随机鼠疫病模型的核范数子空间辨识

Nuclear norm subspace identification of a stochastic model of bubonic plague

基于连续鼠疫病模型,通过零阶保持器得到相应的离散模型.由于随机扰动的存在,提出相应的随机鼠疫病模型.设计卡尔曼滤波器,估计随机模型的状态变量以及降低噪声影响.采用核范数最小化方法代替奇异值分解,得到输入输出投影矩阵的低秩矩阵逼近.通过交替方向乘子法求解此优化问题,得到输出变量的最优解.根据世界卫生组织的非洲人类鼠疫病数据,利用本文提出的方法得到随机鼠疫病模型.仿真研究表明提出方法的有效性和精确性.

Based on the continuous-time model of plague,the discrete-time model is given by the zero-order holder.Due to the fact that the stochastic disturbances are existing,the stochastic model of bubonic plague is proposed corresponding to the discrete-time model.The state estimation and noise reduction of the model are obtained by means of designing a Kalman filter.Nuclear norm minimization is used,instead of the singular value decomposition,to structure the low-rank matrix approximation of the input-output projection matrix.In addition,the nuclear norm optimization problem is solved by the alternating direction method of multipliers and the optimal solution of the output variables of the minimization problem is obtained.According to the data of human plague in Africa from the World Health Organization,the stochastic model of bubonic plague is identified by using the proposed method.The simulation results indicate the efficiency and accuracy of the proposed method.