A nonlinear adaptive observer with excitation-based switching

Abstract

Ahstract-This paper presents a MIMO nonlinear adaptive observer, which is characterized by a robust excitation-based switching strategy. The proposed switching algorithm allows to address the scenario of poor excitation, while a conser vative minimum duration of excitation interval for ensuring a progressive improvement is determined. The robustness of the devised method with respect to the bounded unstructured perturbation is studied by a input-to-state stability analysis. Simple simulation results show the effectiveness of the proposed technique.

An Adaptive-Observer-Based Robust Estimator of Multi-sinusoidal Signals

“…13 and 14, the estimator is capable to gather the frequency and amplitude contents with great accuracy, despite the unavoidable measurement noise due the limitation of the measurement devices. In this paper, a new adaptive-observer based technique [36] is proposed for estimating the amplitudes, frequencies and phases of the sinusoids composing a multi-sinusoidal signal, in presence of bias and bounded additive disturbances. Compared to other adaptive observer methods that estimate the characteristic polynomial's coefficients of the signal-generator system, the proposed algorithm allows for the direct adaptation of the squared-frequencies of the components.…”

“…In the following, we are going to show that the system (5) verifies all the requirements needed for the application of the switched-observer based methodology developed by the authors in [36]. On the other hand, in order to cope with the over-parametrization issue (i.e., the model is established with a number of sinusoids-parameters that is larger than the number of the components of the actual signal), the adaptation mechanism presented in [36] is completely re-designed in this paper, thus enabling the adaptation of the sole frequencies for which enough excitation is detected based on instantaneous checking of the excitation level.…”

“…Now, we are going to generalize the switched-mode adaptive observer preliminarily proposed in [36] to the biased multioscillator (5). Specifically, let us augment the dynamics of the observed system with a synthetic low-pass filter driven by the noisy measurement vector:…”

An adaptive observer-based estimator for multi-sinusoidal signals

“…Theorem 4.2: [21] Under the same assumptions of Theorem 4.1, consider the adaptive observer (8), (12), (13), (14) equipped with the excitation-based switching strategy defined in (15). Then, the discrete dynamics induced by sampling the adaptive observer in correspondence of the switching transitions has the asymptotic ISS property if the excitation phases last longer than β −1 ln(L 0 ).…”

“…Among these methods, [15], [17], [18] are capable to handle a biased multi-sinusoidal signal, while [19] has been applied in a nonlinear plant for disturbance cancellation. In addition to the aforementioned adaptive observer-based techniques, an asymptotically convergent estimator for n-frequencies using contraction theory is proposed in [20] Motivated by the adaptive observer proposed in [21] and its extension to the single sinusoidal case [13], the presented paper deals with a new methodology that is capable to offer reliable estimates of amplitudes, frequencies, phases and offset from a biased signal comprising n sinusoids. In contrast with other methods that adapt the coefficients of the characteristic polynomial, a direct adaptation law for the squares of the frequencies is provided.…”