Adaptive statistic tracking control based on two-step neural networks with time delays

Area of Science:

• Control Theory
• Dynamical Systems
• Machine Learning

Background:

• Traditional control systems often target deterministic signals.
• General and non-Gaussian dynamical systems present unique control challenges.
• Statistical information tracking offers a new paradigm for complex system control.

Purpose of the Study:

• To introduce a novel control framework, statistic tracking control (STC), for general, non-Gaussian dynamical systems.
• To develop a variable structure adaptive tracking control strategy using neural networks.
• To enable control systems to match statistical properties of a target probability density function (pdf).

Main Methods:

• Utilized two-step neural network models for adaptive control.
• Employed B-spline neural network approximation for performance function integration.
• Applied dynamic neural networks (DNN) to identify nonlinear system dynamics.
• Developed an adaptive controller based on DNN for trajectory tracking.

Main Results:

• Successfully transferred the control problem to tracking weights related to the integrated performance function.
• Demonstrated the ability of DNN to identify unknown nonlinear dynamics.
• Developed a stable adaptive controller for tracking reference trajectories.
• Validated the approach's efficiency through simulations.

Conclusions:

• The proposed statistic tracking control (STC) framework is effective for non-Gaussian dynamical systems.
• The integration of neural networks provides a robust method for adaptive control and system identification.
• Lyapunov stability analysis confirms the reliability of the identification and tracking error control.