2021
DOI: 10.48550/arxiv.2112.05497
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An Adaptive Observer for Uncertain Linear Time-Varying Systems with Unknown Additive Perturbations

Abstract: In this paper we are interested in the problem of adaptive state observation of linear timevarying (LTV) systems where the system and the input matrices depend on unknown timevarying parameters. It is assumed that these parameters satisfy some known LTV dynamics, but with unknown initial conditions. Moreover, the state equation is perturbed by an additive signal generated from an exosystem with uncertain constant parameters. Our main contribution is to propose a globally convergent state observer that requires… Show more

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Cited by 3 publications
(4 citation statements)
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“…Before closing this section we make the remark that it is actually possible to relax the excitation Assumption 5. Indeed, it has been shown in [15] that global exponential convergence of an LS+FF estimator with dynamic regression extension is ensured with the strictly weaker interval excitation condition [7]. This scheme was also implemented in the simulations but the performance improvement with respect to the LS+FF was negligiblehence, for brevity, the simulated results are omitted.…”
Section: Simulation Resultsmentioning
confidence: 99%
“…Before closing this section we make the remark that it is actually possible to relax the excitation Assumption 5. Indeed, it has been shown in [15] that global exponential convergence of an LS+FF estimator with dynamic regression extension is ensured with the strictly weaker interval excitation condition [7]. This scheme was also implemented in the simulations but the performance improvement with respect to the LS+FF was negligiblehence, for brevity, the simulated results are omitted.…”
Section: Simulation Resultsmentioning
confidence: 99%
“…As expected, this regressor equation is nonlinearly parameterized, which hampers the application of standard estimation techniques. Therefore, we are compelled to appealin Section 4-to the LS+DREM parameter estimator recently reported in (Ortega et al, 2022;Pyrkin et al, 2022). Lemma 1.…”
Section: Regression Equation For Parameter Estimationmentioning
confidence: 99%
“…To estimate the parameters θ from the NLPRE (5) we invoke the recent result of (Ortega et al, 2022), where the LS+DREM estimator proposed in (Pyrkin et al, 2022), which is applicable for linear regression equations, was extended to deal with NLPRE. However, this estimator requires that the mapping of the NLPRE satisfies a monotonicity property, which is not verified by W I (θ) given in (6).…”
Section: Construction Of a Strictly Monotonic Mappingmentioning
confidence: 99%
“…Before closing this section we make the remark that it is actually possible to relax the excitation Assumption 5. Indeed, it has been shown in Ortega et al 42 that global exponential convergence of the LS+FF estimator with dynamic regression extension is ensured with the strictly weaker interval excitation condition 43 -see also Pyrkin et al 44 This scheme was also implemented in the simulations but the performance improvement with respect to the LS+FF was negligible-hence, for brevity, the simulated results are omitted.…”
mentioning
confidence: 99%