Control Design Problem with continue and discrete signals;

Question

I met a real application problem within my research.

The control signal will be three dimension, $u_1$,$u_2$,and $u_3$.

$u_1$ and $u_2$ are continous. Unfortuately, $u_3$ is disrete with the 6 selections with {1,2,3,4,5,6}. I have to design this control from optimal perspective.

Is there anyone who has done this situation before? Could you give me a hint.

thanks

Jie

Answer 1

Model predictive control is a general framework for optimization-based control, and having discrete control inputs does not make the control structure any more complicated conceptually, although the actual computation of control inputs might become prohibitively expensive as it will lead to mixed-integer optimization problems.