Fuzzy SMC for Quantized Nonlinear Stochastic Switching Systems With Semi-Markovian Process and Application

Area of Science:

• Control Theory
• Nonlinear Systems
• Stochastic Systems

Background:

• Existing control methods struggle with nonlinear stochastic switching systems under semi-Markovian parameters.
• Signal quantization and T-S fuzzy strategies present significant design challenges.

Purpose of the Study:

• To develop a quantized sliding-mode control (SMC) design for nonlinear stochastic switching systems.
• To address semi-Markovian switching, T-S fuzzy logic, uncertainty, and signal quantization simultaneously.
• To ensure finite-time reachability of the sliding-mode dynamics.

Main Methods:

• A mode-independent sliding surface is employed to mitigate repetitive jumping effects.
• Lyapunov functions are utilized to derive sojourn-time-dependent stochastic stability criteria.
• A fuzzy-model-based SMC law is designed for finite-time convergence.

Main Results:

• The proposed method successfully incorporates quantized control inputs into T-S fuzzy stochastic switching systems.
• Novel stability criteria are established, considering sojourn times and system uncertainties.
• Finite-time reachability of the sliding-mode dynamics is guaranteed.

Conclusions:

• The developed quantized SMC methodology is effective for nonlinear stochastic switching systems.
• The approach provides a robust framework for systems with semi-Markovian switching and signal quantization.
• Demonstrated effectiveness through an application to a modified series DC motor model.