considering 3 allows us to work on more realistic hybrid systems. The analysis of them often generates a large number of branches which could cause an exponential growth of the computation time.

hybrid automata

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hybrid automata

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hybrid automata

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