Stable neural-network-based adaptive control for sampled-data nonlinear systems

Area of Science:

• Control Systems Engineering
• Artificial Intelligence
• Nonlinear Dynamics

Background:

• Controlling complex multi-input-multi-output (MIMO) sampled-data nonlinear systems with unknown dynamics presents significant challenges.
• Existing adaptive control methods may struggle with inherent nonlinearities and uncertainties in such systems.

Purpose of the Study:

• To develop a stable neural-network (NN)-based adaptive control approach for MIMO sampled-data nonlinear systems.
• To integrate NN approximation capabilities with variable structure control (VSC) for robust performance.

Main Methods:

• The proposed method combines a neural network (NN) approach with an adaptive implementation of variable structure control (VSC) with a sector.
• VSC is utilized to maintain system states within the NN's operational region and provide supplementary control.
• Stability and tracking error convergence are rigorously proven, and parameter tuning is discussed.

Main Results:

• The adaptive control strategy ensures complete stability and convergence of the tracking error.
• The asymptotic error is shown to depend on NN approximation errors and unmodeled dynamics frequency range.
• Effectiveness demonstrated through simulation studies on a two-link manipulator.

Conclusions:

• The integrated NN and VSC approach offers a stable and effective solution for controlling complex nonlinear sampled-data systems.
• The method provides robust performance by managing unknown nonlinearities and system uncertainties.
• This technique holds promise for applications requiring precise control of dynamic systems.