This is the case for exact recovery of LQR case. Formulated as an SDP problem, solved by YALMIP solver.
The code is loosely based on:
[1] K. Mombaur, A. Truong, and J.-P. Laumond, “From human to humanoid locomotion—an inverse optimal control approach,” Auton Robot, vol. 28, no. 3, pp. 369–383, Apr. 2010, doi: 10.1007/s10514-009-9170-7.
Relaxing the equation condition in the LMI solution is more conducive to the convergence of the solution
Refer to the file TCST15_inverse_lqr.m