基于混沌理论的控制轨道函数构造

Construction of the control orbit function based on the chaos theory

简述了混沌理论和方法在控制过程中的应用。利用非线性函数的混沌性质,通过部分离散采样值,对一类控制过程演化函数提出一种新的构造方法,得到方程的代数形式,为参数选择、轨道摄动提供了基础。提出了构造过程和构造方程形式的析出定理的理论证明,提供了构造函数的误差公式。研究表明,对于具有有限项多项式型演化函数的控制过程,如果离散采样值满足条件,则构造函数没有模型误差。

Chaos is a general quasi-stochastic property of the non-linear system. A few non-linear elements are expected to produce sophisticated and practical function in application. A new approach to construct the evolutive function for a class of control process is proposed by using partially discrete sampling values and utilizing the chaos property of the non-linear function after classifying the application of the chaos theory and method in controlling process. Then the equation of the algebraic form which provides a basis for the selection of parameters and orbit oscillation can be gained. The separated theorem is proved for constructing the functions and polynomial equation, the error formula for the construction function is also obtained. Simulation proves the function of construction without model error on the suitable condition of the discrete sampling values if the evolutive function is a finite polynomial of control process. And the essence between the construction process and the chaos is also be demonstrated.