Regularity of Optimal Controls for State Constrained Problems

Conditions are given under which optimal controls are Lipschitz continuous, for dynamic optimization problems with functional inequality constraints. The linear independence condition on active state constraints, present in the earlier literature, can be replaced by a less restrictive, positive linear independence condition, that requires linear independence merely with respect to non-negative weighting parameters. Smoothness conditions on the data are also relaxed. A key part of the proof involves an analysis of the implications of first order optimality conditions in the form of a nonsmooth Maximum Principle.     

Regularity properties of optimal controls for problems with time-varying state and control constraints

In this paper we report new results on the regularity of optimal controls for dynamic optimization problems with functional inequality state constraints, a convex time-dependent control constraint and a coercive cost function. Recently, it has been shown that the linear independence condition on active state constraints, present in the earlier literature, can be replaced by a less restrictive, positive linear independence condition, that requires linear independence merely with respect to non-negative weighting parameters, provided the control constraint set is independent of the time variable. We show that, if the control constraint set, regarded as a time-dependent multifunction, is merely Lipschitz continuous with respect to the time variable, then optimal controls can fail to be Lipschitz continuous. In these circumstances, however, a weaker Hölder continuity-like regularity property can be established. On the other hand, Lipschitz continuity of optimal controls is guaranteed for time-varying control sets under a positive linear independence hypothesis, when the control constraint sets are described, at each time, by a finite collection of functional inequalities.     

Determination of Residual Pesticide in Plant Materials Using Planar Cholinesterase Sensors Modified with Nafion

Amperometric cholinesterase biosensors based on planar screen-printed carbon electrodes modified with Nafion were developed for determining residual pesticides exhibiting anticholinesterase activity in plant materials. When stored under dry conditions, biosensors retained their normal operation for six months. Simplified extraction methods were proposed to eliminate the effects of the matrix and organic solvents. The developed procedure provides the direct determination of down to 0.1 mg/kg pesticides in wheat, barley, sorghum, and rice grains without the removal of organic solvents.     

Strategic approaches to drug design. II. Modelling studies on phosphodiesterase substrates and inhibitors

Summary Modelling studies have been carried out on the phosphodiesterase (PDE) substrates, adenosine- and guanosine-35-cyclic monophosphates, and on a number of non-specific and type III-specific phosphodiesterase inhibitors. These studies have assisted the understanding of PDE substrate differentiation and the design of potent, selective PDE type III inhibitors.     

Application of duality theory to a class of composite cost control problems

Let a control system be described by a continuous linear map * from the input spaceU* (some dual Banach space) into the output spaceX* (some finite-dimensional normed space). Within the class of control problems where the constraints and cost are expressed in terms of the norms on the input and output spaces, the following two have had extensive coverage: (i)minimum effort problem: find, from amongst all inputs which have corresponding outputs lying in some closed sphere inX* centered on some desired outputx _d *, an output of minimum norm; and (ii)minimum deviation problem: find, from amongst all inputs lying in some closed sphere inU*, an input having corresponding output at a minimum distance fromx _d *. However, thecomposite cost problem, where we seek to minimizeF(u*, x _d * –x*) over elements satisfyingx* = *u* (F a certain kind of convex functional), has not received the same attention. This paper presents results for the composite cost problem paralleling known results for the minimum effort and deviation problems. It is hoped that a gap in the literature is thereby filled. We show that (a) a solution exists, (b) the solution can be characterized in terms of some closed hyperplaneH inX, and (c)H can be computed as being an element on which some concave functional over closed hyperplanes inX achieves its maximum. The treatment allows of infinite-dimensional output spaces. We make extensive use of recently developed duality theory.This research was supported by the Science Research Council of Great Britain and the Commonwealth Fund (Harkness Fellowship).