不确定非自治混沌陀螺仪在非线性输入下的有限时间稳定性

Finite-Time Stabilization of Uncertain Non-Autonomous Chaotic Gyroscopes With Nonlinear Inputs

陀螺仪是一个非常有趣,又是永恒的非线性非自治动力系统课题,它可以显示出非常复杂的动力学行为,如混沌现象.在一个给定的有限时间内,研究非线性非自治陀螺仪鲁棒稳定性问题.假设陀螺仪系统受到模型不确定的外部扰动而摄动,系统参数并不知道,同时考虑了非线性输入的影响.为未知参数提出了适当的自适应律.以自适应律和有限时间控制理论为基础,提出非连续有限时间控制理论,来研究系统的有限时间稳定性.解析证明了闭循环系统的有限时间稳定性及其收敛性.若干数值仿真结果表明,该文的有限时间控制法是有效的,同时验证了该文的理论结果.

Gyroscopes were one of the most interesting and everlasting onlinear non-autono- mous dynamical systems that exhibited very complex dynamical behavior such as chaos. The problem of robust stabilization of the nonlinear non-autonomous gyroscopes in a given finite time was studied. It was assumed that the gyroscope system was perturbed by model uncertain- ties, external disturbances and unknown parameters. Besides, the effects of input nonlineari- ties were taken into account. Appropriate adaptive laws were proposed to tackle the unknown parameters. Based on the adaptive laws and the finite-time control theory, discontinuous finite- time control laws were proposed to ensure the finite-time stability of the system. The finite-time stability and convergence of the closed-loop system are analytically proved. Some numerical simulations are presented to show the efficiency of the proposed finite-time control scheme and to validate the theoretical results.