For the first order system x(t) = ax(t) + bu(t) find the optimal open-loop and closed-loop...

 

Transcribed Image Text:

For the first order system x(t) = ax(t) + bu(t) find the optimal open-loop and closed-loop control to minimize the performance index 1 J = [ [qx² (1) + ru² (1)]dt 2 where tf is unspecified, x(0) = xo and x(t) = 0. Also, find tf. No need to calculate J in any problem. In closed-loop control, you need to calculate the Riccati coefficient matrix. For the first order system x(t) = ax(t) + bu(t) find the optimal open-loop and closed-loop control to minimize the performance index 1 J = [ [qx² (1) + ru² (1)]dt 2 where tf is unspecified, x(0) = xo and x(t) = 0. Also, find tf. No need to calculate J in any problem. In closed-loop control, you need to calculate the Riccati coefficient matrix.