不确定分数阶Genesio混沌系统的反演滑模同步

Backstepping sliding mode synchronization of uncertain fractional-order Genesio-Tesi chaotic systems

针对带有参数不确定与外部扰动的分数阶Genesio-Tesi混沌系统,采用反演控制和滑模控制相结合的策略,设计了一种新的分数阶反演滑模控制器,实现了此类分数阶混沌系统的同步问题。首先,基于反演设计方法给出子系统的李雅普诺夫函数和虚拟控制量;其次,在反演设计过程中引入滑模变结构控制策略,基于李雅普诺夫稳定性理论,设计能够使分数阶驱动Genesio系统与分数阶响应Genesio系统全局渐近同步的分数阶反演滑模控制器。所设计的控制器为单一控制器,在实际应用中与多输入控制相比更易于实现系统的同步。最后,通过数值仿真验证了所设计的分数阶反演滑模控制算法对于参数不确定与外部扰动的鲁棒性及控制器设计方法的有效性。

A new fractional-order backstepping sliding mode controller was designed by adopting the backstepping control approach and sliding mode control technique to realize the synchronization of fractional-order(FO)Genesio-Tesi chaotic systems with parameter uncertainty and external disturbance.Firstly,the Lyapunov subsystem function was constructed and the virtual input was designed in the backstepping procedure.Secondly,the sliding mode variable structure control strategy was introduced to design a fractional-order backstepping sliding mode controller which can achieve the asymptotic synchronization of the FO drive Genesio-Tesi system and FO response system based on Lyapunov stability theorem.Compared with the multi-input schemes,the proposed single controller could realize the synchronization more easily in practical applications.Finally,the effectiveness of the proposed controller and the robustness of backstepping sliding mode control algorithm for uncertain parameter and external disturbance were testified by numerical simulation results.