Том 58, № 5 (2019)

The problem of time quasi-optimal deceleration of the rotations of a rigid body that includes elements with distributed and lumped parameters is studied. It is assumed that the body contains a spherical cavity filled with a highly viscous fluid (at small Reynolds numbers) and a viscoelastic element that is modeled by a moving mass connected to the body by a strong damper. The moving mass models loosely attached elements in a space vehicle, which can significantly affect the vehicle’s motion relative to its center of mass during a long period of time. In addition, the body is affected by a small medium resistance torque and a small control torque localized in a ellipsoidal domain. The problem is solved asymptotically based on the procedure of averaging the unperturbed precession over the phase. A numerical solution is obtained.

The estimation problem for a linear parametric function in a linear regression model with uncertain symmetric unimodal noise distributions and given noise covariances is solved. The quality of estimation is determined by the probability that the error exceeds specified limits. For taking the uncertainty into account, a minimax optimization problem is formulated. The main result of this paper is that the Gauss inequality defines a tight upper bound of the error probability for any linear unbiased estimate. The worst-case distribution of the noise vector is constructed by using a linear transformation of a Gaussian random vector and a uniform random variable. The estimate that is minimax with respect to the probability criterion coincides with the least-squares estimate. The obtained solution is illustrated by the example of estimating motion parameters for several hypotheses about noise distributions.

In this paper, we provide a substantive description of one of the methods for solving problems of the optimal programmed control of diffusion-type stochastic systems with a quadratic quality functional on a finite time interval that allows reducing the stochastic formulation of the question to a deterministic one. We try to present the main ideas, advantages, and disadvantages of the method, as well as to outline as widely as possible the range of problems, to which this method can be applied in an accessible (but mathematically rigorous) form. Here, we do not provide technical details of using the method for solving specific problems. However, there are references in the paper, where these details can be found. New results, which are illustrated by examples that are directly related to the well-known applied problems of optimal control, are obtained. A rather comprehensive review of the current practical applications of the moment characteristic method is provided.

The problem of minimizing an integral quadratic performance index on the trajectories of a quasi-linear dynamic system with a small parameter multiplying the nonlinearities subject to terminal constraints is considered. Asymptotic approximations of the optimal control in this problem in the form of open loop control and feedback are constructed. The computations are reduced to solving the unperturbed linear-quadratic problem, integrating systems of linear differential equations, and finding the roots of nonsingular linear algebraic systems.

Markov models of systems with heterogeneous servers, various types of requests, and jump priorities are proposed. It is assumed that there are high and low priority requests; the high priority requests are assigned to the server with the high service rate, and the low priority requests are assigned to the server with the low service rate. Models of two types are studied: with separate queues and the shared queue for requests of different types. Jump priorities determine the rules according to which the type of low priority requests changes depending on the state of the queue. Methods for calculating the distribution of the probability of the system states are developed, formulas for the calculation of the characteristics of the system are derived, and the problem of the optimization of these characteristics is solved. The results of numerical experiments are presented.

The model for the representation of declarative and procedural knowledge of an autonomous intelligent robot is developed without reference to a specific subject area. The logic of conditionally dependent predicates underlies the construction of this model. Procedures that allow an autonomous intelligent robot to automatically generate new knowledge needed for a readout in the process of planning goal-seeking behavior in undetermined conditions of a problem-solving environment are proposed. The method of proving the satisfiability of the formulas under the logic of conditionally dependent predicates with linear complexity is based on the attribution of object variables in them as objects of the problem-solving environment and serves to process knowledge that is used by an autonomous intelligent robot to automatically build plans for goal-seeking behavior under undetermined operating conditions.

The article considers the problem of further improving the coordinate-time support of GLONASS, which implies refining the models of a wide range of errors caused by inaccurate knowledge of the geodetic and geodynamic parameters. The problem of aligning coordinate systems on which the application of a particular information technology is based that arises from using this approach is discussed, since such a problem can be solved only by processing navigation measurements using various information technologies, as was shown in the previous article. The results of experiments on aligning the coordinate systems used by global navigation satellite systems and very-long-baseline radio interferometers containing estimates of the misalignment between measurements generated by various information technologies are presented.

The angular motion of a nanosatellite equipped with a hysteresis damping system is studied. The required number and sizes of hysteresis rods needed to achieve the specified transient time and aerodynamic orientation with a given accuracy are chosen. Laboratory measurements of parameters of the chosen hysteresis rods are presented. The transient time in the case of abnormal launch of the nanosatellite is estimated.

An algorithm for controlling a multinozzle engine of a spacecraft operating in the cycle mode that makes it possible to vary the engine’s operation time and thrust in a wide range while accurately maintaining the desired mean thrust is presented. The results of simulation for an axial propulsion unit of the spacecraft consisting of four engines with the identical nominal thrust are presented. The application of the proposed algorithm for the propulsion unit arrangement indicated above makes it possible to prevent the accumulation of angular momentum about all three central axes of inertia of the vehicle simultaneously with producing a correction impulse, while maintaining the given mean thrust. A control algorithm is outlined and specific features of using the improved mathematical model of the engine’s operation in the cycle mode are described.

If a malfunction of equipment is detected, the manipulator control system switches off the power supply of actuators and applies brakes. The resulting motion can significantly differ from the programmed one because the relations of the velocities of the degrees of freedom undergo significant changes. It is proposed to form the emergency braking trajectory by switching on brakes with certain delays. Analytical estimates show that this can reduce the deviation from the programmed trajectory almost by an order of magnitude.