基于变分方法的混沌系统参数估计

Estimating parameters of chaotic system with variational method

提出一种基于变分原理的估计混沌系统未知参数的方法,对以=F(x,θ)为控制方程的所有混沌系统具有普适性.首先将混沌系统方程引入到目标泛函中;接着利用变分原理导出了混沌系统的伴随方程和待辨识参数泛函梯度的通用公式;然后设计了估计混沌系统未知参数的算法;最后对典型的Lorenz混沌系统和超混沌Chen系统的未知参数进行了估计.数值仿真结果表明该方法是一种非常有效的估计混沌系统未知参数的方法.

In this paper a method is presented to estimate the unknown parameters of chaotic system based on the variational principle, which can be applied to all chaotic systems governed by the following equation： X= F（x,θ）. Firstly, the equation of the chaotic system is included into the objective functional. Secondly, the universal formulas of the adjoint equation for chaotic systems and the functional gradient for unknown parameters are derived using the variational principle. Thirdly, the algorithm to estimate unknown parameters of chaotic system is designed according to above formulas. Finally, all unknown parameters of the typical Lorenz chaotic system and the hyperchaotic Chen system are estimated separately. Numerical simulations show that the effectiveness and the feasibility of the proposed method to estimate unknown parameters of chaotic systems.