Andrey A. Galyaev

On the methods for calculation of grammians and their use in analysis of linear dynamic systems

Consideration was given to the methods for solution of the differential and algebraic Lyapunov and Sylvester equations in the time and frequency domains. Their solutions are represented as various finite and infinite grammians. The proposed approach to calculation of the grammians lies in expanding them as the sums of the matrix bilinear or quadratic forms generated with the use of the Faddeev matrices and representing each the solution of the linear matrix algebraic equation corresponding to an individual matrix eigenvalue. A lemma was proved representing explicitly the finite and infinite grammians as the matrix exponents depending on the combined spectrum of the original matrices. This result is generalized to the cases where the spectrum of one matrix contains an eigenvalue of the multiplicity two. Examples illustrating calculation of the finite and infinite grammians were discussed.

Optimization of the law of moving object evasion from detection under constraints

Consideration was given to optimization of the laws of moving object evasion from detection under the coordinate and phase constraints.

On the detection functional in motion of an object in a threat environment

The homeomorphic transformation of a signal density in the detection functional to a quadratic form is considered.

On one problem of optimal control at the impact phase and unification of the interaction end instants

Consideration was given to the problem of optimal control of a mechanical system at the impact phase and the influence of different instants of phase end on the performance criterion.

Impact of a system of material points against an absolutely rigid obstacle: A model for its impulsive action

The impact of a system of elastically linked material points against an absolutely rigid obstacle is analytically described and limit to an elastic homogeneous rod is studied.

Optimal pulse control of dynamic systems in the shock phase

For minimization and maximization of the kinetic energy of a body hitting a fixed visco-elastic obstacle with the energy calculated at the instant of body detachment from the obstacle, the optimal control laws in the impact phase were obtained.

Evasion of a moving object from detection by a system of heterogenous observers in the threat environment

This paper presents a formalization and the results of solution for the problem of moving object evasion from detection on a plane. Detection is performed by a system of heterogenous stationary observers by the last transmitted signals of the primary and reflected (secondary) fields in the passive and active modes, respectively. Simulation results are given.

Evasion on plane from a single mobile observer in the conflict environment

Consideration was given to the problem of evasion of a mobile object from the moving observer in a conflict environment. A law of control of the mobile object speed was established. The optimal motion trajectory was constructed, and the time dependence of the accumulated signal was compared for other laws of control.

On the problem of break-through between two sensors for a craft moving in the conflict environment

Planning of the path of a craft moving between two sensors was considered with the aim of minimizing the total signal arriving to the sensors in the passive mode.

Problem of optimal oscillator control for nulling its energy under bounded control action

Consideration was given to the problem of optimal control based on two performance criteria with the aim of full oscillator stopping from the initial state.