Computational methods for parametric LQ problems--A survey

Iterative methods for finding the optimal constant feedback gains for parametric LQ problems, notably for optimal constant output feedback problems, are surveyed. The connections of several methods to loss function expansions are discussed with important implications to the understanding of their convergence properties. Especially, the descent Anderson-Moore method, Levine-Athans like methods, and the Newton method are considered. Convergence results are also included. The initialization problem and the output feedback stabilization problem are also discussed. Furthermore, it is shown that the concepts and methods surveyed in this paper are useful in solving many realistic generalized parametric LQ problems as well, notably so-called robust parametric LQ problems.