Continuous-time Model Identification by Using Adaptive Observer

Abstract

This paper proposes a new method of continuous-time model identification from sampled I/O data by using an adaptive observer. The boundedness of the parameter estimate and the exponential convergence of the parameter estimate error to 0 under the PE assumption are guaranteed. In order to identify the plant from a finite number of I/O data, an adaptive observer of a backward system is also proposed.

Bias-Compensated Adaptive Observer for a Continuous-Time Model Estimation

“…The proposing adaptive observer is based on the structure depicted in Fig. 1, in which there is an estimation mechanism of the intersample output (Ikeda et al, 2006a). When the parameter estimateθ i is a constant vector, the continuoustime signals z i (t) can be easily discretized without any approximations because of the zeroth order hold input assumption.…”

“…by usingz iΔ [k] andz iν [k] in (20). It can be shown that ε iΔ → 0 whenθ i → θ * (Ikeda et al, 2006a). The asymptotic bias is caused by ε iν [k] and is analyzed in the next section.…”

“…Among the many approaches to the direct identification of continuous-time models, a use of state variable filters is one of the basic approaches and has a long history (Wang and Gawthrop, 2001;Young, 1981). In order to recover the information loss incurred by the sampling, the authors have proposed a continuous-time model identification method by using an adaptive observer, which estimates the inter-sample output of the plant as well as the plant parameters with the ZOH input assumption (Ikeda et al, 2006a;Ikeda et al, 2006b). The output of the state variable filter becomes a pseudo regression vector and a bootstrap method is adopted.…”

“…The output of the state variable filter becomes a pseudo regression vector and a bootstrap method is adopted. The parameter convergence and the parameter estimation error of the proposed method are analyzed in (Ikeda et al, 2006a;Ikeda et al, 2006b).…”

“…In this paper, bias compensating method is applied for the previously proposed method (Ikeda et al, 2006a;Ikeda et al, 2006b) in order to achieve the consistency of the estimate. Bias compensating least squares methods were origninally developed for the discrete-time model estimation (Sagara and Wada, 1977) and applied for the continuoustime model estimation (Zhao et al, 1991;Garnier et al, 2000).…”