《现代控制理论基础》第五章(讲义) K=RBP [l10 因此,最优控制信号为 利用 MATLAB Program5.2也能求解该问题。 MATLAB Pro -Design of quadratic optimal regulator system %*****Determination of feedback gain matrix K for quadratic optimal control o***** Enter state matrix A and control matrix b***** B=01l o*****Enter matrices Q and R of the quadratic performance =[1001 R=[l] %The optimal feedbck gain matrix K(if such matrix K exists)can be obtained by entering the following command 1.0000 1.0000 [例5.12]考虑下列系统 Bu 式中 10 A=0 091,B=0《现代控制理论基础》第五章(讲义) 9 K R B'P −1 = 因此，最优控制信号为 u = −Kx = −x − x 1 2 利用 MATLAB Program 5.2 也能求解该问题。 MATLAB Program 5.2 %——Design of quadratic optimal regulator system %*****Determination of feedback gain matrix K for quadratic %optimal control***** %*****Enter state matrix A and control matrix B***** A=[0 1;0 -1]; B=[0;1]; %*****Enter matrices Q and R of the quadratic performance %index***** Q=[1 0;0 1]; R=[1]; %The optimnal feedbck gain matrix K (if such matrix K % exists)can be obtained by entering the following command ***** K=lqr(A,B,Q,R) K= 1.0000 1.0000 ------------------------------------------------------------------ [例 5.12] 考虑下列系统 x  = Ax + Bu 式中           =           − − − = 1 0 0 35 27 9 0 0 1 0 1 0 A ，B [1 1] 1 1 2 1 [1][ 0 1] =      =