Hi all,
I am solving a lineair constrained MPC problem, which could be seen in the attached image.
In this optimal control problem Q and R are both symmetric positive definite matrices.
When I rewrite this optimal control problem to a constrained QP problem and solve this with a QP solver (e.g. Quadprog or Gurobi) I get a negative objective function value. Is this correct? I would expect a positive value, because Q and R are both positive definite and the terms in the objective function are quadratic.
Dear Jason,
The objective function shows the minimization of the differences between the references and the calculated values, this does not mean that this tracking error is negative. The error will be very small in the case of a proportional tracking and zero for a perfect tracking.
Best regards
Thanks for your reply.
I think you misunderstood my question. I am asking if the objective function value could be negative. However, in my opinion, the objective function value will always be positive and zero at its lowest.
From your answer, I think you mean the same. Correct me, if I am wrong.
Kind regards,
Indeed the objective function can only be positive in the case of an evolution of a normal process.
Regards
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