网络环境下基于量化观测值的系统辨识研究

Along with the coming of information revolution, the systems for human beings tend to be large and complicated. The problems of network caused by related systems and quantization caused by digital systems commonly exist in a system. This project will study the system identification based on the quantized observations in a networked environment. The networked environment we concern includes packet loss, delay, packet disorder and so on, and the system model includes ARMA model, Wiener model, Hammerstein model and so on. Firstly, we study the identification problem based on the uniform quantized observations using the methods of empirical measure and maximum likelihood estimate, respectively. The estimator of the unknown parameter is obtained and its convergence is analyzed. The feasible identification algorithm is also given. The numerical simulation is used to analyze the merits and demerits of the two methods. Secondly, the optimal quantized strategy is studied to reduce the error of the system identification. The analytic formula of the optimal quantized strategy is obtained using the least square method. The relationship is analyzed between this optimal quantized strategy and that in the field of stabilization. Finally, we further study the identification problem based on the optimal quantized observations. The identification results of the unknown parameter are obtained. The numerical simulation is used to compare the merits and the demerits between this results with that of the uniform quantization. The research issue of this proposal belongs to one of the unsolved topics in the identification area. The results have certain significance in theoretical and practical fields.

信息技术革命的到来使得人类所面临的系统趋于大型化、复杂化，由于系统相互关联所导致的网络问题以及由数字系统导致的量化问题在一个系统中普遍存在。本课题在丢包、延时、数据包错序等不确定网络环境下基于量化观测值研究系统为ARMA模型、Wiener模型、Hammerstein模型等模型的辨识问题。首先，分别采用经验估计法和最大似然估计法基于均匀量化观测值对系统进行辨识研究，得到未知参数的估计量，分析其收敛性，给出可行的辨识算法，通过数值仿真分析两种辨识方法的优劣；其次，研究可以减少系统的辨识误差的最优量化策略，基于最小二乘法得到最优量化控制策略的解析式，通过分析其性质揭示与镇定领域的最优量化策略的内在联系；最后，进一步研究基于最优量化观测值的辨识问题，得到未知参数的辨识结果，将其与均匀量化的辨识结果进行比较，分析其优劣。本课题的研究内容是辨识领域尚未解决的课题之一，其结果具有一定的理论及现实意义。

随着信息技术革命的到来，人类所面临的系统逐渐趋于大型化、复杂化，这给系统辨识的研究带来挑战的同时也带来了很多机遇。本课题主要以系统中存在网络因素和量化因素为切入点，在网络环境下，基于量化观测值对系统进行辨识研究。相比均匀量化器，对数量化器虽然形式复杂，但具有使系统达到稳定所需的信息更少、所占用的网络带宽也更小等优点，因此，本课题主要基于对数量化观测值对系统进行了辨识研究。首先，对对数量化器输出量的统计特性进行了分析。当对数量化器的输入为随机变量时，给出了其量化输出量的分布函数、特征函数、矩估计量等，并在此基础上给出了未知参数的辨识算法。其次，分别研究了丢包网络系统、不确定网络系统、有限脉冲响应系统及有理系统的量化辨识问题。根据对数量化器的扇形界性质，利用基于分位数的估计方法、二次规划方法等方法得到了未知参数的估计量，分析了估计量的收敛性，给出了估计误差的上界，并用数值例子验证了所得结果的有效性。最后，对网络攻击环境下的量化反馈控制系统进行了安全性及可靠性研究。采用两组独立同分布的随机变量描述网络攻击的随机性与任意性，将量化问题转化为鲁棒控制问题，得到了判断系统安全性的充分条件，并借助线性矩阵不等式给出了控制器的设计方法。本课题的研究内容是辨识领域尚未解决的内容之一，其研究结果具有一定的理论及实际意义。