Robust Smoothing for Discrete-Time Uncertain Nonlinear Systems

TL;DR

This paper develops a robust smoothing method for discrete-time nonlinear systems with uncertainties, using set-valued estimators and optimal control techniques to derive recursive filtering equations.

Contribution

It introduces a novel recursive smoothing approach for uncertain nonlinear systems employing set-valued estimation and Hamilton-Jacobi-Bellman equations.

Findings

Derivation of recursive Riccati difference equations

Formulation of forward and reverse-time filters

Application to systems with quadratic uncertainty constraints

Abstract

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.