Periodic Event-Triggered Integral Sliding-Mode Control for T-S Fuzzy Systems

Area of Science:

• Control Systems Engineering
• Fuzzy Logic Systems
• Nonlinear Control Theory

Background:

• Sliding-mode control (SMC) is crucial for robust control of uncertain systems.
• Takagi-Sugeno (T-S) fuzzy systems offer a framework for modeling nonlinearities.
• Event-triggered control (ETC) aims to reduce communication load in control systems.

Purpose of the Study:

• To develop an integral sliding-mode control (ISMC) strategy for T-S fuzzy systems using a periodic event-triggered method.
• To overcome the limitation of uniform upper bounds on inter-execution times in existing ETC methods.
• To ensure the ultimate boundedness of the sliding motion under the proposed control law.

Main Methods:

• A novel sliding variable error function is incorporated into the event-triggering mechanism to relax inter-execution time constraints.
• A new sliding-mode switching function, utilizing triggering state information, is proposed for designing the event-triggered ISMC law.
• Linear matrix inequality (LMI) conditions are derived to guarantee system boundedness and facilitate controller gain computation.

Main Results:

• The proposed event-triggered ISMC law ensures the ultimate boundedness of the sliding motion for T-S fuzzy systems.
• The method effectively removes the assumption of a uniform upper bound on inter-execution times.
• Controller gains can be systematically determined by solving the derived LMI conditions.

Conclusions:

• The developed event-triggered ISMC provides a robust and communication-efficient control solution for T-S fuzzy systems.
• The proposed approach enhances stability guarantees by ensuring ultimate boundedness of the sliding mode.
• The theoretical findings are validated through three illustrative examples, demonstrating practical applicability.