An optimal control problem in estimating the cooling condition for a cemented hip replacement system

An optimal control problem utilizing the Levenberg–Marquardt method (LMM) is examined in this study to determine the unknown optimal control heat flux function for a cemented hip replacement system based on the desired temperature distributions at the cement–bone interface to prevent the death of bone tissues. The validation of this optimal control problem is verified by using the numerical experiments. Results show that an optimal control function can be obtained using the present algorithm for the test cases considered in this work to reduce the temperature variation and to save the bone tissues at the cement–bone interface.