Multi-criteria model of laser radiation control

Abstract

The paper formalizes a model of laser beam control. Working with real equipment implies occurence of various perturbations influencing on optical parameters of the laser beam. This increases divergence of beams and causes diminishing surface density of energy beacause of irradiation and affecting the pointing accuracy of optical navigation systems. One of the approaches to partial compensation of the perturbations influence is using adaptive optical control systems. [1], [6]-[8], [20], [22], [23] In the case it is reasonable to raise the problem of controlling the elements of laser optics system. In the paper this problem is formulated as a differential zero-sum two-person game. The game may be solved by means of analytical and numerical methods.

A New Method to Study the Periodic Solutions of the Ordinary Differential Equations Using Functional Analysis

“…Periodic solutions take an important part in the qualitative theory of differential equations and in applied problems [3]. The analysis problems for periodic solutions of differential equations arise in classical mechanics, celestial mechanics [4][5][6][7][8][9][10][11][12][13][14][15], space robotics [16][17][18][19][20][21][22][23][24], in modeling of economic processes [25][26][27][28][29]. However, there is no general approach to study periodic solutions of differential equations.…”

Stochastic models of social-economic dynamics

“…Analysis of existance and stability conditions for solutions [2] is also required. Other approaches to study of complex systems are mathematical modelling and computer simulations ( [3], [4], [5], [6]. We propose methods of the mathematical modelling which are based on the Markov chain Monte-Carlo methods widely used in other fields of computational science and more general approach which is based on simultaion of branching stochastic processes.…”

Robot master slave and supervisory control with large time delays of control signals and feedback

“…The researches in this field and close to it directions are hold by the German Space Agency (DARA) [1,2], the National Aeronautics and Space Administration (NASA), as well as in Canada and Japan. This article presents the results of searches in St.-Petersburg National Research University (ITMO) [3][4][5], St.-Petersburg Institute of Informatics and Automation of RAS (SPIIRAS) [6][7][8][9][10] and in St. Petersburg State University (SPSU) [12][13][14][15][16][17][18][19]. The main crucial obstacle while constructing efficient systems of remote control over space robots is a significant delay of control signals transferring to the space robots from the ground control center, as well as delay of feedback signals receiving mainly in case of control over robot manipulators moving objects with constraints, in particular, holonomic [9,10].…”