Pseudo dynamic hybrid systems (original) (raw)

Dynamic Systems (DS) whose behavior results from the interaction of continuous time processes with discrete-event processes, are called Hybrid Dynamic Systems (HYDS). These systems arise in a wide range of applications [l], which explains why a generally accepted notion of HYDS has not yet appeared. In the search for a general mathematical concept of such systems, we have previously presented a linguistic description of some continuous time processes [2]. This approach can be justified by means of the non linear realization theory of the systems [3]. In this way, we obtain a more accurate mathematical description of the dynamic interaction between the continuous device and the discrete event subsystems of the HYDS. We modeled a DS by means of the triplet (X, S, Cp), where X is the state space, S a transformation semigroup, and ip : X x S -+ X the state transition function. In a classical Continuous Time Dynamic System (C-T DS) S is the set of real numbers R, and states evolve with time, according to a set of differential equations. Following the framework developed by Ramadge and Wonham in [4] a Discrete Event Dynamic System (DEDS) can be modeled as a DS over an alphabet U (or event set), where the change of the states takes place in response to the events. In both C-T DS and DEDS theories, it is very natural to use semigroups acting over state spaces which are not everywhere defined; hence we introduce the concept of Pseudo Dynamic Systems (Ps-DS), where we suppose the existence of a partially defined semigroup action. These results are developed in Section 2. Following these preliminaries we present our main result in Section 3, concerning the concept of Pseudo Dynamic Hybrid Systems and some applications.