Suboptimal nonlinear moving horizon estimation

TL;DR

This paper introduces a suboptimal moving horizon estimator for nonlinear systems that guarantees stability using a feasibility-based approach, and demonstrates its effectiveness through chemical reactor process applications.

Contribution

It develops a novel suboptimal MHE framework with stability guarantees that is flexible in cost function choice and solver implementation, applicable to nonlinear systems.

Findings

Robust stability is achieved independently of horizon length.

Few optimizer iterations significantly improve estimation accuracy.

Performance compares favorably with existing fast MHE schemes.

Abstract

In this paper, we propose a suboptimal moving horizon estimator for a general class of nonlinear systems. For the stability analysis, we transfer the "feasibility-implies-stability/robustness" paradigm from model predictive control to the context of moving horizon estimation in the following sense: Using a suitably defined, feasible candidate solution based on an auxiliary observer, robust stability of the proposed suboptimal estimator is inherited independently of the horizon length and even if no optimization is performed. Moreover, the proposed design allows for the choice between two cost functions different in structure: the former in the manner of a standard least squares approach, which is typically used in practice, and the latter following a time-discounted modification, resulting in better theoretical guarantees. We apply the proposed suboptimal estimator to a nonlinear chemical reactor process, verify the theoretical assumptions, and show that even a few iterations of the optimizer are sufficient to significantly improve the estimation results of the auxiliary observer. Furthermore, we illustrate the flexibility of the proposed design by employing different solvers and compare the performance with two state-of-the-art fast MHE schemes from the literature.