Optimal Control-Based Adaptive NN Design for a Class of Nonlinear Discrete-Time Block-Triangular Systems.

Area of Science:

• Control Theory
• Artificial Intelligence
• Systems Engineering

Background:

• Designing controllers for unknown nonlinear discrete-time systems with block-triangular multi-input-multi-output pure-feedback structures is challenging due to state/input couplings and nonaffine functions.
• Existing methods often struggle to guarantee both stability and optimal performance simultaneously for such complex systems.

Purpose of the Study:

• To develop an optimal control scheme using adaptive neural networks for a class of unknown nonlinear discrete-time systems.
• To achieve guaranteed system stability and optimal control performance, which is a novel contribution for this system class.

Main Methods:

• Transformation of the nonlinear systems into an output predictor form.
• Approximation of the ideal control signal and strategic utility function using an action-critic neural network architecture.
• Construction of an optimal control signal via gradient descent-based weight update rules.

Main Results:

• The proposed adaptive neural network design successfully achieves optimal control performance for the first time in this class of systems.
• Stability of the closed-loop system is rigorously proven using the difference Lyapunov method.
• Numerical simulations demonstrate the effectiveness and performance of the proposed optimal control scheme.

Conclusions:

• The developed optimal control scheme effectively addresses the challenges of controlling unknown nonlinear discrete-time systems with complex structures.
• The integration of adaptive neural networks provides a robust solution for achieving both stability and optimal performance.
• This work represents a significant advancement in optimal control for pure-feedback systems.