Supervisory observer for parameter and state estimation of nonlinear systems using the DIRECT algorithm

TL;DR

This paper introduces a supervisory observer framework for nonlinear systems that employs the DIRECT global optimization algorithm to adaptively sample parameter sets, improving estimation accuracy with convergence guarantees.

Contribution

It proposes an automatic parameter sampling method using the DIRECT algorithm within a supervisory observer, reducing the need for large initial sample sets and providing convergence guarantees.

Findings

Effective parameter and state estimation demonstrated on neural population model.

Adaptive sampling improves estimation accuracy over fixed sampling methods.

Convergence guarantees under persistency of excitation conditions.

Abstract

A supervisory observer is a multiple-model architecture, which estimates the parameters and the states of nonlinear systems. It consists of a bank of state observers, where each observer is designed for some nominal parameter values sampled in a known parameter set. A selection criterion is used to select a single observer at each time instant, which provides its state estimate and parameter value. The sampling of the parameter set plays a crucial role in this approach. Existing works require a sufficiently large number of parameter samples, but no explicit lower bound on this number is provided. The aim of this work is to overcome this limitation by sampling the parameter set automatically using an iterative global optimisation method, called DIviding RECTangles (DIRECT). Using this sampling policy, we start with 1 + 2np parameter samples where np is the dimension of the parameter set. Then, the algorithm iteratively adds samples to improve its estimation accuracy. Convergence guarantees are provided under the same assumptions as in previous works, which include a persistency of excitation condition. The efficacy of the supervisory observer with the DIRECT sampling policy is illustrated on a model of neural populations.