A moving horizon state and parameter estimation scheme with guaranteed robust convergence

TL;DR

This paper introduces a moving horizon estimation method for nonlinear systems that guarantees robust exponential convergence of state and parameter estimates despite disturbances, using a novel Lyapunov function approach.

Contribution

It develops a joint $oldsymbol{ extdelta}$-IOSS Lyapunov function framework for guaranteed convergence in nonlinear joint state-parameter estimation.

Findings

Proves robust exponential convergence under disturbances.

Provides conditions for constructing a joint $oldsymbol{ extdelta}$-IOSS Lyapunov function.

Demonstrates effectiveness through a numerical example.

Abstract

We propose a moving horizon estimation scheme for joint state and parameter estimation for nonlinear uncertain discrete-time systems. We establish robust exponential convergence of the combined estimation error subject to process disturbances and measurement noise. We employ a joint incremental input/output-to-state stability ($\delta$-IOSS) Lyapunov function to characterize nonlinear detectability for the states and (constant) parameters of the system. Sufficient conditions for the construction of a joint $\delta$-IOSS Lyapunov function are provided for a special class of nonlinear systems using a persistence of excitation condition. The theoretical results are illustrated by a numerical example.