Stabilization in finite time for fractional-order hyperchaotic electromechanical gyrostat systems. (October 2018)

• Record Type: Journal Article
• Authors: Wang, Zhibo; Wu, Huaiqin
• Is Part Of: Mechanical systems and signal processing. Volume 111(2018)
• Page Start: 628
• Page End: 642
• Publication Date: 2018-10
• Subjects: Fractional-order gyrostat system -- Hyperchaos -- Stabilization in finite time -- Adaptive control law -- Unknown parameter -- Robustness; Structural dynamics -- Periodicals; Vibration -- Periodicals; Constructions -- Dynamique -- Périodiques; Vibration -- Périodiques; Structural dynamics; Vibration; Periodicals; 621
• DOI: 10.1016/j.ymssp.2018.04.009
• Languages: English
• ISSNs: 0888-3270

Abstract

Highlights: A FEGS is proposed. The existence of chaotic/hyperchaotic attractors in the FEGSs proposed is verified. An appropriate controller is designed to stabilize the FEGS in finite time globally. The unknown parameters of the FEGS are estimated via fractional-order adaptive laws. The stabilization conditions and upper bounds of the settling time are addressed. Abstract: This paper is concerned with adaptive robust stabilization in finite time for fractional-order chaotic and hyperchaotic Electromechanical Gyrostat Systems (EGSs) with unknown parameters and uncertainties. Firstly, a fractional-order EGS mathematical model is proposed, and the existence of chaotic and hyperchaotic attractors is verified with the related Lyapunov exponents, phase portraits and Poincaré sections. Then, fractional-order adaptive laws are proposed to estimate the unknown parameters. Based on the fractional-order convergence theory in finite time, a novel discontinuous state feedback controller with the proposed fractional-order adaptive laws is designed to stabilize the fractional-order EGSs in finite time globally, and the stabilization conditions are analytically addressed. Finally, numerical simulations are employed to demonstrate the validity of the theoretical results.