  This paper derives recursion equations for a robust smoothing problem for a
class of nonlinear systems with uncertainties in modeling and exogenous noise
sources. The systems considered operate in discrete-time and the uncertainties
are modeled in terms of a sum quadratic constraint. The robust smoothing
problem is solved in terms of a forward-time and a reverse-time filter. Both
these filters are formulated in terms of set-valued state estimators and are
recast into subsidiary optimal control problems. These optimal control problems
are described in terms of discrete-time Hamilton-Jacobi-Bellman equations,
whose approximate solutions lead to recursive Riccati difference equations,
filter state equations, and level shift scalar equations for the forward-time
and the reverse-time filters.
