Adaptive Neural Control of Pure-Feedback Nonlinear Time-Delay Systems via Dynamic Surface Technique

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Adaptive Control Theory

Background:

• Nonaffine pure-feedback systems present significant control challenges due to unknown nonlinearities and time delays.
• Traditional backstepping methods can lead to computational complexity, known as the 'explosion of complexity'.
• Robust stabilization is crucial for systems operating under uncertain conditions and time variations.

Purpose of the Study:

• To develop a robust stabilization technique for nonaffine pure-feedback systems with unknown time-delay functions and perturbed uncertainties.
• To overcome the control design difficulties associated with nonaffine structures and unknown time-varying parameters.
• To reduce the number of adaptive parameters required in the control design while ensuring system stability.

Main Methods:

• Introduction of novel continuous packaged functions to handle unknown nonlinear terms and time delays without requiring approximation by radial basis function (RBF) neural networks.
• Application of dynamic surface control (DSC) to mitigate the 'explosion of complexity' inherent in backstepping designs.
• Utilization of function separation, Lyapunov-Krasovskii functionals, and hyperbolic tangent functions to address challenges posed by unknown time-delay functions.

Main Results:

• The proposed adaptive neural DSC significantly reduces the number of adaptive parameters.
• Semiglobal uniform ultimate boundedness of all closed-loop system signals is guaranteed.
• Simulation studies validate the effectiveness of the developed robust stabilization scheme.

Conclusions:

• The novel control strategy effectively addresses robust stabilization for nonaffine pure-feedback systems with uncertainties and time delays.
• The integration of continuous packaged functions, DSC, and adaptive neural networks offers a computationally efficient and stable control solution.
• The presented method provides a reliable approach for enhancing the performance and stability of complex dynamic systems.