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We consider n observations from the GARCH-type model: Z = UY, where U and Y are independent random variables. We aim to estimate density function Y where Y have a weighted distribution. We determine a sharp upper bound of the associated mean integrated square error. We also make use of the measure of expected true evidence, so as to determine when model leads to a crisis and causes data to be lost.
In this work, a nonlinear model predictive
controller is developed for a batch polymerization process. The physical model
of the process is parameterized along a desired trajectory resulting in a
trajectory linearized piecewise model (a multiple linear model bank) and the
parameters are identified for an experimental polymerization reactor. Then, a multiple
model adaptive predictive controller is designed for thermal trajectory
tracking of the MMA polymerization. The input control signal to the process is
constrained by the maximum thermal power provided by the heaters. The
constrained optimization in the model predictive controller is solved via genetic
algorithms to minimize a DMC cost function in each sampling interval.