WORST-CASE SYSTEM-IDENTIFICATION IN H-INFINITY - VALIDATION OF A-PRIORI INFORMATION, ESSENTIALLY OPTIMAL-ALGORITHMS, AND ERROR-BOUNDS

In this paper we resolve several important open issues pertaining to a worst-case control-oriented system identification problem known as id entification In H-infinity. First, a method Is presented for developin g confidence that certain a priori information available for identific ation is not invalid. This method requires the solution of a certain n ondifferentiable convex program. Second, an essentially optimal identi fication algorithm is constructed. This algorithm is (worst-case stron gly) optimal to within a factor of two. Finally, new upper and lower b ounds on the optimal identification error are derived and used to esti mate the identification error associated with the given algorithm. Int erestingly, the development of each of these results draws heavily upo n the classical Nevanlinna-Pick interpolation theory. As such, our res ults establish a clear link between the areas of system identification and optimal interpolation theory. Both the formulation and techniques in this paper are applicable to problems where the frequency data ava ilable for identification may essentially be arbitrarily distributed.