关于极大加线性系统参数模型的输入信号设计

发布时间：2018-04-13 13:23

本文选题：极大加线性系统 + 参数鉴定　；参考：《河北师范大学》2017年硕士论文

【摘要】：极大加线性系统有效地描述了一类离散事件系统的事件时间序列的动态性.极大加线性系统参数模型的鉴定对于生产系统的最优控制起着至关重要的作用.鉴定系统参数的模型,一是参数估计的算法,二是输入信号设计的方法.对于参数估计的算法相关专家已经用不同的方法解决了当测量受到噪音干扰和不受噪音干扰时参数模型的鉴定问题.对于输入信号设计的方法,学者们的研究仍局限于不受噪音干扰的情况,虽然可以使得预测误差变小,但是实际生活中很难达到无噪音干扰.本文主要研究输入信号设计问题,给出了当测量受到相同高斯白噪声干扰时,用线性扩展互补问题和上界约束算法两种不同的方法对输入信号进行设计,然后用已有的算法解决输入信号问题使得参数的估计值与真实值之间的误差达到最小,从而可以鉴定极大加线性系统的参数模型.这种输入信号设计的方法允许加入附加目标和约束条件,例如加入输入信号满足最大或最小时间间隔,时间顺序约束等.本文在给出极大加线性系统、高斯白噪音、扩展线性互补问题、上界约束算法和结构矩阵概念的基础上,给出了测量受到相同高斯白噪音干扰时,参数的真实值等于估计值应满足的充分必要条件,确定系统模型的参数使得预测误差最小.然后,利用将输入信号设计的条件改写成一个扩展线性互补问题,从而解决了对输入信号设计的问题.另外,利用上界约束算法对输入信号进行设计.证明了当满足指定条件时误差最小的输入信号序列是存在的,再将其满足的条件改写成一组上界约束条件,利用上界约束算法完成了对输入信号序列求解.从而完成了当测量受到相同高斯白噪音的干扰时,参数的估计值与真实值的误差达到最小时的输入信号设计.
[Abstract]:Max plus linear system effectively describe dynamic event time series of a class of discrete event systems. Identification of Max plus linear system parameter model plays a vital role in the optimal control of the production system. The identification parameters of the system model, a parameter estimation algorithm, two is designed for signal input method. The algorithm of parameter estimation has experts use different methods to solve the measurement when subjected to noise interference and noise interference by the identification problem of parameter model. For the method of input signal design, researchers are still limited to is not affected by noise disturbance, although can make the prediction error is smaller, but in real life it is difficult to achieve without noise. This paper mainly studies the problem of input signal design, are subject to the same measurement when Gauss white noise interference, extended linear complementarity problems and The upper bound constraint algorithm in two different methods to design the input signal, and then use the existing estimation algorithm to solve the problem of the parameter values of the input signal and the error between the true value of the minimum, which can model identification of Max plus linear system. The input method of signal design allows additional objectives and constraints, for example add to the input signal to meet the maximum or minimum time interval, time sequence constraint. This paper gives the max plus linear system, Gauss white noise, the extended linear complementarity problem, upper bound algorithm and matrix structure based on the concept of measurement is given by the same Gauss white noise, the real value of parameters is equal to the estimated value of the necessary and sufficient conditions should meet, make the minimum prediction error to determine the parameters of system model. Then, using the input signal design conditions rewritten into an extension The linear complementarity problem, so as to solve the design problem of the input signal. In addition, design of the input signal by using the upper bound algorithm. It is proved that when meet specified conditions when the input signal sequence of the minimum error exists, then rewrite the condition into a set of upper bound constraints, using the upper bound algorithm for solving the input signal sequence. Thus finished when the interference measurement by the same Gauss white noise, the estimated values of the parameters of input signal design the most hours of the error and the true value is reached.

【学位授予单位】：河北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O23

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