MHE in Output Feedback Control of Uncertain Nonlinear Systems via IQCs

TL;DR

This paper introduces a moving horizon estimation scheme for uncertain nonlinear systems using IQCs, ensuring input-to-state stability in the closed-loop system with a robustly stabilizing controller.

Contribution

It develops a new robust detectability concept based on IQCs and formulates an MHE approach that guarantees stability despite uncertainties.

Findings

The proposed MHE achieves input-to-state stability for uncertain nonlinear systems.

The detectability notion is robust to non-parametric uncertainties and practically verifiable.

The approach integrates with existing controllers to enhance robustness and stability.

Abstract

We propose a moving horizon estimation (MHE) scheme for general nonlinear constrained systems with parametric or static nonlinear uncertainties and a predetermined state feedback controller that is assumed to robustly stabilize the system in the absence of estimation errors. Leveraging integral quadratic constraints (IQCs), we introduce a new notion of detectability that is robust to possibly non-parametric uncertainties and verifiable in practice. Assuming that the uncertain system driven by the controller satisfies this notion of detectability, we provide an MHE formulation such that the closed-loop system formed of the uncertain system, the controller and MHE is input-to-state stable w.r.t. exogenous disturbances.