一类混沌系统的状态量化反馈镇定控制器设计

用状态反馈法对含量化器的一类混沌系统的渐进镇定进行了研究.混沌系统的动力学状态方程的非线性项为任意整数阶的齐次函数.设计的更新律中量化器针对一类非线性项为高次齐次函数的混沌系统，数值仿真结果表明，若非线性控制器中存在量化环节时，原非线性控制器将无法镇定此类系统.为有效反馈镇定此类混沌系统，设计了一种新的含自适应量化器的非线性控制器.量化器中设置两个互为倒数的自适应放大器，使量化器具有自适应的量化范围和量化误差界，从而可自适应量化系统各种状态.同时应用Lyapunov原理和滑模变结构控制理论，推导得到量化器的放大系数和量化误差上界的更新律.一些典型混沌系统的数值仿真结果表明，所设计的非线性控制器可以有效自适应量化系统状态，并反馈镇定上述类型的混沌系统.

Stabilization for a Class of Chaotic Systems with Adaptive Quantizers

This paper investigates the asymptotical stabilization via state feedback for a class of chaotic systems with a quantizer connected on the input channel. The nonlinear terms in the dynamic equation of the chaotic system are represented as the homogeneous functions with arbitrary known orders. The quantizer has one adjustable time varying parameter with the updated law to be designed, and thus it can quantify adaptively online the state variables of the chaotic systems according to control scheme. With the help of the updated law and adaptive law of estimated boundary error of quantization, the nonlinear adaptive controller is proposed in this paper to ensure the chaotic system to be stabilized asymptotically in the presence of the quantizer. Finally, some simulation examples are utilized to demonstrate the validity of the results in this paper.