Structural Sensitivity Analysis of Discrete Event Systems by Inversion

We consider a Discrete Event System (DES) modeled by a generalized semi-Markov scheme. We view the system as an input-output system, where the input is a sequence of event lifetimes, and the output is the resulting sequence of events, states, and transition epochs. The system is observed via an observation map, and we investigate the problem of extracting the event lifetimes from observations of the output, referred to as inversion. We give a general set of neceesary and sufficient conditions for invertibility of the system, and specialize those conditions for various senarios of the observation map. For an invertible system, we give an algorithm for inverting the observations to get the event lifetimes. We propose a method of using the extracted event lifetimes of a nominal system to construct the output trajectories of structurally perturbed systems. Our results extend the method of perturbation analysis to the problem of constructing the perturbed trajectory for a system which changes in state-space and transition structure.