Novel flexible fixed-time stability theorem and its application to sliding mode control nonlinear systems

Area of Science:

• Control Theory
• Nonlinear Systems
• Applied Mathematics

Background:

• Fixed-time stability (FxTS) is crucial for nonlinear system control, balancing speed and energy.
• Existing FxTS inequalities can be conservative, limiting performance.
• Sliding Mode Control (SMC) is a robust control technique often used in nonlinear systems.

Purpose of the Study:

• To develop a new FxTS theorem with less conservative inequalities for improved control performance.
• To propose a novel integral sliding mode surface and controller for fixed-time control.
• To demonstrate the effectiveness of the proposed method in controlling chaotic and electromechanical systems.

Main Methods:

• Development of a new FxTS theorem using less conservative inequalities with flexible parameter settings.
• Design of a new integral sliding mode surface and sliding mode controller.
• Application and numerical simulation of the proposed control algorithm to chaotic Lorenz systems and permanent magnet synchronous motor systems.

Main Results:

• The proposed FxTS theorem allows for more flexible parameter settings and provides an exact upper bound on settling time.
• The new integral sliding mode controller achieved an 18% reduction in convergence time compared to traditional FxTS SMC.
• An estimated 41% reduction in the upper bound of fixed-time waiting time was observed, with improved convergence velocity through parameter adjustment.

Conclusions:

• The proposed FxTS theorem and integral sliding mode control offer a more flexible and superior approach to fixed-time control of nonlinear systems.
• The method demonstrates significant improvements in convergence time and efficiency.
• The findings are validated through successful application to complex chaotic and electromechanical systems.