This is a survey of works on main properties, application and development of the Krotov method of global control improvement very popular among researchers of modern problems in quantum physics and quantum chemistry, applying actively optimal control methods. The survey includes a brief description of the method in comparison with well known gradient method demonstrating such its serious advantage as absence of tuning parameters; investigations aimed to make its special version for the quantum system well defined and more effective; and generalization for wide classes of control systems, including the systems of heterogeneous structure.

We consider the robust stabilization problem for linear multivariable systems whose physical parameters may deviate from computed (nominal) in some known bounds, and the control object is subject to non-measurable polyharmonic external disturbances (with unknown amplitudes and frequencies) bounded in power. We pose the problem of synthesizing a controller that guarantees robust stability of the closed-loop system and additionally ensures given errors with respect to controlled variables in the established nominal mode. The solution of this problem is based on the technique of opening the object–controller system with respect to varying object parameters and can be reduced to a standard H∞-optimization procedure, while the necessary accuracy is achieved by choosing the weight matrix for controlled object variables. We show the solution for a well-known benchmark problem.

For linear multivariable systems, we construct discrete output controllers that guarantee a given stability margin radius on the input or output of a control plant. Besides, given control time is also taken into account. We show that solving such problems reduces to a certain specially constructed standard H∞-optimization problem. A numerical solution has been implemented in MATLAB with the Robust Control Toolbox suite based on the method of linear matrix inequalities (LMI).

Аппарат линейных матричных неравенств применяется к решению классической задачи о линейно-квадратичном регуляторе. Показано, каким образом эта техника может приводить к оптимальному решению, получаемому через уравнение Риккати. Рассмотрены некоторые нежелательные эффекты, возникающие при использовании иных методов решения, известных из литературы; приведены численные примеры.

Mesh-free methods allow one to perform engineering calculations directly via a geometrical model constructed in the CAD system. They help to avoid the difficulties and errors in generation of a finite element mesh. In the present work, the most suitable techniques for analysis of complex solid-state constructions of polymeric composites are selected among mesh-free methods. A computation algorithm is also developed on the basis of these methods.