Robust Moving-horizon Estimation for Nonlinear Systems: From Perfect to Imperfect Optimization

TL;DR

This paper analyzes the stability of moving-horizon estimators for nonlinear systems under disturbances, establishing conditions for both exact and imperfect optimization solutions, with practical demonstrations through numerical examples.

Contribution

It provides new theoretical stability guarantees for robust moving-horizon estimators considering imperfect optimization solutions.

Findings

Robust stability proven for exact optimization cases.

Practical stability established with imperfect minimization.

Numerical examples demonstrate estimator performance.

Abstract

Robust stability of moving-horizon estimators is investigated for nonlinear discrete-time systems that are detectable in the sense of incremental input/output-to-state stability and are affected by disturbances. The estimate of a moving-horizon estimator stems from the on-line solution of a least-squares minimization problem at each time instant. The resulting stability guarantees depend on the optimization tolerance in solving such minimization problems. Specifically, two main contributions are established: (i) the robust stability of the estimation error, while supposing to solve exactly the on-line minimization problem; (ii) the practical robust stability of the estimation error with state estimates obtained by an imperfect minimization. Finally, the construction of such robust moving-horizon estimators and the performances resulting from the design based on the theoretical findings are showcased with two numerical examples.