V. A. Baturin

Iterative methods for solution of problems of optimal control of logic-dynamic systems

Optimal control problem for logic-dynamic systems is considered. Based on sufficient optimality conditions, similar to Krotov’s conditions, a method for successive control improvement is developed. First- and second-order computational algorithms are constructed.

Super-oxidation of silicon nanoclusters: magnetism and reactive oxygen species at the surface

Oxidation of silicon nanoclusters depending on the temperature and oxygen pressure is explored from first principles using the evolutionary algorithm, and structural and thermodynamic analysis. From our calculations of 90 SinOm clusters we found that under normal conditions oxidation does not stop at the stoichiometric SiO2 composition, as it does in bulk silicon, but goes further placing extra oxygen atoms on the cluster surface. These extra atoms are responsible for light emission, relevant to reactive oxygen species and many of them are magnetic. We argue that the super-oxidation effect is size-independent and discuss its relevance to nanotechnology and miscellaneous applications, including biomedical ones.

Measure-controlled dynamic systems: Polyhedral approximation of their reachable set boundary

An algorithm for polyhedral approximation of the reachable set of impulsive dynamic control systems is designed. The boundary points of the reachable set are determined by recursively generating and solving a family of auxiliary optimal impulsive control problems with state-linear objective functional. The impulsive control problem is solved with an algorithm that implicitly reduces the problem an ordinary optimal control problem. The reduced problem thus obtained is solved with an algorithm based on local approximations of the reachable set.

Electronic Properties and Stability of Silicon Nanoclusters Passivated by Hydrogen

The total energy, geometry and electronic spectra of nanoclusters \shm{} (

Second-Order Improvement Methods for Linear Unlimited Control Problems

m=0\ldots11

Second Order Methods for the Optimal Control Problems

) are calculated using the evolutionary algorithm and density functional theory (DFT). It is shown, that the features of electron spectrum, namely HOMO-LUMO gap and valence band width, correlate with cluster geometry and stability. The HOMO-LUMO gap becomes wider as the number of hydrogen atoms increases whereas the width of valence band gets lower. The widening of the band gap indicates the increasing of cluster stability which is consistent with existing data on reaction energy.

Second-order successive improvement method for discrete control systems

Abstract Optimal control problem in which differential system is linear on control is considered. Such problem has some singularities. The method of improvement based on special transformations is suggested. Algorithms of the successive improvement using the second order method of improvement for regular problem are considered.

Improving method for discrete control system with network structure

The paper considers the iterative improvement algorithms, the efficiency of which substantially depends on the chosen parameters values. The problem of control of these parameters is formulated and discussed. We designed the modified algorithms where parameters are automatically adjusted at each iteration. The original and modified algorithms are applied to solve the problem of optimal control for the ecology-economic system.

Modifications of the methods of successive approximations for problems of optimal control of logic-dynamic systems

A second-order improvement algorithm for a discrete-time optimal control problem with a free right endpoint is considered. The solution is based on the expansion of the constructs proposed in [1] in a parameter. A new algorithm for such systems is proposed.

Second-order improvement method to solve problems of optimal control of the logic-dynamic systems

This paper is dedicated to designing approximate methods of solving discrete optimal control problems with network structure; the methods involve sufficient optimality conditions derived by V.F. Krotov.