State dependent observer synthesis-a module for supervisory control of stochastic discrete event dynamic systems

Abstract

Stochastic Petri net (SPN) models are successfully used to study the dynamics of stochastic discrete events dynamic systems (SDEDS). This paper deals with a state dependent automatic observer synthesis for SDEDS, used as a module for supervisory control of DEDS. The underlying theory arises naturally in the field of performability analysis of stochastic system. In order to explain the procedure a digital computer control and communication system is considered for which the SPN model is obtained. For this model the transition probabilities are assumed to be exponentially distributed. The model order is reduced using the knowledge of the system and the standard procedure. For this reduced order model the state transition rate matrix is obtained. This matrix is state dependent and the transition rate matrix is used to synthesise the state observer. Results obtained on the system are included.