COMPUTATIONAL METHODS FOR PARAMETRIC LQ PROBLEMS - A SURVEY

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