How to implement discrete constraints and boundary conditions per time step using casadi.Opti()

[Leo Bakker]

Dear all,

I like to create an MPC using a vector with discrete constraints and do not know how to implement this using casadi.Opti(). 

(In my MPC I have hourly values for set points and boundary conditions as solar radiation and outdoor temperatures). 

Please let me clarify my question using the Slot car racing problem (https://web.casadi.org/blog/ocp/): 

opti = casadi.Opti(); % Optimization problem

limit = @(pos) 1-sin(2*pi*pos)/2;
opti.subject_to(speed<=limit(pos)); % track speed limit
opti.subject_to(0<=U<=1);           % contrDear all,

Here the speed limit is a function of position (pos). 

My question is how can I replace this function with a vector with discrete values in the time horizon.

And how can I do the same in the cost function.

Thanks in advance for answering my question.

Leo Bakker 

[Joris Gillis]

Dear Leo,

Speed is a vector; just put a vector at the right-hand side as well:

opti.subject_to(speed<=[1 2 3 4 8 ... ]);

Probably, you want to use an opti.parameter instead of hard-coded numerial values.

Best,

  Joris

opti.subject_to(speed<=limit(pos));

[Leo Bakker]

Thanks !!! 

That works if I use for instance: 

limitt = [1.1]*21
opti.subject_to(speed.T<=limitt)

I need to use the transposed value  (speed.T) to make it work.

My next question is if it is possible to add controllable variables (e.g. breaking power) ? 
and how to implement this ?

Thanks in advance,

Leo Bakker    

[Joris Gillis]

Dear Leo,

What do you mean with controllable variables?

Best regards,

  Joris