Sub-optimal control of fuzzy linear dynamical systems under granular differentiability concept.

Area of Science:

• Control Theory
• Fuzzy Systems
• Dynamical Systems

Background:

• Fuzzy linear dynamical systems present challenges due to inherent uncertainties in coefficients and initial conditions.
• Traditional control methods struggle with the granular nature of fuzzy derivatives and interval arithmetic.

Purpose of the Study:

• To develop a sub-optimal control strategy for fuzzy linear dynamical systems that ensures state variables remain close to zero.
• To address limitations of existing fuzzy interval arithmetic approaches in accurately determining system eigenvalues and control laws.

Main Methods:

• Utilizes relative-distance-measure (RDM) fuzzy interval arithmetic and calculus of variations to derive an optimal control law.
• Defuzzification of fuzzy feedback gains to obtain a practical sub-optimal control law.
• Introduces granular eigenvalues, granular controllability, and granular stabilizability concepts for fuzzy systems.

Main Results:

• The proposed RDM-based approach accurately determines system eigenvalues, unlike fuzzy standard interval arithmetic (FSIA) methods.
• Demonstrates effective sub-optimal control for a Boeing 747 longitudinal model and an uncertain bus suspension system.
• Validates the robustness of the control strategy under uncertain initial conditions and parameters.

Conclusions:

• The RDM fuzzy interval arithmetic offers a more accurate and reliable method for controlling uncertain fuzzy linear dynamical systems.
• The developed sub-optimal control law is effective in practical applications, including aerospace and automotive systems.
• The study advances the understanding of granular properties like controllability and stabilizability in fuzzy dynamical systems.