Vol 58, No 2 (2019)

A displacement effect of a linear optimal control in stabilization problems for diffusion-type stochastic systems that operate on an unbounded time interval is studied. Hidden asymmetry of perturbations is shown to exist in systems without deterministic drift, where the equilibrium state of the open-loop system is zero. A displaced linear controller helps improve stabilization quality despite the asymmetry of the oscillations of the system.

This paper suggests some algorithms for decomposing a system of Boolean functions into subsystems of connected functions for representations such as truth tables (TTs), systems of disjunctive normal forms (DNFs), and binary decision diagrams (BDDs). The connectivity of functions consists of the presence of identical parts in the domains of functions from a given system. The algorithms are heuristic and can be used in computer-aided synthesis systems for real-dimension problems with several hundred functions, each having several tens of arguments. The experiments described below prove the efficiency of this decomposition approach in the logic optimization of a system of Boolean functions based on Shannon’s decomposition with the possible use of subfunction inversions.

The main scientific results of Professor Yurii B. Germeier are presented, including the results of calculations of combat effectiveness indices of aviation systems and theories of non-zero-sum games, hierarchical games, reliability, and operations research. Milestones of his scientific, teaching, and life paths are listed. Directions for the further development of the Moscow school of operations research created by him are given.

Restrictions of the method of fault trees in risk analysis problems are analyzed. As an alternative to this method, we consider the possibility to apply fuzzy cognitive maps; this new modelling technique is not sufficiently propagated in the reliability theory. Based on fuzzy cognitive maps, we propose a method to rank risk factors and illustrate it by an example of a man-machine system.

A direct method for finding the optimal open loop control of an aircraft is proposed. It is based on the preliminary parameterization of controls with the subsequent parameter estimation using the numerical minimization of a given functional. Conditions for the application of this method and possible constraints are discussed. The efficiency of the method is confirmed by examples that use the results of simulation and flight data. The results are compared with the solutions obtained using the classical approach to finding the optimal control based on the solution of a two-point boundary value problem.

The problem of controlling the orientation of a rigid body using a movable internal mass is studied. A method for calculating the motion of a point mass relative to the rigid body under which the body acquires a desired attitude in space is proposed. The reorientation maneuver consists of three planar turns about the principal central axes of inertia of the body. Finding the required planar turns is based on solving the corresponding optimal control problems.

This paper considers the motion of a low-orbit electrodynamic tether system designed to raise the orbit of a small spacecraft or nanosatellites. The system operates in the thrust generation mode. The orbit is raised by the Ampere force resulting from the interaction of the conducting tether with the Earth’s magnetic field. The mathematical model of motion is constructed using the Lagrange method taking into account the effect of the distributed loads from the Ampere force and the aerodynamic forces on the tether. It is shown that the motion of the system relative to the center of mass is unstable if the current is constant. It is proposed to use a linear regulator to stabilize the motion of the system with respect to the local vertical. Bellman’s dynamic programming principle is used to synthesize the regulator.

Inverted pendulums can be considered as an approximation for the stabilization problem for legged robots. In this paper we design a linear observer for a reaction wheel inverted pendulum under biased angle measurements. The reaction wheel is a flywheel that allows the free spinning motor to apply the control torque on the pendulum. In this paper we consider the stabilization problem in the presence of a constant unknown bias in the pendulum angle measurements; this problem has important practical implications, allowing for less precise sensor placement as well as a closer approximation for the control of legged robots. This paper provides a theoretical and experimental basis for the estimation of the velocities and the bias in the system.

We consider the problem of controlling a manipulator during the operation of the automatic grasping of a noncooperative object. The manipulator is equipped with a gripper in the form of a multifinger hand. The solution of the problem includes the planning and execution stages. When planning, the coordinates of contact points on the surface of the object, along with the coordinates of the manipulator and the fingers of the hand at the instant of a grasping are determined. When executing, the manipulator and the hand move from the initial position into the planned position.