Adaptive Fuzzy Finite-Time Control for Nonstrict-Feedback Nonlinear Systems.

Area of Science:

• Control Engineering
• Nonlinear Systems Theory
• Adaptive Control Systems

Background:

• Nonstrict-feedback nonlinear systems (NFNSs) often possess unknown dynamics, posing significant control challenges.
• Existing finite-time control methods can face singularity issues, particularly with virtual control laws.
• Adaptive control strategies are crucial for systems with uncertain parameters and structures.

Purpose of the Study:

• To develop a novel adaptive fuzzy finite-time control (AFFTC) strategy for NFNSs with unknown dynamics.
• To overcome the limitations of nonstrict-feedback structures and unknown system uncertainties.
• To address and surmount singularity hindrances in finite-time control design.

Main Methods:

• Utilized the backstepping technique for recursive controller design.
• Introduced a smooth switch function (SSF) to manage system non-linearities and uncertainties.
• Developed a novel C¹ adaptive fuzzy finite-time control strategy.

Main Results:

• The proposed AFFTC strategy effectively counteracts nonstrict-feedback structures and unknown dynamics.
• Singularity issues associated with differentiating virtual control laws were successfully surmounted.
• The tracking error was demonstrated to converge to a small neighborhood of the origin in finite time.

Conclusions:

• The developed AFFTC method provides an effective solution for controlling NFNSs with unknown dynamics.
• The strategy offers improved robustness and finite-time convergence compared to existing methods.
• Simulation results validate the theoretical findings and practical efficacy of the proposed control approach.