Stackelberg differential game-based fuzzy adaptive hierarchical optimal control for a nonlinear system with unknown...

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Game Theory

Background:

• Hierarchical control is crucial for complex systems.
• Unknown dynamics pose significant challenges in control design.
• Stackelberg differential games offer a framework for leader-follower control.

Purpose of the Study:

• To develop a hierarchical optimal control strategy for high-order nonlinear systems with unknown dynamics.
• To address two-player scenarios within a Stackelberg game framework.
• To design controllers using command filtered backstepping and adaptive dynamic programming.

Main Methods:

• Stackelberg differential game theory for sequential decision-making.
• Command filtered backstepping for controller design in subsystems.
• Adaptive dynamic programming with actor-critic functions to approximate cost functions and control policies.
• Fuzzy logic systems for estimating unknown system dynamics.
• Command filters to mitigate computational load from virtual control differentiation.

Main Results:

• The proposed method successfully designs controllers for subsystems.
• An adaptive dynamic programming architecture derives the Stackelberg equilibrium solution.
• Fuzzy logic systems effectively estimate unknown nonlinear dynamics.
• Command filters reduce computational complexity.
• Simulation results validate the control scheme's effectiveness.

Conclusions:

• The hierarchical optimal control strategy effectively manages high-order nonlinear systems with unknown dynamics.
• The integration of adaptive dynamic programming and fuzzy logic provides a robust solution for leader-follower control problems.
• The proposed approach achieves desired control objectives under a hierarchical performance index.