Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

MHE in Output Feedback Control of Uncertain Nonlinear Systems via IQCs

Yang Guo, Stefan Streif

TL;DR

The paper tackles state estimation for nonlinear constrained systems with non-parametric uncertainties by introducing a robust detectability notion based on IQCs. It develops an MHE that preserves ISS of the closed-loop when driving the uncertain plant with a predetermined controller, under IQC-specified disturbances. The main contributions include a rigorous IQC-based detectability framework, LMI-based verification for slope-restricted and parametric uncertainties, and a robust MHE design with provable RGES-type stability. A numerical example demonstrates improved performance over standard MHE, highlighting practical viability for uncertain nonlinear control applications. The approach offers a pathway to extend MHE to broader uncertainty classes via more general IQCs and diverse controllers.

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.

MHE in Output Feedback Control of Uncertain Nonlinear Systems via IQCs

TL;DR

The paper tackles state estimation for nonlinear constrained systems with non-parametric uncertainties by introducing a robust detectability notion based on IQCs. It develops an MHE that preserves ISS of the closed-loop when driving the uncertain plant with a predetermined controller, under IQC-specified disturbances. The main contributions include a rigorous IQC-based detectability framework, LMI-based verification for slope-restricted and parametric uncertainties, and a robust MHE design with provable RGES-type stability. A numerical example demonstrates improved performance over standard MHE, highlighting practical viability for uncertain nonlinear control applications. The approach offers a pathway to extend MHE to broader uncertainty classes via more general IQCs and diverse controllers.

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.

Paper Structure

This paper contains 9 sections, 7 theorems, 65 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Problem Setup
  3. Robust Detectability with IQCs
  4. Verification of Detectability
  5. Slope restricted Nonlinearity
  6. Parametric Uncertainty
  7. MHE-based Robust Stabilization
  8. Numerical Example
  9. Conclusion

Key Result

Lemma IV.1

The function $\Phi: {\mathbb{R}}^n \to {\mathbb{R}}^m$ is Lipschitz continuous on $\overline{\mathbb{X}}:=\mathbb{X}_1 \times \ldots \times \mathbb{X}_n \subseteq {\mathbb{R}}^n$ with $\mathbb{X}_i \subseteq {\mathbb{R}}$ and $i\in \mathbb{I}_{[1,n]}$, i.e., there exists $\gamma \geq 0$ such that if and only if there exist functions $\phi_{ij}: {\mathbb{R}}^n \times {\mathbb{R}}^n \to {\mathbb{R}

Figures (2)

  • Figure 1: Interconnection of the uncertain system \ref{['eq:sys']}, i.e., \ref{['eq:sys_1']}--\ref{['eq:sys_3']} with uncertainty $\Delta$, MHE and controller$\kappa$.
  • Figure 2: Closed-loop trajectories and estimation errors

Theorems & Definitions (22)

  • Definition III.1: Point-wise $\rho$--IQC
  • Remark III.2
  • Definition III.3: Robust Detectability
  • Remark III.4
  • Definition III.5: Robust i-IOSS
  • Lemma IV.1
  • proof
  • Proposition IV.2
  • proof
  • Remark IV.3
  • ...and 12 more