Mixed ℋ︁₂/ℋ︁∞ nonlinear filtering

In this paper, we consider the mixed ℋ︁₂/ℋ︁∞ 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 Hamilton–Jacobi–Isaacs equations (HJIEs). 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 the infinite-horizon problems are discussed. Simulation results are presented to show the usefulness of the scheme, and the results are generalized to include other classes of nonlinear systems