Reliable LQ fuzzy control for continuous-time nonlinear systems with actuator faults

Area of Science:

• Control Systems Engineering
• Nonlinear System Analysis
• Fuzzy Logic Applications

Background:

• Nonlinear systems with actuator faults pose significant control challenges.
• Existing control methods may exhibit conservatism or fail under fault conditions.
• Takagi-Sugeno (T-S) fuzzy models offer a framework for representing nonlinear dynamics.

Purpose of the Study:

• To develop a reliable linear quadratic (LQ) fuzzy control strategy for continuous-time nonlinear systems susceptible to actuator faults.
• To reduce the conservatism often associated with Lyapunov stability analysis in fault-tolerant control.
• To guarantee closed-loop system stability and optimize performance across normal and fault scenarios.

Main Methods:

• Employing the Takagi-Sugeno (T-S) fuzzy model to represent the nonlinear system dynamics.
• Utilizing multiple Lyapunov functions to improve stability analysis and reduce conservatism.
• Applying an improved linear matrix inequality (LMI) method for designing reliable LQ fuzzy controllers.
• An LMI optimization procedure to derive a suboptimal controller offering guaranteed stability and optimized performance bounds.

Main Results:

• Derivation of distinct upper bounds for the LQ performance cost function under normal and various actuator fault conditions.
• A suboptimal reliable LQ fuzzy controller designed via LMI optimization.
• Demonstration of guaranteed closed-loop stability for the fuzzy system in all considered cases (normal and faulty).
• Provision of an optimized upper bound for a weighted average LQ performance cost function.

Conclusions:

• The proposed multiple Lyapunov function-based LMI method effectively designs reliable LQ fuzzy controllers for nonlinear systems with actuator faults.
• The method successfully guarantees system stability and optimizes performance, outperforming single Lyapunov function approaches.
• Numerical simulations on the chaotic Lorenz system validate the practical applicability and effectiveness of the proposed fault-tolerant control design.