Boundedness Analysis Research Articles

Boundedness analysis of finitely recursive processes. II. Sequential and hybrid processes

Part I of this paper has shown that a subclass of the finitely recursive processes (FRP), composed without the sequential composition operator (SCO), is bounded. In this sequel it is first shown that boundedness is not guaranteed but decidable for the subclass of FRP built using the SCO, but without the parallel composition operator (PCO). To overcome the limitation in modeling using the SCO only, some bounded hybrid subclasses have been proposed where both the SCO and PCO can be used, although in a restricted fashion. Finally, the proposed hybrid framework is used to model a job-shop, and its potential in the specification and design of supervisory control systems is demonstrated.

Lagrange stability and boundedness of discrete event systems

Recently it has been shown that the conventional notions of stability in the sense of Lyapunov and asymptotic stability can be used to characterize the stability properties of a class of “logical” discrete event systems (DES). Moreover, it has been shown that stability analysis via the choice of appropriate Lyapunov functions can be used for DES and can be applied to several DES applications including manufacturing systems and computer networks (Passino et al. 1994, Burgess and Passino 1994). In this paper we extend the conventional notions and analysis of uniform boundedness, uniform ultimate boundedness, practical stability, finite time stability, and Lagrange stability so that they apply to the class of logical DES that can be defined on a metric space. Within this stability-theoretic framework we show that the standard Petri net-theoretic notions of boundedness are special cases of Lagrange stability and uniform boundedness. In addition we show that the Petri ent-theoretic approach to boundedness analysis is actually a Lyapunov approach in that the net-theoretic analysis actually produces an appropriate Lyapunov function. Moreover, via the Lyapunov approach we provide a sufficient condition for the uniform ultimate boundedness of General Petri nets. To illustrate the Petri net results, we study the boundedness properties of a rate synchronization network for manufacturing systems. In addition, we provide a detailed analysis of the Lagrange stability of a single-machine manufacturing system that uses a priority-based part servicing policy.