Distributed Stabilization by Probability Control for Deterministic-Stochastic Large Scale Systems : Dissipativity Approach

TL;DR

This paper introduces a dissipativity-based method for stabilizing large-scale deterministic-stochastic systems using probability control, with applications in manufacturing systems to ensure global stability and local balance.

Contribution

It extends dissipativity theory to large-scale systems with stochastic components, providing a new framework for stability analysis and control design.

Findings

Established stability conditions for deterministic-stochastic feedback systems.

Designed procedures for global stabilization of manufacturing systems.

Validated approach through application to production process balancing.

Abstract

By using dissipativity approach, we establish the stability condition for the feedback connection of a deterministic dynamical system $\Sigma$ and a stochastic memoryless map $\Psi$. After that, we extend the result to the class of large scale systems in which: $\Sigma$ consists of many sub-systems; and $\Psi$ consists of many "stochastic actuators" and "probability controllers" that control the actuator's output events. We will demonstrate the proposed approach by showing the design procedures to globally stabilize the manufacturing systems while locally balance the stock levels in any production process.