SOS based robust H(∞) fuzzy dynamic output feedback control of nonlinear networked control systems

Area of Science:

• Control Engineering
• Systems Science
• Fuzzy Logic Systems

Background:

• Networked control systems (NCS) face challenges from network-induced delays.
• Nonlinear systems require advanced control strategies for stability and performance.
• Fuzzy logic offers a robust framework for handling system uncertainties.

Purpose of the Study:

• To design a fuzzy dynamic output feedback controller for discrete-time nonlinear NCS.
• To accommodate network-induced delays modeled by a finite state Markov process.
• To address practical scenarios with partially known transition probability matrices and mismatched fuzzy models.

Main Methods:

• Utilized Takagi-Sugeno fuzzy models for nonlinear plant representation.
• Modeled network delays using a finite state Markov process with partially known transition probabilities.
• Developed a fuzzy controller with potentially different membership functions and premise variables than the plant, approximating them as polynomial functions.

Main Results:

• Derived sufficient conditions for controller existence using sum of square inequalities.
• Successfully solved the design conditions using YALMIP optimization toolbox.
• Demonstrated the methodology's validity through a numerical example.

Conclusions:

• The proposed methodology provides a practical approach for designing fuzzy controllers in nonlinear NCS with network delays.
• The flexibility in handling mismatched fuzzy models enhances applicability to real-world systems.
• The use of sum of square inequalities and YALMIP offers an effective computational solution.