一类非光滑系统的无模型自适应混沌控制

Chaos control of a non-smooth system based on model-free adaptive control method

以一类单自由度非光滑系统为研究对象。分析了系统n-1周期运动经周期倍化分岔通向混沌运动的动力学行为。研究了系统混沌运动的控制问题,提出了一种无模型自适应参数反馈混沌控制方法。该混沌控制方法基于无模型自适应控制方法的思想设计混沌控制器:仅利用被控系统的输入/输出数据在线估计伪偏导数以建立系统的非参数时变动态线性化模型,进而基于该非参数时变动态线性化模型进行混沌控制器设计。当系统进入混沌运动状态后,利用混沌控制器输出微幅调整量施加于系统的可控参数,对混沌系统进行参数反馈控制,将系统的混沌运动控制为期望的周期运动。该混沌控制方法不依赖被控系统的数学模型,可适用于系统模型未知而仅获得系统输入/输出数据的情况,且具有控制器设计简单、计算量小等优点。数学证明了控制系统的稳定性和收敛性,仿真结果验证了该控制方法的可行性和有效性。

A single-degree-of-freedom non-smooth system is considered.The dynamic behaviors of the system from n-1periodic motion to chaotic motion via period-doubling bifurcation are analyzed by numerical simulation.By studying the chaotic motion control of the system,a parameter feedback chaos control method based on model-free adaptive control is proposed in this paper.The chaos controller is designed based on model-free adaptive control method:the pseudo-partial-derivative is estimated on-line by using the input/output data of the controlled system so that the non-parametric time-varying dynamic linear model of the controlled system can be established,and on this basis the chaos controller is designed.When the motion is chaotic?the chaos controller will be used to output a small perturbation to adjust the controllable parameter of the system so that the chaotic system can be controlled by using the parameter feedback chaos control method based on model-free adaptive control,thus the chaotic motion is controlled to the expected periodic motion.The proposed method in this paper does not need the exact mathematical model of the controlled system,so it is suitable for the cases where the exact mathematical model of the controlled system is unknown and only the I/O data can be obtained,and it has advantages of simpler controller design and smaller computing load,and so on.The stability and the convergence of the control system are proved mathematically,and the effectiveness and feasibility of the proposed method in this paper are verified by simulation results.