Discrete-time mixed H2/H∞ nonlinear filtering

In this paper, we consider the discrete-time mixed H-2/H-infinity filtering problem for affine nonlinear systems. Necessary and sufficient conditions for the solvability of this problem with a finite-dimensional filter are given in terms of a pair of coupled discrete-time Hamilton-Jacobi-Isaac's equations (DHJIE) with some side-conditions. For linear systems, it is shown that these conditions reduce to a pair of coupled discrete-time algebraic-Riccati-equations (DAREs) or a system of linear matrix inequalities (LMIs) similar to the ones for the control case. Both the finite-horizon and infinite-horizon problems are discussed. Moreover, sufficient conditions for approximate solvability of the problem are also derived. These solutions are especially useful for computational purposes, considering the difficulty of solving the coupled DHJIEs. An example is also presented to demonstrate the approach. Copyright (C) 2010 John Wiley & Sons, Ltd.