A new least squares parameter estimator for nonlinear regression equations with relaxed excitation conditions and forgetting factor

Romeo Ortega (1, 2) , Jose Guadalupe Romero (1, 3) , Stanislav Aranovskiy (4, 5)

1 ITAM - Instituto Tecnológico Autónomo de México
2 ITMO University [Russia]
3 POLYU - The Hong Kong Polytechnic University [Hong Kong]
4 CentraleSupélec [campus de Rennes]
5 IETR - Institut d'Électronique et des Technologies du numéRique

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 timevarying 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.

Mots clés: Parameter estimation; Least Squares; Least squares identification algorithm; Exponentially convergent identification; Nonlinear regression model

Domaines: Automatique / Robotique; Systèmes et contrôle [cs.SY]

Romeo Ortega, Jose Guadalupe Romero, Stanislav Aranovskiy. A new least squares parameter estimator for nonlinear regression equations with relaxed excitation conditions and forgetting factor. Systems and Control Letters, 2022, 169, pp.105377. ⟨10.1016/j.sysconle.2022.105377⟩. ⟨hal-03793150⟩