Stabilization in finite time for fractional-order hyperchaotic electromechanical gyrostat systems

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.