Worst case system identification in H/sub ∞/: validation of a priori information, essentially optimal algorithms, and error bounds

Abstract

Resolves several important open issues pertaining to a worst-case control-oriented system identification problem known as identification in H/sub /spl infin//. First, a method is presented for developing confidence that certain a priori information available for identification is not invalid. This method requires the solution of a certain nondifferentiable convex program. Second, an essentially optimal identification algorithm is constructed. This algorithm is (worst-case strongly) optimal to within a factor of two. Finally, new upper and lower bounds on the optimal identification error are derived and used to estimate the identification error associated with the given algorithm. Interestingly, the development of each of these results draws heavily upon the classical Nevanlinna-Pick interpolation theory. As such, the authors' results 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 available for identification may essentially be arbitrarily distributed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>