Necessary conditions for optimal control problems with state constraints

Necessary conditions of optimality are derived for optimal control problems with pathwise state constraints, in which the dynamic constraint is modelled as a differential inclusion. The novel feature of the conditions is the unrestrictive nature of the hypotheses under which these conditions are shown to be valid. An Euler Lagrange type condition is obtained for problems where the multifunction associated with the dynamic constraint has values possibly unbounded, nonconvex sets and satisfies a mild `one-sided' Lipschitz continuity hypothesis. We recover as a special case the sharpest available necessary conditions for state constraint free problems proved in a recent paper by Ioffe. For problems where the multifunction is convex valued it is shown that the necessary conditions are still valid when the one-sided Lipschitz hypothesis is replaced by a milder, local hypothesis. A recent `dualization' theorem permits us to infer a strengthened form of the Hamiltonian inclusion from the Euler Lagrange condition. The necessary conditions for state constrained problems with convex valued multifunctions are derived under hypotheses on the dynamics which are significantly weaker than those invoked by Loewen and Rockafellar to achieve related necessary conditions for state constrained problems, and improve on available results in certain respects even when specialized to the state constraint free case.

Proofs make use of recent `decoupling' ideas of the authors, which reduce the optimization problem to one to which Pontryagin's maximum principle is applicable, and a refined penalization technique to deal with the dynamic constraint.

     

Design and fabrication of infrared detectors based on lattice-matched InAs0.91Sb0.09 on GaSb

The InAs_0.91Sb_0.09 ternary compound grown on GaSb substrates is a promising alloy for light detection in the 3–5 μm window. Nevertheless, its development is still limited due to difficulties occurring during device processing. For example, the use of dry etching for the processing of InAs_0.91Sb_0.09 p–i–n photovoltaïc detectors induces a strong leakage current along the mesa edge. In this letter, we show an improvement of the R₀A characteristic by several orders of magnitude at low temperature by using an ion beam etching (IBE) followed by a wet chemical etching. This optimized and reliable device processing allows us to demonstrate that the detector performance is actually limited by the diffusion current of holes. Finally, we discuss the ability of an n-type barrier made of the InAs/AlSb super-lattice to prevent hole diffusion and to improve the R₀A characteristic of these detectors.     

The equivalence of “strong calmness” and “calmness” in optimal control theory

In an earlier paper optimality conditions expressed in terms of a Lipschitz continuous function which satisfies a condition resembling the Hamilton-Jacobi-Bellman equation were derived. It was shown that a certain hypothesis, strong calmness, is the weakest hypothesis under which such developments are possible. In the present paper it is shown that strong calmness is equivalent to calmness for a wide class of problems. Support is thereby given to strong calmness as being a reasonable hypothesis, since calmness is apparently the weakest known hypothesis assuring normality, in the sense that the Pontryagin maximum principle applies with the cost multiplier nonzero.     

Photochromism of palmitoylamide-substituted indoline spiropyrans

A comparative spectral-kinetic and luminescent study of photochromic transformations of two palmitoylamide-substituted indoline spiropyrans was performed in solvents with various polarities and polyvinylbutyral binding and amorphous layers. The compounds were found to be photochromic and form aggregates of two types in addition to the monomeric merocyanine form under the action of UV irradiation. The formation of these photoproducts depended on solvent polarity and the state of aggregation of the substances.     

State constrained optimal control problems with time delays

In a recent, related, paper, necessary conditions in the form of a Maximum Principle were derived for optimal control problems with time delays in both state and control variables. Different versions of the necessary conditions covered fixed end-time problems and, under additional hypotheses, free end-time problems. These conditions improved on previous conditions in the following respects. They provided the first fully non-smooth Pontryagin Maximum Principle for problems involving delays in both state and control variables, only special cases of which were previously available. They provide a strong version of the Weierstrass condition for general problems with possibly non-commensurate control delays, whereas the earlier literature does so only under structural assumptions about the dynamic constraint. They also provided a new ‘two-sided’ generalized transversality condition, associated with the optimal end-time. This paper provides an extension of the Pontryagin Maximum Principle of the earlier paper for time delay systems, to allow for the presence of a unilateral state constraint. The new results fully recover the necessary conditions of the earlier paper when the state constraint is absent, and therefore retain all their advantages but in a setting of greater generality.     

Multiconformational composite molecular potential fields in the analysis of drug action. I. Methodology and first evaluation using 5-HT and histamine action as examples

Summary The quality of molecular electrostatic maps generated by non-quantum mechanical methods has been improved using extended electron distributions. Further simplification has been achieved by distilling these maps down to their energy extrema. A new means of defining surface interaction has been added and the resulting composite map has been plotted for a limited number of low-lying conformers of a series of agonists and antagonists of the H₂ and H₃ receptors and 5-HT_1A and 5-HT_1D receptors. The results from the cross-comparison of these maps indicate their ability to distinguish the specific receptor. Interesting consequences of the method are that structural overlay is irrelevant, that several conformations may contribute to the overall binding pattern and that lesser pharmacological activities may be deduced from the results.