Optimization of sampling intervals for tracking control of nonlinear systems: A game theoretic approach

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Machine Learning Applications

Background:

• Tracking control of affine nonlinear continuous-time systems presents challenges in communication and computation efficiency.
• Existing methods often require continuous state feedback, leading to high resource utilization.

Purpose of the Study:

• To develop a near-optimal adaptive event-based sampling scheme for tracking control.
• To significantly reduce feedback communication and computational load while maintaining system stability.

Main Methods:

• A zero-sum game approach with a novel performance index was formulated.
• A functional link neural network (FLNN) approximated the Hamilton-Jacobi-Issac (HJI) equation's solution.
• An impulsive weight update scheme and Lyapunov stability theory were used for analysis.

Main Results:

• A near-optimal event-based control policy and sampling condition were designed.
• The scheme demonstrated Zeno-freeness and guaranteed local ultimate boundedness.
• Numerical simulations confirmed a 48.82% reduction in feedback communication and computational load.

Conclusions:

• The proposed adaptive event-based sampling scheme is effective for tracking control of nonlinear systems.
• The method offers significant reductions in communication and computation, validated by simulations.
• The approach ensures system stability and efficient operation.