Newton's method for solving parametric linear quadratic control problems
Hannu T. T. Toivonen, Pertti M. Mäkilä · International Journal of Control · 1987
Newton's method is applied to parametric linear quadratic control problems, including the optimal output feedback problem and the optimal decentralized control problem. Newton's equations are obtained as a system of coupled linear matrix equations. They are solved iteratively using the conjugate gradient method. In order to reduce the amount of work associated with the procedure, an inexact newtonian algorithm is also considered. In this algorithm, an approximate solution of the Newton equations is computed in such a way that the asymptotic convergence rate is quadratic.