Precise Tracking Control for Articulating Crane: Prescribed Performance, Adaptation, and Fuzzy Optimality by Nash...

Area of Science:

• Robotics
• Control Systems Engineering
• Fuzzy Logic Applications

Background:

• Articulating cranes (AC) face challenges in precise tracking control due to complex nonlinearities and uncertainties in their multisection arms.
• Existing control methods struggle with time-variant uncertainties, especially when their bounds are unknown.
• Fuzzy logic has been explored, but often relies on rule-based systems and approximations.

Purpose of the Study:

• To propose an Adaptive Prescribed Performance Tracking Control (APPTC) for articulating cranes (AC).
• To achieve robust and precise trajectory tracking control in the presence of unknown time-variant uncertainties.
• To develop an approximation-free control strategy using fuzzy set theory.

Main Methods:

• A state transformation is employed to simultaneously achieve trajectory tracking and satisfy prescribed performance criteria.
• Fuzzy set theory is utilized to model uncertainties without relying on IF-THEN fuzzy rules.
• Lyapunov analysis ensures deterministic performance via uniform boundedness and uniform ultimate boundedness.
• An optimal design using a two-player Nash game is formulated to enhance fuzzy-based performance.

Main Results:

• The proposed APPTC method demonstrates robust precise tracking control for articulating cranes.
• The control strategy effectively adapts to time-variant uncertainties with unknown bounds.
• Deterministic performance is guaranteed through rigorous Lyapunov stability analysis.
• The optimal design using Nash game theory improves control parameter selection and fuzzy-based performance.

Conclusions:

• This research presents the first control strategy for precise tracking control of fuzzy articulating cranes.
• The APPTC offers an approximation-free and robust solution for complex robotic control tasks.
• The combination of fuzzy set theory, Lyapunov analysis, and game theory provides a powerful framework for advanced control systems.