Adaptive Prescribed-Time Control of Uncertain Self-Restructuring Nonaffine Nonlinear Systems

Area of Science:

• Control theory
• Nonlinear systems
• Adaptive control

Background:

• Strict-feedback nonlinear systems often exhibit complex dynamics, including self-restructuring structures and nonaffine terms.
• Achieving exact full state stabilization within a prescribed finite time remains a significant challenge for these systems.

Purpose of the Study:

• To develop an adaptive prescribed-time control scheme for uncertain strict-feedback nonlinear systems.
• To guarantee exact full state zero-error stabilization within a user-specified finite settling time, regardless of initial conditions.

Main Methods:

• A time-varying scaling state transformation is employed in controller design.
• The Nussbaum function is utilized to manage unknown self-restructuring control gains.
• A novel adaptive estimation strategy is proposed for time-state-dependent lumped uncertainties, involving freezing time and states.

Main Results:

• The proposed adaptive control scheme ensures all system states converge to zero within the prescribed finite time.
• The controller effectively handles uncertainties arising from self-restructuring structures and nonaffine dynamics.
• Numerical simulations validate the scheme's effectiveness on a piezoelectric-actuated stage and a second-order nonlinear system.

Conclusions:

• The developed adaptive prescribed-time control strategy offers a robust solution for stabilizing complex nonlinear systems.
• The method provides precise finite-time convergence, addressing limitations of traditional control approaches for systems with unknown dynamics.