Application of (min,+) semiring to the optimal control of disassembly manufacturing systems

Abstract

Komenda et al. showed (2001) that deterministic continuous Petri nets can be represented by systems of functional (min,+)-linear equations of the fixed-point type, which can be viewed as linear integral equations in the sense of idempotent integration. In this paper these results on modelling and control are applied to disassembly manufacturing systems. This approach addresses questions like determination of transient and periodic regimes and leads to the optimal control with respect to the "Just in time criterion". Throughout a small scale example the application of our approach to the determination of asymptotic behaviour and transfer function of a manufacturing system is illustrated. Moreover, a concept of modified optimal control is presented in this example.