Vol 79, No 2 (2018)

The paper suggests analysis methods for optimal planning models in oil refining. The basic trends of optimization models construction are described. It is shown that parametric analysis is vital for improving the efficiency of activity. Finally, the economic efficiency of the suggested methods is estimated.

The paper discusses the evaluation of potential benefits of mass production automation where a specified set of automation tools is used. Automata operation efficiency, their cost and lifetime are allowed for. The algorithm developed enables the selection of automata set ensuring minimum product cost. The estimate of minimum attainable manufacturing cost is calculated.

We distinguish some cases of existence of a stationary equilibrium in nonantagonistic games on directed graphs with terminal payoffs along trajectories. The proof of the existence of stationary equilibria implies polynomial search algorithms for them.

This paper considers the problem of moving object evasion from detection in the plane. Detection is performed by a system of heterogenous observers that consists of one sensor and a group of detectors. We establish the optimal evasion law in explicit form for the case when the level of transmitted signal has power-type dependence on the evader’s speed. The paths to evade the system of observers and penetrate through the system are constructed.

We propose an approach to organizing self-tuning for a controller based on an artificial neural network that uses information on the contradictions arising in the creation of the value for the control signal between accumulated memory of the neural network and the learning algorithm based on backpropagation. The activity of neural network memory is estimated as its reaction to changing the state of the control system. Self-tuning is done by controlling the learning rate coefficient with an integral controller in order to stabilize the integral criterion for estimating the contradictions. Based on this modeling, we show a conceptual possibility for the operation of the self-tuning system with constant tuning parameters in a wide range of changes of the control object’s dynamical properties.

We solve the optimization problem for space trajectories of spacecraft flights with an auxiliary fuel tank from a low round orbit of a man-made Earth satellite to a geotransitional orbit. Control over the spacecraft motion is performed with a jet engine of bounded thrust. To discard the auxiliary tank, one has to turn off the engine, which takes some known time. The mass of the discarded tank is assumed to be proportional to the mass of fuel spent, and the mass of the engine and additional constructions is proportional to the thrust-to-weight ratio. We minimize the value of injection impulse needed to transfer to the geostationary orbit for a given useful mass.

In the second part of the paper the problem at hand is formalized as an optimal control problem for a collection of dynamical systems and is solved based on the corresponding maximum principle. In this work we solve boundary problems of the maximum principle numerically with the shooting method. As a result of solving the problem, we construct one- and two-revolution Pontryagin extremals. We perform a series of parametric computations that are used to determine optimal parameters of the spacecraft construction: the best thrust-to-weight ratio and the best distribution of fuel among the tanks.

With the methods of H₂/H_∞-control theory, in the presence of noise we solve the optimization problem for a multiplicative stochastic system with several external disturbances (the multiperturbation problem) and vector Wiener processes with arbitrary intensity matrices. We obtain matrix differential equations of Riccati type, reducing the original optimization problem to solving these equations.

We study the one-sided convergence of the modified Anbar’s process in previously unexplored cases of the choice of the sequence of steps.

For the linear regression model, the problem of relaxing conditions for sustained excitation in the problems of estimation of the unknown constant parameters of the model was discussed. An approach was suggested enabling one to form from a damped regressor a new signal for which the conditions of sustained excitation are satisfied. The cases of one and two unknown parameters giving one an insight into the root idea of the proposed approach were analyzed in detail. Operability of the algorithms considered in the paper was illustrated by computer-aided modeling.

We consider the two-stage stochastic linear programming problem with quantile criterion in case when the vector of random parameters has a discrete distribution with a finite number of realizations. Based on the confidence method and duality theorems, we construct a decompositional algorithm for finding guaranteeing solutions.

Consideration was given to the optimal control of discrete stochastic systems by the probabilistic quality criterion. The new characteristics of the Bellman equation for this class of problems were examined, and the two-sided estimate of the Bellman function was determined. The problem of optimal control of the security portfolio with one riskless and a given number of risk assets was considered by way of example. The class of strategies featuring asymptotic optimality was established using the two-sided estimate of the Bellman function.