On Numerical Methods for Parametric LQ Problems

Iterative methods for finding the optimal constant feedback gains for parametric LQ problems, notably for optimal output feedback problems, are studied. The methods are classified into two groups, such that the explicit gain space methods are based on solving the necessary optimality conditions explicitly in the controller parameter space, while the implicit methods do not have this property. The connections of several methods to loss increment expansions are discussed with important implications to the understanding of the convergence properties of these methods. Several open research topics are indicated.