Parameter Estimation-Based Extended Observer for Linear Systems with Polynomial Overparameterization

TL;DR

This paper introduces an extended adaptive observer for uncertain linear systems with overparameterization, capable of reconstructing states and disturbances with minimal excitation requirements and algebraic estimation methods.

Contribution

It presents a novel exponentially stable observer that reconstructs physical states and disturbances without Luenberger gain, using algebraic methods and weak excitation conditions.

Findings

Observer accurately reconstructs states and disturbances in simulations.

Convergence achieved under weak regressor excitation.

Method simplifies observer design by avoiding differential correction gains.

Abstract

We consider a class of uncertain linear time-invariant overparametrized systems affected by bounded disturbances, which are described by a known exosystem with unknown initial conditions. For such systems an exponentially stable extended adaptive observer is proposed, which, unlike existing solutions, simultaneously: (i) allows one to reconstruct original (physical) states of the system represented in arbitrarily chosen state-space form rather than virtual states of the observer canonical form; (ii) ensures convergence of the state observation error to zero under weak requirement of the regressor finite excitation; (iii) does not include Luenberger correction gain and forms states estimate using algebraic rather than differential equation; (iv) additionally reconstructs the unmeasured external disturbance. The proposed solution is based on the new parametrizations to identify the observer parameters obtained with the help of the heterogeneous mappings and the dynamic regressor extension and mixing procedure. Illustrative simulations support obtained theoretical results.