Solving control problems - a numerical perspective

There is a continuing and growing need in the control community for good algorithms and robust numerical software for increasingly challenging applications. Consequently, during the past several decades, the control field has been a rich source of computational problems for applied mathematicians and numerical analysts alike. This has led to the development of several control design software packages, both as commercial and free software. In view of this positive situation, the question arises: Is numerical awareness in control still an issue of pressing importance? Along the lines of this question we will address, from both user and algorithm developer perspectives, several important aspects related to strategies to solve control problems, algorithms quality assessment, principles of algorithms development, problem conditioning, role of scaling, caveats of tolerance based computations, implementation of robust numerical software. Our presentation of these aspects will be illustrated by simple examples and by present day computational challenges.