We discuss the optimal design problem in regression models with long range dependence error structure. Asymptotic optimal designs are derived and it is demonstrated that these designs depend only indirectly on the correlation function. Several examples are investigated to illustrate the theory. Finally the optimal designs are compared with asymptotic optimal designs, which were derived by Bicke...

In this paper, we propose an idea which can solve the complexity of the overlapping situation observed in control system of living things. We introduce an another element between controlled object and control law. This newly introduced element is named as Implicit Control Law and decided by interaction of the controlled object , the control law and the field. Furthermore, the Implicit Control L...

In the common trigonometric regression model we investigate the optimal design problem for the estimation of the individual coeecients, where the explanatory variable varies in the interval ?a; a]; 0 < a : It is demonstrated that the structure of the optimal design depends sensitively on the size of the design space. For many cases optimal designs can be found explicitly, where the complexity o...

This report summarizes some of our recent work (Guo and Tomecek (2008b,a)) on a new theoretical connection between singular control of finite variation and optimal switching problems. This correspondence not only provides a novel method for analyzing multi-dimensional singular control problems, but also builds links among singular controls, Dynkin games, and sequential optimal stopping problems.

We give the explicit solution of optimal control problem which consists in minimizing epidemic peak SIR model when is an attenuation factor infectious rate, subject to a L1 constraint on represents budget constraint. The strategy given as feedback singular arc maintaining infected population at constant level until immunity threshold reached, and no intervention outside arc. discuss compare thi...