Volume 57, Nº 5 (2018)

This paper addresses the problem of the time-optimal braking of rotations of a dynamically symmetric rigid body under a small control moment in the ellipsoidal range with close unequal values of the ellipsoid’s semiaxes. This problem is considered a problem of quasi-optimal control. The body is assumed to have a moving mass connected to it through elastic coupling with quadratic dissipation. In addition, the body is exposed to a small braking moment of the linear resistance of the medium. The problem of synthesizing the quasi-optimal braking of the rotations of a dynamically symmetric body in a resisting medium is investigated analytically and numerically. An approximate solution is found by the phase-averaging of the processional motion. The qualitative properties of quasi-optimal motion are analyzed and the corresponding graphs are presented.

This paper considers a refinement problem for the flight altitude, speed, and flight-path angle of an aircraft during aerodynamic deceleration in the atmosphere of Mars using inaccurate discrete g-load measurements. For solving this problem, several suboptimal discrete nonlinear filters of higher accuracy than the extended Kalman filter based on the Taylor linearization procedure with static (Gaussian) linearization of the nonlinearities are applied and compared with each other. The equations of these filters are derived, the Gaussian moments of their structural functions are calculated, and the resulting accuracy of these filters is analyzed in statistical terms.

The time-optimal problem is considered for the orientation of a satellite in the plane of a circular orbit and bringing it to the desirable angular position. The constraint on the control torque module is considered as the main parameter of the problem. It turned out that even in the case when the admissible control torque exceeds the gravitational moment in magnitude, additional switching curves corresponding to the relay control with two switchings are possible in the phase plane. As a result, a simple numerical algorithm is proposed, and with its help for each terminal angular position the threshold absolute control value is found at which the indicated switching curves are infinitesimal. Their coordinates in the phase plane are found in the most well-known case of the gravitationally stable terminal angular position. A suboptimal control law, which does not need a numerical calculation of the switching curve, is offered.

A constructive technology of the solution of the parametrized problems of the programmed optimal control of systems with the distributed parameters under the conditions of different requirements for the permissible deviation of the resulting spatial distribution of the controlled value from the set magnitude in the uniform metric is proposed. The developed technique uses a special procedure of the one-criterion convolution of the considered constraints and the subsequent reduction to the typical form of the problems of mathematical programming on the extremum of a function of a finite number of variables with an infinite number of constraints (semi-infinite optimization problem), which is solved by the scheme of the previously developed alternance method. An example of optimization by the criteria of the speed and energy consumption of unsteady heat conduction processes with two different restrictions on the accuracy of approximation to the given temperature conditions, which is of independent interest, is given.

This article describes a method of synthesizing finite-state machines (FSMs) on programmable logic devices (PLDs) while using the values of the input variables for coding the internal states. For this purpose, it is suggested to combine the structural models of FSMs of class A and E. The method of synthesizing a combined FSM model of AE class, which consists of splitting the internal states for fulfilling the necessary conditions of synthesizing an E-class machine and coding the internal states of an AE-class machine, is discussed. It is shown that this method allows reducing the cost of implementing FSMs for various families of PLDs by up to factors of 1.57 to 2.33 for binary coding and 3.00 for unary coding. This method also allows increasing the operation speed by up to 1.22–1.59 factors for binary coding and 1.34–2.93 for unary coding. In conclusion, recommendations are given regarding the practical use of the method, and possible areas for further development are suggested.

This paper gives examples of optimization problems on a lattice of cubes in the single- and multiobjective cases. We describe a method for calculating the local curvature of a given surface of a large-area geological object at each point and for constructing its curvature surface based on these geophysical data. Such information is used in geology and geophysics for detecting the most probable storage areas of hydrocarbons [1–5]. Based on these results, we develop mathematical models and state single- and multiobjective optimization problems on a lattice of cubes for arranging a finite number of oil wells in an explored field. We describe a method for designing an equivalence set for solving multiobjective problems on the lattices of cubes of any dimensions. Finally, we show that a similar approach is applicable for stating and solving optimization problems on a lattice of cubes in different sectors of the economy.

Markov models of perishable inventory systems where some customers are withdrawn after completion of the service without buying the stock are studied. It is assumed that the service time and filling supply orders are positive random variables. The inventory replenishment size is a variable and depends on the current inventory level. Exact and approximate methods for calculating the joint distribution of the inventory level and the number of orders in the system are developed. Formulas for calculating the main characteristics of the studied systems are proposed and the problem of their optimization is solved. The high level of accuracy of the proposed formulas is confirmed by the numerical experiments.

An algorithm for interpreting the results of measurements made by a tunneling microscope that takes into account the specific features of the microscope control is studied. Conditions under which the model of the nanotopography constructed based on the measurements exactly reproduces the original surface are derived. The features of nanotopography that cannot be reproduced using the proposed interpretation techniques are described.

The paper proposes an algorithm of guaranteeing unmanned interceptor trajectory control when approaching a maneuvering air target as a game solution. The conditions for the existence of a saddle point are studied for a version of air combat duel under consideration. The presented simulation results confirm that the use of the proposed guaranteeing control algorithm provides a tactical advantage of the unmanned interceptor.

An algorithm for designing the motion of a hexapod robot aimed at shipping the robot together with a cargo to the other shore of a body of water on a raft in the simple case when the robot imparts the initial push to the raft from the shore is described. The proposed motion control algorithm includes transporting the cargo from the shore to the raft, moving the cargo across the moving raft, and carrying the cargo from the raft to the other shore. The algorithm is worked out using computer simulation within the complete dynamical model of motion taking into account the nonstationary action of water on the raft. The numerical results prove the validity of the algorithm as long as sufficient data about the motion for the purpose of control is available.