Robust Adaptive Neural Tracking Control for a Class of Stochastic Nonlinear Interconnected Systems

Area of Science:

• Control Systems Engineering
• Artificial Intelligence
• Stochastic Systems Analysis

Background:

• Multiple Input and Multiple Output (MIMOs) systems often exhibit complex nonlinearities and uncertainties.
• Stochastic systems with strong interconnections in drift and diffusion terms pose significant control challenges.
• Existing control methods may struggle with the simultaneous presence of nonlinearity, stochasticity, and strong interconnection.

Purpose of the Study:

• To propose an adaptive neural decentralized control strategy for uncertain stochastic nonlinear strongly interconnected systems.
• To address the control of systems where nonlinearities affect both drift and diffusion terms, dependent on all system states.
• To ensure robust stability and accurate tracking performance for these complex systems.

Main Methods:

• Utilizing Radial Basis Function (RBF) neural networks to approximate unknown nonlinear system dynamics.
• Employing the backstepping technique to design a stable adaptive neural decentralized controller.
• Analyzing system stability using Lyapunov methods in the sense of the fourth moment for stochastic processes.

Main Results:

• Demonstrated semiglobal uniform ultimate boundedness of all closed-loop system signals in the fourth moment.
• Achieved convergence of tracking errors to a small neighborhood around the origin.
• Successfully controlled stochastic systems with strong interconnected nonlinearities in both drift and diffusion terms.

Conclusions:

• The proposed adaptive neural decentralized control approach is effective for uncertain stochastic nonlinear strongly interconnected systems.
• The controller design successfully handles complex nonlinearities and stochastic effects present in the system dynamics.
• Simulation results validate the theoretical guarantees of stability and tracking performance.