Stackelberg-Theoretic Approach for Performance Improvement in Fuzzy Systems

Area of Science:

• Control Theory
• Fuzzy Systems
• Robotics

Background:

• Dynamical systems often face unpredictable, time-varying uncertainties.
• Existing robust control methods may struggle with unknown uncertainty bounds.
• Fuzzy dynamical systems offer a framework for modeling such uncertainties.

Purpose of the Study:

• To develop a robust control strategy for fuzzy dynamical systems with unknown bounded uncertainties.
• To guarantee deterministic system performance, including uniform boundedness.
• To optimize control performance using a game-theoretic approach.

Main Methods:

• Proposing a class of deterministic robust controls with tunable parameters.
• Utilizing the Lyapunov minimax approach to prove control effectiveness.
• Formulating optima-seeking as a two-player Stackelberg game with custom cost functions.

Main Results:

• Guaranteed uniform boundedness and ultimate uniform boundedness of the fuzzy system.
• Existence of the Stackelberg strategy for optimal parameter tuning.
• Demonstrated effectiveness through simulations on a biped robot model.

Conclusions:

• The proposed robust control approach effectively manages uncertainties in fuzzy dynamical systems.
• The Stackelberg game formulation provides a viable method for optimizing control parameters.
• This methodology shows promise for complex control applications, such as legged robotics.