The Extreme Guaranteed Accuracy of Filtering For A Class of Signals (γ2-Robust Optimization)

Abstract

The problem of finding the linear quadratic criterion optimal filter with the accuracy guaranteed is solved for a class of signals with bounded dispersions of derivatives (class γ2). A quick algorithm for parameter optimization based on simplex-method is proposed. The exact solution derived in the class L2 of filter transfer functions and thus, being physically unrealizable is obtained by means of calculus of variations. The appropriate filter is named Ideal Filter. Using the exact solution the extreme guaranteed accuracy of γ2-robust filtering is found. The results obtained can be applied in control theory.