H-INFINITY OPTIMIZATION WITH PLANT UNCERTAINTY AND SEMIDEFINITE PROGRAMMING

The fundamental H-infinity problem of control is that of finding the s table frequency response function that best fits worst case frequency domain specifications. This is a non-smooth optimization problem that underlies the frequency domain formulation of the H-infinity problem o f control; it is the main optimization problem in qualitative feedback theory for example. It is shown in this article how the fundamental H -infinity optimization problem of control can be naturally treated wit h modern primal-dual interior point (PDIP) methods. The theory introdu ced here generalizes and unifies approaches to solving large classes o f optimization problems involving matrix-valued functions, a subclass of which are commonly treated with linear matrix inequalities techniqu es, Also, in this article new optimality conditions for H-infinity opt imization problems over matrix-valued functions are proved, and numeri cal experience on natural(PDIP) algorithms for these problems is repor ted. In experiments we find the algorithms exhibit (local) quadratic c onvergence rate in many instances. Finally, H-infinity optimization pr oblems with an uncertainty parameter are considered. It is shown how t o apply the theory developed here to obtain optimality conditions and derive algorithms. Numerical tests on simple examples are reported. (C ) 1998 John Wiley & Sons, Ltd.