迟延状态空间系统的辨识

发布时间：2018-04-25 14:47

本文选题：状态空间模型 + 迟延系统　；参考：《江南大学》2016年博士论文

【摘要】：数学模型是系统控制的基础。状态空间模型能够描述动态系统。一些实际被控对象都会包含迟延。论文研究迟延状态空间系统的辨识,选题具有重要的理论意义和应用前景。论文基于数据滤波技术、递阶辨识原理、滚动时域估计原理,研究规范型迟延状态空间模型的参数辨识、状态和迟延估计问题,取得了如下的成果。(1)针对单步迟延状态空间系统,使用移位算子,推导了对应的输入-输出表达及其辨识模型。由于信息向量包含未知变量,使用系统的可测信息建立一个辅助模型,用辅助模型的输出代替未知变量,提出了单步迟延状态空间模型的辅助模型最小二乘辨识算法。进一步,针对输入非线性单步迟延状态空间系统,推导了其辨识模型,其信息向量包含的未知状态变量使用基于参数估计的状态观测器的状态代替,提出了基于状态观测器的梯度迭代参数辨识算法和最小二乘迭代参数辨识算法。(2)针对多步迟延状态空间系统,导出了系统的辨识模型,其特征是信息向量包含了系统的未知状态变量,采用估计的状态代替信息向量中的未知状态,提出了基于状态估计的递推最小二乘算法交互估计参数,利用参数估计值来计算系统的状态。针对多步迟延多变量状态空间系统,其输入输出变量多、参数数目大、辨识算法计算量大,利用递阶辨识原理和Kalman滤波估计系统状态,提出了基于状态估计的递阶最小二乘辨识算法,提高了计算效率。(3)针对多迟延多变量状态空间系统,使用分解技术将系统分解为两个子系统,推导了递阶梯度迭代辨识算法和递阶最小二乘迭代辨识算法。对于双率多迟延状态空间系统,利用辅助模型辨识思想,通过建立一个辅助模型,使用辅助模型的输出代替不可测变量,用估计残差代替噪声变量,提出了辅助模型递推最小二乘算法。进一步为提高估计精度,基于数据滤波技术,采用交互估计滤波后的系统模型和噪声模型的参数,提出了基于滤波的辅助模型最小二乘算法。(4)针对不确定迟延状态空间系统,假设迟延服从马尔可夫模型,采用滚动时域的数据和代价函数,对目标函数进行优化,提出了滚动时域估计算法。当迟延服从均匀分布时,推导了多率不确定迟延状态空间模型的期望最大化估计算法,此算法分为E步和M步,E步计算完整数据的条件期望(通常称为Q函数),M步用来极大化Q函数,重复这两步迭代直到收敛。论文对提出的一些参数估计算法进行了数值仿真,验证了方法的有效性。
[Abstract]:Mathematical model is the basis of system control. The state space model can describe the dynamic system. Some actual controlled objects contain delays. In this paper, the identification of delayed state space system is studied, and the topic is of great theoretical significance and application prospect. Based on the technology of data filtering, hierarchical identification and rolling time domain estimation, this paper studies the parameter identification, state and delay estimation of the canonical delay state space model. The following results are obtained. (1) the corresponding input-output expression and its identification model are derived by using shift operators for single-step delay state space systems. Because the information vector contains unknown variables, an auxiliary model is established by using the testable information of the system, and the output of the auxiliary model is used to replace the unknown variable. An auxiliary model least square identification algorithm for single-step delay state space model is proposed. Furthermore, for the input nonlinear single-step delay state space system, the identification model is derived. The unknown state variables contained in the information vector are replaced by the state observer based on parameter estimation. A gradient iterative parameter identification algorithm based on state observer and a least square iterative parameter identification algorithm. 2) for a multistep delayed state space system, the identification model of the system is derived. The feature is that the information vector contains the unknown state variables of the system, the estimated state is used instead of the unknown state in the information vector, and a recursive least square algorithm based on state estimation is proposed to estimate the parameters interactively. The state of the system is calculated by parameter estimation. For multistep delay multivariable state space system, its input and output variables are many, the number of parameters is large, and the computation of identification algorithm is large. The hierarchical identification principle and Kalman filter are used to estimate the state of the system. A hierarchical least square identification algorithm based on state estimation is proposed. The computational efficiency is improved. The decomposition technique is used to decompose the system into two subsystems for multi-delay multivariable state space system. The iterative identification algorithm of step degree and the iterative identification algorithm of hierarchical least squares are derived. For two-rate multi-delay state space systems, by using the idea of auxiliary model identification, an auxiliary model is established, the output of the auxiliary model is used to replace the unmeasurable variables, and the estimation residuals are used to replace the noise variables. An auxiliary model recursive least square algorithm is proposed. In order to improve the estimation accuracy, based on the data filtering technology, the parameters of the filtered system model and the noise model are estimated by using the interactive filtering technique. A filter based least square algorithm for the auxiliary model is proposed. The objective function is optimized by using the rolling time domain data and cost function, and a rolling time domain estimation algorithm is proposed. When the delay service is distributed uniformly, the expected maximization estimation algorithm of multi-rate uncertain delay state space model is derived. This algorithm can be divided into E step and M step E step to calculate the conditional expectation of complete data (usually called Q function / M step to maximize Q function, and repeat these two steps until convergence). In this paper, some parameter estimation algorithms are numerically simulated to verify the effectiveness of the method.
【学位授予单位】：江南大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O231

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