In this paper, I have found that there is a concept called inverse optimal control method as follows
The optimal control problem for nonlinear systems is usually attributed to the solvability of the Hamilton-Jacobi-Bellman (HJB) equation. Because the HJB equation involves partial differential equations, optimal control design is generally too difficult to be solved analytically, with the exception of a few special cases. An alternative method is the so-called inverse optimal control method, which does not require a solution to the HJB equation [15]. In this case, the minimization of the performance index is determined a posteriori according to the given controller, so the aforementioned difficulty can be alleviated.
However, this is not enough for me to understand what is the definition of inverse optimal. Does it also relate to LQR optimal control?
In addition, what does "a posteriori" here mean?