本文選題：狀態(tài)空間模型 + 遲延系統(tǒng)��； 參考：《江南大學》2016年博士論文

【摘要】：數(shù)學模型是系統(tǒng)控制的基礎。狀態(tài)空間模型能夠描述動態(tài)系統(tǒng)。一些實際被控對象都會包含遲延。論文研究遲延狀態(tài)空間系統(tǒng)的辨識,選題具有重要的理論意義和應用前景。論文基于數(shù)據(jù)濾波技術(shù)、遞階辨識原理、滾動時域估計原理,研究規(guī)范型遲延狀態(tài)空間模型的參數(shù)辨識、狀態(tài)和遲延估計問題,取得了如下的成果。(1)針對單步遲延狀態(tài)空間系統(tǒng),使用移位算子,推導了對應的輸入-輸出表達及其辨識模型。由于信息向量包含未知變量,使用系統(tǒng)的可測信息建立一個輔助模型,用輔助模型的輸出代替未知變量,提出了單步遲延狀態(tài)空間模型的輔助模型最小二乘辨識算法。進一步,針對輸入非線性單步遲延狀態(tài)空間系統(tǒng),推導了其辨識模型,其信息向量包含的未知狀態(tài)變量使用基于參數(shù)估計的狀態(tài)觀測器的狀態(tài)代替,提出了基于狀態(tài)觀測器的梯度迭代參數(shù)辨識算法和最小二乘迭代參數(shù)辨識算法。(2)針對多步遲延狀態(tài)空間系統(tǒng),導出了系統(tǒng)的辨識模型,其特征是信息向量包含了系統(tǒng)的未知狀態(tài)變量,采用估計的狀態(tài)代替信息向量中的未知狀態(tài),提出了基于狀態(tài)估計的遞推最小二乘算法交互估計參數(shù),利用參數(shù)估計值來計算系統(tǒng)的狀態(tài)。針對多步遲延多變量狀態(tài)空間系統(tǒng),其輸入輸出變量多、參數(shù)數(shù)目大、辨識算法計算量大,利用遞階辨識原理和Kalman濾波估計系統(tǒng)狀態(tài),提出了基于狀態(tài)估計的遞階最小二乘辨識算法,提高了計算效率。(3)針對多遲延多變量狀態(tài)空間系統(tǒng),使用分解技術(shù)將系統(tǒng)分解為兩個子系統(tǒng),推導了遞階梯度迭代辨識算法和遞階最小二乘迭代辨識算法。對于雙率多遲延狀態(tài)空間系統(tǒng),利用輔助模型辨識思想,通過建立一個輔助模型,使用輔助模型的輸出代替不可測變量,用估計殘差代替噪聲變量,提出了輔助模型遞推最小二乘算法。進一步為提高估計精度,基于數(shù)據(jù)濾波技術(shù),采用交互估計濾波后的系統(tǒng)模型和噪聲模型的參數(shù),提出了基于濾波的輔助模型最小二乘算法。(4)針對不確定遲延狀態(tài)空間系統(tǒng),假設遲延服從馬爾可夫模型,采用滾動時域的數(shù)據(jù)和代價函數(shù),對目標函數(shù)進行優(yōu)化,提出了滾動時域估計算法。當遲延服從均勻分布時,推導了多率不確定遲延狀態(tài)空間模型的期望最大化估計算法,此算法分為E步和M步,E步計算完整數(shù)據(jù)的條件期望(通常稱為Q函數(shù)),M步用來極大化Q函數(shù),重復這兩步迭代直到收斂。論文對提出的一些參數(shù)估計算法進行了數(shù)值仿真,驗證了方法的有效性。
[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.
【學位授予單位】：江南大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：O231

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