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热力机组辨识与控制状态反馈增益矩阵的计算为了确定反馈增益矩阵,目标函数定义为 J=Esum from i=1 to K(Z′(i)·Q·Z(i)+y′(i-1)·R·y(i-1)) (4)式中符号“′”表示矩阵转置,Z(i)和y(i)为由式(3)定义的向量,而E表示统计量数学期望。式中Q和R为正定矩阵,其元素规定了用来调整Z(i)和y(i)的方差的数。 通过动态规划(DP)过程求y(i-1)(i=1,2,…K)使(4)极小,得到y(1)=G(1)Z(1)。在最优控制中我们设置增益矩阵G等于G(1),而在每一时间点的最优输入采用式y(n)=GZ(n)。
Calculation of State Feedback Gain Matrix for Heat Power Plant Identification and Control To determine the feedback gain matrix, the objective function is defined as J = Esum from i = 1 to K (Z ’(i) · Q · Z (i) + y’ ) · R · (i-1)) (4) where symbol “” "denotes matrix transpose, Z (i) and y (i) are vectors defined by equation (3), and E denotes statistics math expect. Where Q and R are positive definite matrices whose elements specify the number used to adjust the variance of Z (i) and y (i). Obtain y (1) = G (1) Z (1) by minimizing (4) from the dynamic programming (DP) process for y (i -1) (i = 1,2, ... K). In the optimal control we set the gain matrix G equal to G (1) and the optimal input at each time point uses the formula y (n) = GZ (n).