Output-Feedback Control for Fuzzy Singularly Perturbed Systems: A Nonhomogeneous Stochastic Communication Protocol...

Area of Science:

• Control Systems Engineering
• Fuzzy Logic Systems
• Stochastic Processes

Background:

• Takagi-Sugeno fuzzy systems are widely used but can be sensitive to communication constraints.
• Existing stochastic communication protocols (SCPs) often assume homogeneous Markov chains, which may not accurately reflect real-world network dynamics.
• Output-feedback control (OFC) design for singular perturbed systems with communication uncertainties remains a challenge.

Purpose of the Study:

• To design an output-feedback control (OFC) strategy for Takagi-Sugeno fuzzy singular perturbed systems.
• To propose a novel stochastic communication protocol (SCP) based on a nonhomogeneous Markov chain to improve communication reliability and reduce load.
• To develop an asynchronous OFC law using a hidden Markov process observer for uncertain network modes.

Main Methods:

• Design of a novel stochastic communication protocol (SCP) scheduled by a nonhomogeneous Markov chain with a polytope-structure-based transition probability matrix.
• Development of a hidden Markov process observer to detect network modes under partly unidentified detection probabilities.
• Formulation of an asynchronous output-feedback control (OFC) law.
• Establishment of a new Lyapunov-Krasovskii functional incorporating singular perturbation and nonhomogeneous Markov processes to guarantee stochastic stability.

Main Results:

• A sufficient condition for the stochastic stability of the closed-loop system is derived.
• The asynchronous controller design is explicitly presented.
• The proposed methodology demonstrates improved performance and reliability in handling communication uncertainties.

Conclusions:

• The developed asynchronous OFC strategy effectively addresses the challenges posed by communication constraints in Takagi-Sugeno fuzzy singular perturbed systems.
• The nonhomogeneous Markov chain-based SCP offers a more realistic approach to modeling network behavior compared to homogeneous SCPs.
• The study validates the proposed methodology through a practical example, confirming its effectiveness.