Adaptive Neural Network Based Control of Noncanonical Nonlinear Systems

Area of Science:

• Control Systems Engineering
• Artificial Intelligence
• Nonlinear Dynamics

Background:

• Adaptive control of nonlinear systems is challenging, especially for noncanonical forms lacking explicit relative degrees.
• Neural network (NN) models of noncanonical systems also lack explicit relative degree structures, complicating adaptive controller design.
• Existing adaptive control methods often rely on canonical system structures, leaving noncanonical NN models under-addressed, particularly with parametric uncertainties.

Purpose of the Study:

• To develop an adaptive neural network-based control strategy for noncanonical nonlinear systems with significant parametric uncertainties.
• To address the challenge of designing adaptive controllers for noncanonical NN system models that lack explicit relative degree structures.
• To introduce a novel reparameterization technique for noncanonical NN models to facilitate adaptive control design.

Main Methods:

• Utilized neural network approximation to model noncanonical nonlinear systems.
• Developed a reparameterization method for noncanonical NN system models based on relative degree formulation.
• Derived parameterized adaptive controllers ensuring closed-loop stability and asymptotic output tracking.
• Validated the control design through simulations on an illustrative example.

Main Results:

• Successfully demonstrated the necessity of reparameterizing noncanonical NN system models for adaptive control.
• Introduced and applied a relative degree formulation for reparameterizing general NN system models.
• Achieved guaranteed closed-loop stability and asymptotic output tracking for the controlled noncanonical systems.
• Verified the effectiveness of the proposed adaptive control design method via simulation.

Conclusions:

• The proposed adaptive control strategy effectively handles noncanonical nonlinear systems with large parametric uncertainties.
• Reparameterization using relative degree formulation is crucial for designing adaptive controllers for noncanonical NN models.
• The developed method offers a viable solution for a previously open research problem in adaptive control.