Design of a Fixed-Time Stabilizer for Uncertain Chaotic Systems Subject to External Disturbances

• Published in: Mathematics (Basel) Vol. 11; no. 15; p. 3273
• Main Authors: Rezaie, Amir, Mobayen, Saleh, Ghaemi, Mohammad Reza, Fekih, Afef, Zhilenkov, Anton
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.08.2023
• Subjects: Chaos theory; chaotic systems; Control algorithms; Controllers; Design; Disturbances; Dynamical systems; fixed-time stability; Food science; Inequality; Initial conditions; Lyapunov function; Methods; Ordinary differential equations; Robust control; Sliding mode control; Stability; Tests, problems and exercises; Uncertainty (Information theory); Taiwan
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math11153273

This paper addresses the fixed-time stability problem of chaotic systems with internal uncertainties and external disturbances. To this end, new sliding-mode surfaces are introduced to design fixed-time controllers for the stabilization of perturbed chaotic systems. First, the required conditions for deriving fixed-time stability are determined. Then, using the obtained stability theorems and sliding mode techniques, the controllers are synthesized. The proposed controller enables the convergence of the trajectories of the chaotic system to the origin in finite time, independently of the initial conditions. The performance of the proposed approach is assessed using a simulation study of a PMSM system and the Matouk system. Among the advantages of the proposed controller are its robustness to external disturbances and the boundedness of the settling time to a constant value for any initial condition.