DC optimization approach to robust controls: the optimal scaling value problem

The optimal scaling problem (OSP) for constant scaling in output feedback control is an inherently difficult nonconvex problem for which in general existing local search algorithms can at best locate a local solution. However, it can be restated as a problem of globally minimizing a convex function under DC constraints, i.e., constraints that can be expressed in terms of differences of convex functions. A particular structure of this DC optimization problem is that it becomes convex when a relatively small number of "complicating" variables are held fixed. We propose alternative branch and bound algorithms for OSP, which exploit this structure by branching upon the complicating variables and use adaptive sub-division strategies to speed-up the convergence to the global solution.