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

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.

Adaptive Two-Degrees-of-Freedom Current Control for Solenoids: Theoretical Investigation and Practical Application

“…Further research is to be conducted to improve the parameter convergence in situations of low excitation, which is an active field of research, see, e.g., [28]. The proposed adaptive control scheme strongly benefits from its property that the control error convergence does not rely on the convergence of the parameters.…”

“…Recall that the objective of this article is to design an adaptive control strategy for (4) that exhibits the same closed-loop performance independent of L and R. Since we do not have any information about the exact characteristics of L and R, we assume for the controller design that L and R are unknown but constant. Note that this is a common assumption in the context of adaptive control in the literature, see, e.g., [27], [28] and the references therein. Thus, in the following, we focus on the simplified controller design model…”

Real-time parameter estimation of polymer electrolyte membrane fuel cell in absence of excitation

“…A limitation of the pre-processing dynamics in (10) proposed in [28]. Specifically, similar to the algorithm in Subsection 4.2, the signals y and φ are pre-processed through the following set of dynamics:…”

“…The main convergence properties of the estimator can be summarized as follows [28]. If the regressor vector φ satisfies the interval excitation condition in Definition 4.2, then the GD+PD+FF dynamics in (15) satisfies the convergence property in (7).…”

“…Multiple authors from the control community have proposed novel real-time parameter estimation algorithms that overcome this excitation limitation [23][24][25][26][27][28]. Precisely, the stringent persitence of excitation condition, that is rarely satisfied in PEMFC, is relaxed to a much less restrictive interval excitation condition that can be satisfied in PEMFC systems.…”