基于随机与区间分析的状态方程不确定性比较
发布时间：2018-11-15 17:14
【摘要】：基于现代控制理论中状态方程的求解算法,对具有参数不确定性的控制系统采用非概率区间分析方法与随机控制理论进行研究。首先明确实际工程应用中不确定性的概念和影响,分别建立了区间值和随机过程2种描述方法,求解系统的响应区间,并分为与初始条件和输入相关的零输入和零状态两部分不确定量。根据区间数学中的区间函数扩张原理和概率统计理论中的切比雪夫不等式,从数学证明和数值计算2个方面,分别用非概率区间分析和概率统计方法求解不确定系统的响应,并对二者进行比较,分析其相容性。结果表明,在由概率统计信息得到不确定性变量的区间向量为系统输入的情况下,非概率区间分析方法得到的响应区间包含由随机控制理论得到的响应区间。
[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.
【作者单位】： 北京航空航天大学自动化科学与电气工程学院;
【基金】：中航工业创新基金(cxy2012BH01)~~
【分类号】：O231
本文编号：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.
【作者单位】： 北京航空航天大学自动化科学与电气工程学院;
【基金】：中航工业创新基金(cxy2012BH01)~~
【分类号】：O231
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