Data-based Identifiability and Observability Assessment for Nonlinear Control Systems using the Profile Likelihood Method

Thomas Schmitt,Bastian Ritter

doi:10.1016/j.ifacol.2020.12.1312

Abstract

This paper introduces the profile likelihood method in order to assess simultaneously the parameter identifiability and the state observability for nonlinear dynamic state-space models with constant parameters. While a formal definition of a parameter’s identifiability has been used before, the novel idea is to investigate also the state’s observability by the identifiability of its initial value. Using the profile likelihood, both qualitative as well as quantitative statements are drawn from the analysis based on the nonlinear model and (possibly noisy) sensor data. A simplified wind turbine model is presented and used as an application example for the profile likelihood approach in order to investigate the model’s usability for state and parameter estimation. It is shown that the critical model parameters and initial states are identifiable in principle. The analysis with more complex models and realistic data reveals the limitations when assumptions are deliberately violated in order to meet reality.

Highlights

Today, in many control applications the system is described by ordinary differential equations (ODEs) and its states are used by the control algorithm, e. g. state space or model predictive control
This paper introduces the profile likelihood method in order to assess simultaneously the parameter identifiability and the state observability for nonlinear dynamic state-space models with constant parameters
It is shown that the critical model parameters and initial states are identifiable in principle

Summary

Introduction

In many control applications the system is described by ordinary differential equations (ODEs) and its states are used by the control algorithm, e. g. state space or model predictive control. In many control applications the system is described by ordinary differential equations (ODEs) and its states are used by the control algorithm, e. G. state space or model predictive control. For nonlinear systems, a state’s observability is not an invariant system property (as is the case for linear systems), but depends on the system’s stimulation. Let us assume a nonlinear model described by ODEs of the form x (t) = f (x(t), u(t), θ),. (1b) where x(t) ∈ Rn is the state vector, u(t) ∈ Rm the input vector, y(t) ∈ Rr the output vector. Whether a state xi is observable depens on the input u and the selection of unknown parameters θ. A state can be more or less well observable, depending on how the system is stimulated

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Conclusion