On the ergodic and the adaptive control of stochastic differential delay systems

Some problems of ergodic control and adaptive control are formulated and solved for stochastic differential delay systems. The existence and the uniqueness of invariant measures that are solutions of the stochastic functional differential equations for these systems are verified. For an ergodic cost criterion, almost optimal controls are constructed. For an unknown system, the invariant measures and the optimal ergodic costs are shown to be continuous functions of the unknown parameters. Almost self-optimizing adaptive controls are feasibly constructed by an approximate certainty equivalence principle.This research was partially supported by NSF Grants ECS-91-02714 and ECS91-13029.     

The stabilizing effect of a random parametric perturbation on an unstable linear system

For two-dimensional autonomous linear systems we establish the possibility of mean-square stabilization using a time-independent parametric random perturbation.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 116–118.     

Methanol adsorption on Cu(110) and the angular distribution of the reaction products

Integral and angle resolved thermal desorption spectroscopies were used to study methanol adsorption and oxidation on clean and oxygen covered Cu(110) surfaces. Special emphasis was put on the Cu-CuO stripe phase, which forms when the Cu(110) surface is covered with 0.25 ML of oxygen. In the temperature regime between 200 and 300 K associative desorption of methanol and water takes place, showing a normal desorption character with peaks shifting to lower temperature with increasing coverage and with a nearly cosine angular desorption distribution. In the temperature range of about 350 K formaldehyde, hydrogen, and again methanol desorb nearly concomitantly in the form of a very narrow peak (full width at half maximum=10 K), with peaks shifting to higher temperature with increasing methanol coverage. The angular distribution of these peaks is strongly forward focused, indicating activation barriers being involved. In the case of the Cu-CuO stripe phase the angular distribution of the desorption products is clearly different in the [110] and [001] azimuthal directions, demonstrating the influence of the border lines between the copper and the copper oxide stripes on the desorption process.     

The electromagnetic energy and momentum of finite charged bodies moving at constant velocity

It is shown that a purely electromagnetic, divergence-free tensorS ^ij , can be defined for any electrically charged body which is held in equilibrium by some cohesive force and moving at some constant velocity. This tensor appears to represent the electromagnetic energy-momentum of the body; the integral (1/c) ∝S ^ij dS _j (dS _j is the differential element of any spacelike hypersurface) iscM ₀ μ ⁱ the electromagnetic four-momentum of the system (M ₀ is the electromagnetic rest mass of the system,U _i is the four-velocity). The divergence-free property ofS ^ij depends only on Maxwell's equation and the condition of uniform motion. It is suggested that whatever the nature of the cohesive forces within such a system the total stress-energy tensor will, in effect, break up into two parts which are separately divergence-free: the purely electromagnetic tensor,S ^ij , and a tensor representing the energy-momentum of the cohesive forces. Just as it makes sense to speak of the electromagnetic mass of a system at rest without regard to the cohesive forces, it makes sense to talk about the electromagnetic momentum of the system, when it is moving at constant velocity, without reference to the cohesive forces.     

High-speed in situ surface X-ray diffraction studies of the electrochemical dissolution of Au(001)

We present in situ X-ray surface diffraction studies of interface processes with data acquisition rates in the millisecond regime, using the electrochemical dissolution of Au(001) in Cl-containing solution as an example. This progress in time resolution permits monitoring of atomic-scale growth and etching processes at solid-liquid interfaces at technologically relevant rates. Au etching was found to proceed via a layer-by-layer mechanism in the entire active dissolution regime up to rates of ～20 ML/s. Furthermore, we demonstrate that information on the lateral surface morphology and in-plane lattice strain during the electrochemical process can be obtained.     

Zero-sum Markov games with stopping and impulsive strategies

Three kinds of zero-sum Markov games with stopping and impulsive strategies are considered. For these games we find the saddle point strategies and prove that, the value of the game depends continuously on the initial state.     

A branch-and-bound algorithm for solving a fixed charge problem in the profit optimization of sawn timber production

This paper deals with the problem of profit optimization in sawn timber production, utilizing a special type of sawmill. Expected rejects and resetting costs are taken into consideration. The present problem is formulated as a fixed charge linear programming problem involving identical fixed charges, one equality constraint and explicit bounds on the variables. Based on the greedy sorting of the variables we develop a branch-and-bound algorithm working on a special subset of all solutions. Through usage of the problem structure for constructing bounds we arrive at an acceptable CPU-time (on a 80386 personal computer) for practical purposes.     

Ergodic and adaptive control of hidden Markov models

A partially observed stochastic system is described by a discrete time pair of Markov processes. The observed state process has a transition probability that is controlled and depends on a hidden Markov process that also can be controlled. The hidden Markov process is completely observed in a closed set, which in particular can be the empty set and only observed through the other process in the complement of this closed set. An ergodic control problem is solved by a vanishing discount approach. In the case when the transition operators for the observed state process and the hidden Markov process depend on a parameter and the closed set, where the hidden Markov process is completely observed, is nonempty and recurrent an adaptive control is constructed based on this family of estimates that is almost optimal.