具有未知参数的不确定分数阶Sprott-C系统的Terminal滑模同步

基于滑模控制的优良性能,探讨了利用Terminal滑模控制实现分数阶混沌系统的有限时间同步问题,给出了滑模控制实现具有未知参数和扰动的分数阶Sprott-C驱动—响应系统(阶数0<α<1)的同步结论。通过构造合适的滑动模态曲面,针对系统未知参数上界已知和未知两种情况,设计了合适的分数阶控制器和参数自适应率,结合分数阶微分方程相关理论和有限时间稳定性定理,证明了实现该系统的同步控制结论,并对未知参数和扰动上界进行了准确估计。最后选取适当参数,通过数值仿真,验证了所给结论的有效性和可行性。

Terminal sliding-mode synchronization of uncertain fractal Sprott-C chaotic system with unknown parameters

Basing on good performance of sliding-mode controlling,the paper investigated finite-time synchronization of fractal-order chaotic system by Terminal sliding-mode control strategy,and realized synchronization of drive-response chaotic Sprott-C system(with the fractal orderα:0<α<1)with unknown parameters and disturbance by designing property sliding-mode surface and fractal-order controller.Moreover,one estimated the unknown parameters and upper bound of the unknown systematic parameters and disturbance successfully by some appropriate adaptive update laws combining with fractal-order differential equations theory and finite-time stability theory.Finally,by choosing proper parameters,numerical simulations provide illustration to show the effectiveness and feasibility of the theoretical results.