基于隨機與區(qū)間分析的狀態(tài)方程不確定性比較
發(fā)布時間：2018-11-15 17:14
【摘要】：基于現(xiàn)代控制理論中狀態(tài)方程的求解算法,對具有參數(shù)不確定性的控制系統(tǒng)采用非概率區(qū)間分析方法與隨機控制理論進行研究。首先明確實際工程應(yīng)用中不確定性的概念和影響,分別建立了區(qū)間值和隨機過程2種描述方法,求解系統(tǒng)的響應(yīng)區(qū)間,并分為與初始條件和輸入相關(guān)的零輸入和零狀態(tài)兩部分不確定量。根據(jù)區(qū)間數(shù)學(xué)中的區(qū)間函數(shù)擴張原理和概率統(tǒng)計理論中的切比雪夫不等式,從數(shù)學(xué)證明和數(shù)值計算2個方面,分別用非概率區(qū)間分析和概率統(tǒng)計方法求解不確定系統(tǒng)的響應(yīng),并對二者進行比較,分析其相容性。結(jié)果表明,在由概率統(tǒng)計信息得到不確定性變量的區(qū)間向量為系統(tǒng)輸入的情況下,非概率區(qū)間分析方法得到的響應(yīng)區(qū)間包含由隨機控制理論得到的響應(yīng)區(qū)間。
[Abstract]:Based on the solution algorithm of state equation in modern control theory, the non-probabilistic interval analysis method and stochastic control theory are used to study the control system with parameter uncertainty. Firstly, the concept and influence of uncertainty in practical engineering application are defined. Two description methods, interval value and stochastic process, are established to solve the response interval of the system. It is divided into zero input and zero state uncertainty related to initial condition and input. According to the expansion principle of interval function in interval mathematics and the Chebyshev inequality in probability and statistics theory, the non-probabilistic interval analysis and probabilistic statistical method are used to solve the responses of uncertain systems from the two aspects of mathematical proof and numerical calculation, respectively. The compatibility of the two was analyzed by comparing them. The results show that the response interval obtained by the non-probabilistic interval analysis method contains the response interval obtained from the stochastic control theory when the interval vector of the uncertain variable obtained from the probabilistic statistical information is the input of the system.
【作者單位】： 北京航空航天大學(xué)自動化科學(xué)與電氣工程學(xué)院;
【基金】：中航工業(yè)創(chuàng)新基金(cxy2012BH01)~~
【分類號】：O231
本文編號：2333931
[Abstract]:Based on the solution algorithm of state equation in modern control theory, the non-probabilistic interval analysis method and stochastic control theory are used to study the control system with parameter uncertainty. Firstly, the concept and influence of uncertainty in practical engineering application are defined. Two description methods, interval value and stochastic process, are established to solve the response interval of the system. It is divided into zero input and zero state uncertainty related to initial condition and input. According to the expansion principle of interval function in interval mathematics and the Chebyshev inequality in probability and statistics theory, the non-probabilistic interval analysis and probabilistic statistical method are used to solve the responses of uncertain systems from the two aspects of mathematical proof and numerical calculation, respectively. The compatibility of the two was analyzed by comparing them. The results show that the response interval obtained by the non-probabilistic interval analysis method contains the response interval obtained from the stochastic control theory when the interval vector of the uncertain variable obtained from the probabilistic statistical information is the input of the system.
【作者單位】： 北京航空航天大學(xué)自動化科學(xué)與電氣工程學(xué)院;
【基金】：中航工業(yè)創(chuàng)新基金(cxy2012BH01)~~
【分類號】：O231
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