Exponentially Stable Adaptive Observation for Systems Parameterized by Unknown Physical Parameters

TL;DR

This paper introduces a new exponentially stable adaptive observer for linear systems with unknown physical parameters, not restricted to canonical form, ensuring convergence of states and parameters under certain conditions.

Contribution

It presents a novel adaptive observer design that works with the original system description, expanding applicability beyond canonical form restrictions.

Findings

Ensures exponential convergence of state and parameter estimates.

Applicable to systems satisfying specific assumptions including observability and parameter identifiability.

Validated through simulations demonstrating stability and convergence.

Abstract

The method to design exponentially stable adaptive observers is proposed for linear time-invariant systems parameterized by unknown physical parameters. Unlike existing adaptive solutions, the system state-space matrices A, B are not restricted to be represented in the observer canonical form to implement the observer. The original system description is used instead, and, consequently, the original state vector is obtained. The class of systems for which the method is applicable is identified via three assumptions related to: (i) the boundedness of a control signal and all system trajectories, (ii) the identifiability of the physical parameters of A and B from the numerator and denominator polynomials of a system input/output transfer function and (iii) the complete observability of system states. In case they are met and the regressor is finitely exciting, the proposed adaptive observer, which is based on the known GPEBO and DREM procedures, ensures exponential convergence of both system parameters and states estimates to their true values. Detailed analysis for stability and convergence has been provided along with simulation results to validate the developed theory.