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Asynchronous control for semi-Markov switching systems with singular perturbation and an improved protocol.

Lifei Xie¹, Yunliang Wang¹, Jun Cheng¹

¹School of Mathematics and Statistics, Guangxi Normal University, Guilin 541006, China.

ISA Transactions

|March 27, 2023

Summary

This study introduces an improved protocol for semi-Markov switching systems, reducing network resource use and enhancing control performance. It uses a nonhomogeneous hidden semi-Markov model for better system-controller matching.

Keywords:

Dynamic event-triggered protocol Hidden Markov model Semi-Markov switching systems Singularly perturbation

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Area of Science:

Control Systems Engineering
Stochastic Systems Analysis
Networked Control Systems

Background:

Semi-Markov switching systems present challenges in asynchronous control due to mode uncertainties.
Existing triggering protocols often lead to high network resource occupation.
Singular perturbation complicates the stability analysis and control design.

Purpose of the Study:

To develop an improved triggering protocol for semi-Markov switching systems with singular perturbation.
To reduce network communication frequency while maintaining control performance.
To address mode mismatch using a nonhomogeneous hidden semi-Markov model.

Main Methods:

An improved triggering protocol utilizing two auxiliary offset variables.
Application of a nonhomogeneous hidden semi-Markov model to handle system-controller mode discrepancies.
Lyapunov techniques to derive parameter-dependent sufficient conditions for stochastic stability.

Main Results:

The proposed protocol effectively reduces communication frequency by allowing more flexible information transmission.
The nonhomogeneous hidden semi-Markov model accurately captures mode mismatches.
Sufficient conditions ensuring stochastic stability with predetermined performance are established.

Conclusions:

The developed asynchronous control strategy is effective for semi-Markov switching systems with singular perturbation.
The improved protocol offers a practical solution for resource-constrained networked control systems.
Validation through a numerical example and a tunnel diode circuit model confirms the theoretical findings.