Ontology View on Automata Theory

The summary of automata theory ontology is presented in the paper. It is based on the following dependences: a type of an automaton – the language accepted by the automaton – applications. The given ontology does not claim to be exhaustive as automata theory is very extensive and it is a complicated problem to survey all its aspects within one article. Only the main properties of automata and their applications are considered

Complexity of stability and controllability of elementary hybrid systems

Caption title.Includes bibliographical references (p. 16-18).Supported by ARO. DAAL-03-92-G-0115 Supported by NATO. CRG-961115Vincent D. Blondel, John N. Tsitsiklis

Modeling and analysis using hybrid Petri nets

This paper is devoted to the use of hybrid Petri nets (PNs) for modeling and control of hybrid dynamic systems (HDS). Modeling, analysis and control of HDS attract ever more of researchers' attention and several works have been devoted to these topics. We consider in this paper the extensions of the PN formalism (initially conceived for modeling and analysis of discrete event systems) in the direction of hybrid modeling. We present, first, the continuous PN models. These models are obtained from discrete PNs by the fluidification of the markings. They constitute the first steps in the extension of PNs toward hybrid modeling. Then, we present two hybrid PN models, which differ in the class of HDS they can deal with. The first one is used for deterministic HDS modeling, whereas the second one can deal with HDS with nondeterministic behavior. Keywords: Hybrid dynamic systems; D-elementary hybrid Petri nets; Hybrid automata; Controller synthesi

Modeling and Analysis of Hybrid Dynamic Systems Using Hybrid Petri Nets

International audienceWe consider in this paper the extensions of the PN formalism in the direction of hybrid modeling. We briefly presents hybrid dynamic systems. Then the hybrid automata model. Is introduced and we discuss continuous Petri nets. These models are obtained from discrete PNs by the fluidification of the markings. They constitute the first steps in the extension of PNs toward hybrid modeling. Two hybrid PN models, which differ in the class of HDS they can deal with, are studied. The first one is used for deterministic HDS modeling, whereas the second one can deal with HDS with nondeterministic behavior. The general control structure based on hybrid PNs is briefly described

Control Synthesis for a Class of Hybrid Systems Subject to Configuration-Based Safety Constraints

We examine a class of hybrid systems which we call Composite Hybrid Machines (CHM's) that consists of the concurrent (and partially synchronized) operation of Elementary Hybrid Machines (EHM's). Legal behavior, specified by a set of illegal configurations that the CHM may not enter, is to be achieved by the concurrent operation of the CHM with a suitably designed legal controller. In the present paper we focus on the problem of synthesizing a legal controller, whenever such a controller exists. More specifically, we address the problem of synthesizing the minimally restrictive legal controller. A controller is minimally restrictive if, when composed to operate concurrently with another legal controller, it will never interfere with the operation of the other controller and, therefore, can be composed to operate concurrently with any other controller that may be designed to achieve liveness specifications or optimality requirements without the need to reinvestigate or reverify legality of the composite controller. We confine our attention to a special class of CHM's where system dynamics is rate-limited and legal guards are conjunctions or disjunctions of atomic formulas in the dynamic variables (of the type x less than or equal to x(sub 0), or x greater than or equal to x(sub 0)). We present an algorithm for synthesis of the minimally restrictive legal controller. We demonstrate our approach by synthesizing a minimally restrictive controller for a steam boiler (the verification of which recently received a great deal of attention)

Error Propagation in a System Model

Embodiments of the present subject matter can enable the analysis of signal value errors for system models. In an example, signal value errors can be propagated through the functional blocks of a system model to analyze possible effects as the signal value errors impact incident functional blocks. This propagation of the errors can be applicable to many models of computation including avionics models, synchronous data flow, and Kahn process networks