부산대학교 도서관

In this article, the following single-input single-outputcontinuous-time system is considered:$$A(\rho)y(t)=B(\rho)u(t),$$$$A(\rho)=\rho^n+a_1\rho^{n-1}+\cdots+a_{n-1}\rho+a_n,$$$$B(\rho)=b_0\rho^m+b_1\rho^{m-1}+\cdots+b_{m-1}\rho+b_m,$$for $\rho={d\over dt}$ . The regression form with model error $e(t)$ iswritten as$$y_{\rm ref}(t)=\psi^\ssf T(t)\theta+e(t),$$where$y_{\rm ref}=J^n\rho^ny(t) $,$ \theta^\ssf T=[a_1,a_2,\dots,a_n,b_0,\dots,b_m] $, $$\psi^\ssf T(t)=[-J^n\rho^{n-1}y(t),\dots,-J^ny(t),J^n\rho^mu(t),\dots,J^nu(t)],$$and$$J^ny(t)=\int^t_{t-T_h}\cdots\int^{t_{n-1}}_{t_{n-1}-T_h}y(t_n) dt_n\cdotsdt_1.$$\parInstead of the usual least squares error criteria for identification,the least absolute error criteria are introduced by$$\multline V(\theta)= \int^t_0w(t,\tau)|Y_{\rm ref}(\tau)-\psi^\ssf T(\tau)\theta|d\tau=\\\int^t_0w(t,\tau){|Y_{\rm ref}(\tau)-\psi^\ssf T(\tau)\theta|^2\over|e(\tau)|}d\tau,\endmultline$$where $w(t,\tau)$ is a weight function. First the model error $e(t)$is approximated by a current estimate, and then the leastabsolute estimate is derived. Introducing the so-called``instrumental variable'', the authors present a differential representationof thecontinuous estimator. Finally, with the aid of thediscretization scheme, the ``instrumental variable'' is constructed asa noise-free output (from the input $u(t)$ and${\widehat\theta}$), and ${\widehat e}(t)$ is chosen to be an {\it apriori} and/or {\it a posteriori} prediction error. The least absolute errorestimation algorithm is illustrated with some numerical results.