Near-Nash Equilibrium Control Strategy for Discrete-Time Nonlinear Systems With Round-Robin Protocol

Area of Science:

• Control Systems Engineering
• Nonlinear System Dynamics
• Computational Intelligence

Background:

• Discrete-time nonlinear systems present significant control challenges.
• Existing control strategies often struggle with combined complexities like nonlinearities, scheduling protocols, and output feedback.
• The round-robin protocol (RRP) introduces further intricacies in system management.

Purpose of the Study:

• To investigate near-Nash equilibrium (NE) control strategies for discrete-time nonlinear systems.
• To address challenges posed by additive nonlinearities, RRP, and output feedback controllers simultaneously.
• To ensure bounded stability of the closed-loop system under the proposed control strategies.

Main Methods:

• Developed an approximate dynamic programming (ADP) algorithm to solve coupled Bellman's equations for NE control.
• Designed a Luenberger-type observer for state estimation under RRP scheduling.
• Implemented near-NE control strategies using actor-critic neural networks.
• Performed stability analysis to guarantee bounded stability.

Main Results:

• Successfully developed and implemented near-Nash equilibrium control strategies.
• The proposed Luenberger-type observer effectively estimates system states under RRP.
• Actor-critic neural networks facilitated the practical implementation of the control strategies.
• Stability analysis confirmed the bounded stability of the closed-loop system.

Conclusions:

• The developed approximate dynamic programming approach effectively yields near-Nash equilibrium control strategies.
• The integration of state estimation and actor-critic neural networks provides a robust solution for complex systems.
• The proposed control methodology guarantees system stability, demonstrating its practical applicability.