Performance Regulation of Event-Driven Dynamical Systems Using Infinitesimal Perturbation Analysis

TL;DR

This paper introduces a simple, fast performance regulation method for stochastic event-driven systems using Infinitesimal Perturbation Analysis to compute control gains, demonstrated on diverse models including queueing networks and Petri nets.

Contribution

It develops a robust, real-time control technique for complex stochastic systems based on IPA gradient estimation, applicable across various formal models.

Findings

Effective output tracking demonstrated on multiple models.

Robustness to modeling inaccuracies shown in simulations.

Fast computation suitable for real-time control.

Abstract

This paper presents a performance-regulation method for a class of stochastic timed event-driven systems aimed at output tracking of a given reference setpoint. The systems are either Discrete Event Dynamic Systems (DEDS) such as queueing networks or Petri nets, or Hybrid Systems (HS) with time-driven dynamics and event-driven dynamics, like fluid queues and hybrid Petri nets. The regulator, designed for simplicity and speed of computation, is comprised of a single integrator having a variable gain to ensure effective tracking under time-varying plants. The gain's computation is based on the Infinitesimal Perturbation Analysis (IPA) gradient of the plant function with respect to the control variable, and the resultant tracking can be quite robust with respect to modeling inaccuracies and gradient-estimation errors. The proposed technique is tested on examples taken from various application areas and modeled with different formalisms, including queueing models, Petri-net model of a production-inventory control system, and a stochastic DEDS model of a multicore chip control. Simulation results are presented in support of the proposed approach.