A method of computing the gradient and the Hessian of the quality criterion in parametric optimization of continuous-discrete stochastic systems

We propose an effective method of numerical determination of the gradient vector and the Hessian matrix of a quadratic quality criterion in parametric optimization of continuous-discrete stochastic dynamic control systems based on the application of adjoint equations. Translated fromDinamicheskie Sistemy, No. 13, 1994, pp. 20–25.     

Optimal estimation of a state based on deterministic and stochastic discrete measurements

A problem of constructing algorithms of optimal estimation of states of a discrete system accounting for deterministic and stochastic measurements is considered. A low order estimation algorithm is proposed in the form of a two-stage procedure for each instant of time obtained by direct application of the Kaiman optimal filtering algorithm.Translated from Dinamicheskie Sistemy, No. 4, pp. 85–89, 1985.     

On a mixed Poincaré-Steklov type spectral problem in a Lipschitz domain

We consider a mixed boundary value problem for a second-order strongly elliptic equation in a Lipschitz domain. The boundary condition on a part of the boundary is of the first order and contains a weight function and the spectral parameter, while on the remaining part the homogeneous Dirichlet condition is imposed. The aim is to weaken the conditions sufficient for justifying the classical asymptotic formula for the eigenvalues. We show that it suffices to assume the boundary to be C ¹ in a neighborhood of the support of the weight outside a closed subset of zero measure. The work of the author is supported by the RFBR grant no. 04-01-00914.     

An adiabatic local model for the internal structure of charge-transfer excitons: Dimers and trimers

In charge-transfer crystals, the exciton-phonon interaction significantly influences the internal structure of charge-transfer excitons (CTEs). The formation of CTE dimers and trimers is considered in an adiabatic non-centrosymmetric model which includes phonon dispersion. Changes of lattice frequencies near the CTE are analysed.     

Optimal control synthesis for the constrained bilinear biquadratic regulator problem

Optimal process control with control constraints is a challenging task related to many real-life problems. In this paper, a single input continuous time constrained linear quadratic regulator problem, is defined and fully solved. The constraints include both bilinear inequality constraints and customary control force bounds. As a first step, the problem is reformulated as an equivalent constrained bilinear biquadratic optimal control problem. Next, Krotov’s method is used to solve it. To this end, a sequence of improving functions suitable to the problem’s new formulation is constructed and the corresponding successive algorithm is derived. The required computational steps are arranged as an algorithm and proof outlines for the convergence and optimality of the solution are given. The efficiency of the suggested method is demonstrated by numerical example.     

New type of local resonances in thin rough films

A new type of local resonances is predicted. Two different mechanisms of their formation are pointed out. The first one is connected with a peculiarity of the Coulomb interaction in thin films. The second type of resonances appears when spatial dispersion in films is taken into account. The considered local resonances can take place in metal as well as semiconductor and dielectric films.     

Complexation of ferric ions with glucosamine

Conclusion Mathematical modelling was used to show the formation of mono and dihydro complexes with glucosamine and the H₂Gl²⁺ form in physiological solution. The formation constants of these species were calculated.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 4, pp. 937–939, April, 1987.