Optimal fuzzy controller based on non-monotonic Lyapunov function with a case study on laboratory helicopter

ABSTRACT

This paper presents a new approach to design an observer-based optimal fuzzy state feedback controller for discrete-time Takagi–Sugeno fuzzy systems via LQR based on the non-monotonic Lyapunov function. Non-monotonic Lyapunov stability theorem proposed less conservative conditions rather than common quadratic method. To compare with optimal fuzzy feedback controller design based on common quadratic Lyapunov function, this paper proceeds reformulation of the observer-based optimal fuzzy state feedback controller based on common quadratic Lyapunov function. Also in both methodologies, the dependence of optimisation problem on initial conditions is omitted. As a practical case study, the controllers are implemented on a laboratory twin-rotor helicopter to compare the controllers' performance.

Keywords:

• Takagi–Sugeno fuzzy systems
• common quadratic Lyapunov function
• non-monotonic Lyapunov function
• optimal fuzzy control
• laboratory twin-rotor helicopter
• linear matrix inequalities

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Sum absolute error.

2 Mean absolute error

3 Mean square error.