Approximate tracking control for nonlinear multi-player systems with deferred asymmetric time-varying full-state...

Area of Science:

• Control Systems Engineering
• Game Theory
• Nonlinear Dynamics

Background:

• Multi-player nonlinear systems often face challenges with state constraints and unknown initial conditions.
• Existing control strategies may struggle with deferred asymmetric time-varying (DATV) constraints.

Purpose of the Study:

• To develop Nash equilibrium tracking control strategies for continuous-time nonlinear multi-player systems.
• To address systems with DATV full-state constraints and unknown initial states.
• To ensure system states track predefined reference trajectories.

Main Methods:

• An improved shift transformation was applied to handle unknown initial states and DATV constraints.
• A barrier function (BF) transformation created an unconstrained augmented system.
• Mixed zero-sum (MZS) game theory and a critic-only structure were used to derive and approximate control strategies.
• Lyapunov theory validated the uniform ultimate boundedness (UUB) of system states and control parameters.

Main Results:

• The proposed control strategies effectively manage DATV full-state constraints and unknown initial conditions.
• System states successfully followed desired reference trajectories.
• Uniform ultimate boundedness of neural network weights and tracking errors was confirmed through simulations.

Conclusions:

• The developed MZS game-based control provides a robust solution for complex nonlinear multi-player systems.
• The method demonstrates practical applicability in handling challenging state constraints and initial uncertainties.
• The findings contribute to advanced control theory for systems with strict operational requirements.