The adaptive LQG problem--Part I

This paper is concerned with a rigorous study of the "dual control" problem of Fel'dbaum, i.e., the LQG optimal control problem in the presence of Bayesian parameter uncertainty. The solution of this problem involves two parts, one relating to filtering and one to control. Although we establish our filtering result in complete generality in the last section, most of the paper concentrates on the finite parameter case to ease the exposition. The control result that we establish is incomplete in the sense that the smoothness of the optimal cost function is assumed rather than proved. Nevertheless, our results and methods are such that we arrive at a new proof of the classical separation theorem showing that the well-known LQG feedback law is optimal within the widest possible class of admissible controls. As this new proof avoids all talk of "dependence of the sigma algebra on the control," "weak solutions," "measure transformation techniques," etc., we feel that this result will help to clarify what is involved in the classical separation theorem.     

On the adaptive stabilization of linear systems

The problem of adaptively stabilizing a linear system to zero is addressed. A new result is presented, showing that a finite family of linear systems is adaptively stabilizable if and only if the family is simultaneously stabilizable in the wellknown algebraic sense. This result is all the more surprising as the observations available consist of the signal corrupted by additive white Gaussian noise.     

Active Carbon from Microwave Date Stones for Toxic Dye Removal: Setting the Design Capacity

The widely used toxic dye malachite green (MG) poses a significant risk to human health, having a mutagenic effect. Waste date stones were used to produce microwave-activated carbons and were applied to adsorb the highly toxic dye. The critically important task of selecting the correct design adsorption capacity for different effluent pollutant concentrations to meet effluent discharge limit standards is described and a novel design selection criteria approach is presented.     

Front-to-backside alignment using resist-patterned etch control andone etching step

A processing technique that aligns features on the front side of a wafer to those on its backside has been developed for bulk micromachining. A 30 μm-square and 1.6 μm-thick diaphragm serves as an alignment pattern. At the same time that the alignment diaphragm is made, much thicker, large-area diaphragms can be partially etched using `mesh' masking patterns in these areas. The mesh-masking technique exploits the etch-rate differences between (100) and (111) planes to control the depths reached by etch pits in selected areas. The large partially etched diaphragms (2 to 3 mm², roughly 100 μm thick) are sufficiently robust to survive subsequent IC-processing steps in a silicon-foundry environment. The thin alignment diaphragm can be processed through these steps because of its very small area. The partially etched diaphragms can be reduced to useful thicknesses in a final etch step after the circuits have been fabricated