Fixed-Time Fuzzy Control for a Class of Nonlinear Systems

Area of Science:

• Control Theory
• Nonlinear Systems
• Fuzzy Logic Systems

Background:

• Fixed-time control is crucial for systems requiring predictable settling times.
• Existing methods often struggle with completely unknown nonlinearities.
• Approximation errors in fuzzy models pose challenges for fixed-time control design.

Purpose of the Study:

• To develop a fixed-time tracking control for nonlinear systems with unknown nonlinearities.
• To address approximation errors inherent in fuzzy-logic system modeling.
• To propose a novel control scheme distinct from traditional adaptive methods.

Main Methods:

• Utilizing fuzzy-logic systems to model unknown nonlinearities.
• Developing a new criterion for fixed-time stability analysis.
• Proposing a novel fixed-time control scheme.
• Establishing two novel inequalities to analyze system stability.

Main Results:

• The proposed fuzzy control scheme ensures fixed-time stability for the nonlinear system.
• System performance is guaranteed within a fixed settling time.
• The upper bound of the settling time is solely dependent on design parameters.

Conclusions:

• The developed fuzzy control strategy effectively manages unknown nonlinearities in fixed-time control.
• The new stability criterion and inequalities provide robust analytical tools.
• This approach offers a predictable and parameter-dependent settling time for system control.