A New Least Squares Parameter Estimator for Nonlinear Regression Equations with Relaxed Excitation Conditions and Forgetting Factor

TL;DR

This paper introduces a novel least squares estimator for nonlinear regression that guarantees exponential convergence, adapts to time-varying parameters, and offers improved transient performance through a mixing step.

Contribution

It presents a new estimator with relaxed excitation conditions, incorporating a forgetting factor and mixing step, applicable to nonlinear and switched systems, with proven stability and superior performance.

Findings

Guaranteed exponential convergence for identifiable regressions

Effective tracking of time-varying parameters

Demonstrated superior performance through literature examples

Abstract

In this note a new high performance least squares parameter estimator is proposed. The main features of the estimator are: (i) global exponential convergence is guaranteed for all identifiable linear regression equations; (ii) it incorporates a forgetting factor allowing it to preserve alertness to time-varying parameters; (iii) thanks to the addition of a mixing step it relies on a set of scalar regression equations ensuring a superior transient performance; (iv) it is applicable to nonlinearly parameterized regressions verifying a monotonicity condition and to a class of systems with switched time-varying parameters; (v) it is shown that it is bounded-input-bounded-state stable with respect to additive disturbances; (vi) continuous and discrete-time versions of the estimator are given. The superior performance of the proposed estimator is illustrated with a series of examples reported in the literature.