MPC with conditional constraints

[Juan Moreno Nadales]

Hello everyone. Hope you can help me solve this problem

Suppose I want to control a linear system x(k+1) = Ax(k) + Bu(k) solving an MPC problem. I want to set a terminal constraint so that  x(N) = xF, but I also want to impose that at some time instant N-M the state has reached some other point x(N-M) = xF2. I want the latter to be applied until this condition is met and then disable the constaint. The overall problem would be something like

minimize J(u) s.t 

            x(N) >= xF;

            x(N-M) >= xF2;  (constraint applied only if x < xF2. Then disabled)

Thank you very much in advance.

          

[Johan Löfberg]

https://yalmip.github.io/modellingif

https://yalmip.github.io/example/hybridmpc/