基于二次规划的量化随机非线性系统在线辨识

On Line Identification of Quantized Stochastic Nonlinear Systems Based on Quadratic Programming

针对一类带有色噪声的Hammerstein非线性有限脉冲响应量化系统的在线辨识问题,借助二次规划解最优值的方法,得到未知参数的估计值,并对其在不同采样次数和不同噪声方差输入下的参数辨识效果进行分析。讨论待辨识系统的数学模型和量化器的性质,利用量化器的性质推导出将系统辨识问题转化为求二次规划最优解的过程,给出参数估计值取得唯一性的条件,并利用二次规划的KKT定理对其收敛性进行分析与证明,通过仿真实例验证所用方法的有效性。

In this paper, an on-line identification problem for a class of Hammerstein nonlinear finite impulse response quantization system with colored noise was studied. By using the method of quadratic programming to solve the optimal value, the estimated values of unknown parameters were obtained, and the effect of parameter identification under different sampling times and different noise variance inputs was analyzed. Firstly, the mathematical model of the system to be identified and the properties of the quantifier were discussed. Secondly, the process of converting the system identification problem to the optimal solution of quadratic programming was deduced by using the properties of the quantifier. The conditions for uniqueness of the parameter estimates were given, and its convergence was analyzed and proved by using the KKT theorem of quadratic programming. Finally, a simulation example was used to verify the convergence of the system.The validity of the method.