  The quadratic optimal state feedback (LQR) is one of the most popular designs
for linear systems and succeeds via the solution of the algebraic Riccati
equation. The situation is different in the case of non-linear systems: the
Riccati equation is then replaced by the Hamilton Jacobi Bellman equation
(HJB), the solution of which is generally difficult. A compromise can be the
so-called Inverse Optimal Control, a form of which is Sontag's formula [1];
here the minimized cost function follows from the feedback law chosen, not vice
versa. Using Sontag's formula in the variant according to Freeman and Primbs
[2, 9], the actually minimized cost function is given in the following
sections, including cases when it reduces to the quadratic cost. Also some
remarks and thoughts are presented for discussion.
