부산대학교 도서관

In this article, the following single-input single-output continuous-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 $e(t)$ is written 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 $$ J^ny(t)=\int^t_{t-T_h}\cdots\int^{t_{n-1}}_{t_{n-1}-T_h}y(t_n) dt_n\cdots dt_1. $$ \par Instead 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 least absolute estimate is derived. Introducing the so-called ``instrumental variable'', the authors present a differential representation of the continuous estimator. Finally, with the aid of the discretization scheme, the ``instrumental variable'' is constructed as a noise-free output (from the input $u(t)$ and ${\widehat\theta}$), and ${\widehat e}(t)$ is chosen to be an {\it a priori} and/or {\it a posteriori} prediction error. The least absolute error estimation algorithm is illustrated with some numerical results.