Accelerated Gradient Approach For Deep Neural Network-Based Adaptive Control of Unknown Nonlinear Systems.

Area of Science:

• Adaptive control systems
• Neural network applications in control engineering
• Nonlinear system dynamics

Background:

• Recent adaptive control research connects to Nesterov's accelerated gradient methods, yielding new real-time adaptation laws.
• Prior work on accelerated gradient adaptive controllers assumed linear-in-the-parameters (LIP) uncertainties, limiting their application.
• Previous neural network (NN)-based controllers for non-LIP uncertainties were restricted to single-hidden-layer architectures.

Purpose of the Study:

• To develop a generalized deep neural network (DNN) architecture for adaptive control of nonlinear systems with non-LIP uncertainties.
• To create a novel DNN-based accelerated gradient adaptation scheme for real-time estimation of DNN weights.
• To guarantee global asymptotic tracking error convergence for general nonlinear control affine systems with unknown dynamics and disturbances.

Main Methods:

• Development of a generalized deep neural network (DNN) architecture.
• Implementation of a novel DNN-based accelerated gradient adaptation scheme for real-time weight estimation.
• Application of nonsmooth Lyapunov-based analysis to ensure control system stability and performance.

Main Results:

• The developed accelerated gradient-based DNN adaptation scheme achieves global asymptotic tracking error convergence.
• The method effectively handles unknown non-LIP drift dynamics and exogenous disturbances in nonlinear systems.
• Simulation studies on diverse systems demonstrate enhanced tracking and function approximation performance.

Conclusions:

• The proposed DNN-based accelerated gradient adaptive control scheme offers a robust solution for trajectory tracking in complex nonlinear systems.
• The generalized DNN architecture and adaptation scheme outperform previous methods, particularly in handling non-LIP uncertainties.
• This work advances the field of adaptive control by extending accelerated gradient methods to deep neural network architectures for improved real-world applicability.