In this paper we introduce CPDPs (Communicating Piecewise Determin-istic Markov Processes) as an automata formalism for compositional specification of hybrid systems of the type PDP. A CPDP can be seen as an automaton representation of a PDP, with the extra possibility of interaction with other processes via a new concept that we call passive transitions.… (More)
No part of this work may be reproduced by print, photocopy or any other means without the permission in writing from the author.
— 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… (More)
We study the construction of the maximal controlled invariant set of switched linear systems. We consider two cases, based on whether fast switches are allowed or not. For both cases, iterative algorithms are given to construct such sets.
Gene regulatory networks capture interactions between genes and other cell substances, resulting in various models for the fundamental biological process of transcription and translation. The expression levels of the genes are typically measured as mRNA concentration in micro-array experiments. In a so-called genetic perturbation experiment, small… (More)
We study the control problem from the point of view of the behavioral systems theory. Two controller constructions, called canonical controllers, are introduced. We prove that for linear time invariant behaviors, the canonical controllers implement the desired behavior if and only if there exists a controller that implements it. We also investigate the… (More)
A fundamental question in systems and control theory concerns the characterization of the set of achievable closed-loop systems for a given plant system and a controller system to be designed. This problem, for example, shows up in assessing the 'limits of performance' of a controlled system. Similar problems have been studied by researchers in automata… (More)
In this paper we discuss the concept of compatible behavior in-terconnections. We distinguish the case where all variables are available for interconnection (total interconnection) from the case where only a part of them are (partial interconnection). The main idea behind the notion of compatibility for total in-terconnection is causality of (the effect of)… (More)
— Model checking can be used to verify temporal properties of hybrid automata. However, model checking is not decidable in general. We overcome this difficulty by considering a durational graph abstraction, for which model checking is decidable. The contribution of this paper is to show that, given a hybrid automaton and the durational graph abstraction,… (More)
In this paper we formulate a general framework based on the behavioral approach to dynamical systems, in which various issues regarding interconnection of systems can be addressed. The main part of the framework is that interconnections or compositions of systems can be modelled with interconnection of behaviors and generalized projection operations.… (More)