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Robust stability of moving horizon estimation for nonlinear systems with bounded disturbances using adaptive arrival cost

Nestor N. Deniz, Marina H. Murillo, Guido Sanchez, Lucas M. Genzelis, Leonardo Giovanini

TL;DR

The robust stability and convergence to the true state of moving horizon estimator based on an adaptive arrival cost are established for nonlinear detectable systems.

Abstract

In this paper, the robust stability and convergence to the true state of moving horizon estimator based on an adaptive arrival cost are established for nonlinear detectable systems. Robust global asymptotic stability is shown for the case of non-vanishing bounded disturbances whereas the convergence to the true state is proved for the case of vanishing disturbances. Several simulations were made in order to show the estimator behaviour under different operational conditions and to compare it with the state of the art estimation methods.

Robust stability of moving horizon estimation for nonlinear systems with bounded disturbances using adaptive arrival cost

TL;DR

The robust stability and convergence to the true state of moving horizon estimator based on an adaptive arrival cost are established for nonlinear detectable systems.

Abstract

In this paper, the robust stability and convergence to the true state of moving horizon estimator based on an adaptive arrival cost are established for nonlinear detectable systems. Robust global asymptotic stability is shown for the case of non-vanishing bounded disturbances whereas the convergence to the true state is proved for the case of vanishing disturbances. Several simulations were made in order to show the estimator behaviour under different operational conditions and to compare it with the state of the art estimation methods.

Paper Structure

This paper contains 10 sections, 1 theorem, 47 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminaries and setup
  3. Notation
  4. Problem statement
  5. Robust stability of moving horizon estimation under bounded disturbances
  6. Examples
  7. Example 1
  8. MHE in the presence of variable measurement noise
  9. Example 2
  10. Conclusions

Key Result

Theorem 1

Consider an i-IOSS system eq_nonlinsys with disturbances $\boldsymbol{w} \in \mathcal{W}\left(w_{\max} \right)$, $\boldsymbol{v} \in \mathcal{V}\left(v_{\max} \right)$. Assume that the arrival cost weight matrix of the MHE problem $\Gamma_{k-N}$ is updated using the adaptive algorithm eq:updatePk. M

Figures (5)

  • Figure 1: Comparison between ADAP (red dash dotted), MAX (blue dashed), FIEMAX (green dotted), EKF (magenta) estimators, and real system state (black solid).
  • Figure 2: Comparison between ADAP (red dash dotted), MAX (blue dashed), FIEMAX (green dotted), EKF (magenta) estimators, and real system state (black solid).
  • Figure 3: Comparison of the evolution of $trace(P^{-1}_{k-N})$ used by ADAP estimator for time--varying (red dash dotted) and constant (blue dashed) measurement noise parameters.
  • Figure 4: Comparison between ADAP (red dash dotted), MAX (blue dashed), FIEMAX (green dotted) estimators and real system state (black solid) for different horizon length ($N=2,5 \text{ and } 10$).
  • Figure 5: Comparison between ADAP (red dash dotted), MAX (blue dashed), FIEMAX (green dotted) estimators and real system state (black solid) for different horizon length ($N=2,5 \text{ and } 10$).

Theorems & Definitions (4)

  • Definition 1
  • Definition 2
  • Theorem 1
  • Remark 1