Quantized Control of Markov Jump Nonlinear Systems Based on Fuzzy Hidden Markov Model

Area of Science:

• Control Systems Engineering
• Nonlinear Systems Analysis
• Stochastic Processes

Background:

• Nonlinear Markov jump systems are complex due to inherent uncertainties.
• Asynchronous control and stochastic quantization introduce significant challenges in system stability and performance.
• Guaranteed cost control (GCC) is crucial for managing performance bounds in uncertain systems.

Purpose of the Study:

• To develop an asynchronous guaranteed cost control (GCC) strategy for nonlinear Markov jump systems.
• To address the challenges posed by stochastic quantization and nonsynchronous controllers.
• To ensure both asymptotic stability and minimize the upper bound of the GCC performance.

Main Methods:

• Utilizing a Hidden Markov Model (HMM) to represent controller nonsynchronization and quantization randomness.
• Applying the Takagi-Sugeno fuzzy technique for system modeling and controller design.
• Employing the Lyapunov function approach to derive stability and performance conditions.

Main Results:

• A sufficient condition for the existence of the desired asynchronous GCC controller is established.
• The proposed method guarantees the asymptotic stability of the closed-loop system.
• The minimal upper bound of the guaranteed cost control performance is achieved.

Conclusions:

• The developed control approach effectively handles asynchronous control and stochastic quantization in nonlinear Markov jump systems.
• The Takagi-Sugeno fuzzy technique combined with Lyapunov stability analysis provides a robust framework for GCC.
• The presented methods are validated through numerical examples, demonstrating their correctness and reliability.