Discrete-time mixed H<inf>2</inf>/H<inf>&#x221E;</inf> nonlinear filtering

Abstract

In this paper, we consider the discrete-time mixed H ₂ /H _infin filtering problem for affine nonlinear systems. 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. Both the finite-horizon and infinite-horizon problems are discussed for the case when the initial condition of the plant is unknown. 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.