Stochastic optimal control

H. J. Kushner has obtained the differential equation satisfied by the optimal feedback control law for a stochastic control system in which the plant dynamics and observations are perturbed by independent additive Gaussian white noise processes. However, the differentiation includes the first and second functional derivatives and, except for a restricted set of systems, is too complex to solve with present techniques.

This investigation studies the optimal control law for the open loop system and incorporates it in a sub-optimal feedback control law. This suboptimal control law's performance is at least as good as that of the optimal control function and satisfies a differential equation involving only the first functional derivative. The solution of this equation is equivalent to solving two two-point boundary valued integro-partial differential equations. An approximate solution has advantages over the conventional approximate solution of Kushner's equation.

As a result of this study, well known results of deterministic optimal control are deduced from the analysis of optimal open loop control.

Some experiments on solving multistage stochastic mixed 0-1 programs with time stochastic dominance constraints

In this work we extend to the multistage case two recent risk averse measures for two-stage stochastic programs based on first- and second-order stochastic dominance constraints induced by mixed-integer linear recourse. Additionally, we consider Time Stochastic Dominance (TSD) along a given horizon. Given the dimensions of medium-sized problems augmented by the new variables and constraints required by those risk measures, it is unrealistic to solve the problem up to optimality by plain use of MIP solvers in a reasonable computing time, at least. Instead of it, decomposition algorithms of some type should be used. We present an extension of our Branch-and-Fix Coordination algorithm, so named BFC-TSD, where a special treatment is given to cross scenario group constraints that link variables from different scenario groups. A broad computational experience is presented by comparing the risk neutral approach and the tested risk averse strategies. The performance of the new version of the BFC algorithm versus the plain use of a state-of-the-artMIP solver is also reported.

Anisotropic-source-induced changes of the degree of polarization of stochastic electromagnetic beams on propagation

It is shown that stochastic electromagnetic beams may have different degrees of polarization on propagation, even though they have the same coherence properties in the source plane. This fact is due to a possible difference in the anisotropy of the field in the source plane. The result is illustrated by some examples.

Suivi cartographique de l'expansion des macrophytes envahissant le système lagunaire Ebrié (Côte d'Ivoire)

Remote mapping were realised from December 1986 to September 1989 to describe the seasonal evolution of macrophytes colonizing the surface waters of the eastern sector of the Ebrié lagoon. The vegetal cover of this sector and associated lagoons is essentially composed of Eichhornia crassipes (water hyacinth). Its expansion is favored by the decrease in the salinity of the lagoon waters which is due to rain falls. Its migration through the lagoon environment is ensured by the overflow of the Comoé river. The opening of the Bassam inlet induced its temporary disappearence from the newly created estuarian zone.

Influence of vapor transport equilibration on the crystal quality and thermal-expansion coefficients of gamma-LiAlO2

gamma-LiAlO2 (LAO) single crystal has been grown by the Czochralski method. However, its quality was deteriorated due to lithium volatilization during the crystal growth. The full width at half maximum value drops from 116.9 to 44.2 arc sec after the LAO slice was treated by vapor transport equilibration at 1000, 1100, and 1200 degrees C/48 h in sequence. The treated slice shows higher optical transmission than the as-grown one in the measured wavelength range of 190-1900 nm, meanwhile, its absorption edge exhibits a blueshift. According to Raman spectra, the treated slice has homogeneous quality at different depths from surface to 0.01 mm. The expansion coefficient of the treated slice for a axis drops from 17.2398x10(-6)/degrees C to 16.5240x10(-6)/degrees C, and that for c axis drops from 10.7664x10(-6)/degrees C to 10.0786x10(-6)/degrees C.

In situ synthesis of ZrO2/ZrW2O8 composites with near-zero thermal expansion

In this paper, ZrO2 and WO3 were used as the raw materials to prepare ZrO2/ZrW2O8 composites by in situ reaction method and the thermal expansion property of the composites was studied. This novel method included a heating step up to 1473 K for 24 h, which combines the synthesizing and sintering of ZrW2O8. The result indicates that ZrO2/ZrW2O8 composite shows near-zero thermal expansion when the weight ratio of ZrO2 and WO3 is 2.5:1. Compared with composites prepared previously by non-reactive sintering of ZrO2 and ZrW2O8, the composites show higher relative density and lower porosity.