How to implement Optimal Control on a Nonlinear Dynamic Single-Input Multiple-Output (SIMO) System?

Hi,

I have modeled a Nonlinear Dynamic Single-Input Multiple-Output System (SIMO) using Simulink.

The input (U) is a pulse generation function.

Each output is defined by a differential equation where the input is the power of an exponential function. For example, x1_dot = A(x1, x2, x3)+B(x1)*exp(x1, U)+C(x1, x2, x3, U)

Now, I have to optimize the input of the system (ie. the amplitude of each pulse) so that two of the outputs (x1 and x2) are minimized and x3 is maximized.

So, I thought that I have to use PID controllers in my system. However, I am not sure how to implement 3 PID controllers (one for each output) to control the single input of the system.

Any help is highly appreciated.

Thank you!