Discrete-time adaptive backstepping nonlinear control via high-order neural networks

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Artificial Intelligence in Control

Background:

• Discrete-time nonlinear systems, particularly Multiple-Input-Multiple-Output (MIMO) systems, present significant control challenges due to their complexity and inherent nonlinearities.
• Adaptive tracking control is crucial for maintaining system performance in the presence of uncertainties and external bounded disturbances.
• Existing control strategies often struggle with the combined challenges of nonlinearity, MIMO structure, and bounded disturbances in discrete-time domains.

Purpose of the Study:

• To develop an adaptive tracking control scheme for discrete-time nonlinear MIMO systems subject to bounded disturbances.
• To utilize a high-order neural network (HONN) for approximating the control law within a backstepping framework.
• To rigorously analyze the stability of the closed-loop system, including the neural network learning algorithm.

Main Methods:

• Application of the backstepping technique to design a control law for systems in block strict feedback form (BSFF).
• Approximation of the designed control law using a high-order neural network (HONN) structure.
• Stability analysis of the entire controlled system using the Lyapunov approach, incorporating an extended Kalman filter (EKF)-based neural network (NN) learning algorithm.

Main Results:

• Successful implementation of an adaptive tracking control strategy for discrete-time nonlinear MIMO systems.
• Demonstration of the HONN's capability to approximate the complex control law designed via backstepping.
• Validation of system stability through Lyapunov analysis, confirming the robustness of the EKF-based NN learning algorithm.

Conclusions:

• The proposed adaptive tracking control scheme effectively manages discrete-time nonlinear MIMO systems with bounded disturbances.
• The integration of HONN approximation and EKF-based learning ensures robust and stable system performance.
• The approach is validated through simulations on a discrete-time nonlinear electric induction motor model, showcasing practical applicability.