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On Convergence of the Iteratively Preconditioned Gradient-Descent (IPG) Observer

Kushal Chakrabarti, Nikhil Chopra

Abstract

This paper considers the observer design problem for discrete-time nonlinear dynamical systems with sampled measurement data. Earlier, the recently proposed Iteratively Preconditioned Gradient-Descent (IPG) observer, a Newton-type observer, has been empirically shown to have improved robustness against measurement noise than the prominent nonlinear observers, a property that other Newton-type observers lack. However, no theoretical guarantees on the convergence of the IPG observer were provided. This paper presents a rigorous convergence analysis of the IPG observer for a class of nonlinear systems in deterministic settings, proving its local linear convergence to the actual trajectory. Our assumptions are standard in the existing literature of Newton-type observers, and the analysis further confirms the relation of the IPG observer with the Newton observer, which was only hypothesized earlier.

On Convergence of the Iteratively Preconditioned Gradient-Descent (IPG) Observer

Abstract

This paper considers the observer design problem for discrete-time nonlinear dynamical systems with sampled measurement data. Earlier, the recently proposed Iteratively Preconditioned Gradient-Descent (IPG) observer, a Newton-type observer, has been empirically shown to have improved robustness against measurement noise than the prominent nonlinear observers, a property that other Newton-type observers lack. However, no theoretical guarantees on the convergence of the IPG observer were provided. This paper presents a rigorous convergence analysis of the IPG observer for a class of nonlinear systems in deterministic settings, proving its local linear convergence to the actual trajectory. Our assumptions are standard in the existing literature of Newton-type observers, and the analysis further confirms the relation of the IPG observer with the Newton observer, which was only hypothesized earlier.
Paper Structure (6 sections, 56 equations)

This paper contains 6 sections, 56 equations.

Table of Contents

  1. Introduction
  2. Assumptions and Prior Results
  3. Assumptions
  4. Prior Result on Convergence of IPG Optimizer
  5. Convergence of IPG Observer
  6. Conclusion

Theorems & Definitions (3)

  • proof
  • proof
  • proof