Mixed ℋ<inf>2</inf>/ℋ<inf>∞</inf> nonlinear filtering

Abstract

In this paper, we consider the mixed ℋ ₂ /ℋ _∞ 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 of coupled Hamilton-Jacobi-Isaac's equations (HJIE). For linear systems, it is shown that these conditions reduce to a pair of coupled Riccati equations similar to the ones for the control case. Both the finite-horizon and infinite-horizon problems are discussed for the case when the initial condition of the plant is known.