Vol 55, No 2 (2016)

The development of control algorithms, including optimal control ones, in the collision avoidance problem for a system of two pendulums with a controllable common base is considered. Two problems are solved. The first one searches for the law of variation of the bounded control force that makes the system move from its initial state of rest to the given final state of rest during a finite time and ensures the pendulums do not collide in the process of oscillatory motions. The second problem searches for the performance-optimal law of variation of acceleration of the base and the bounded force that generates the acceleration. The algorithms for constructing the sought controls that use Kalman controllability conditions and Pontryagin’s maximum principle method are presented. The dynamics of the system involved is simulated for the constructed control laws. The numerical results of both problems are compared to find that implementation of the developed performance-optimal control algorithm can help significantly decrease the releasing time of the pendulums while preventing a possible collision.

In this paper, we describe the results of the experimental comparison of programs that implement various decomposition methods for disjunctive normal forms of systems of completely defined Boolean functions. The complexity of a system of disjunctive normal forms is expressed in two ways: by the area of a programmable logic array that implements a system of disjunctive normal forms, or by the number of vertices of a binary decision diagram, which represents a system of Boolean functions. The complexity of the functional expansion of a system’s functions is determined as the sum of the complexities of the subsystem of the functions included in this expansion. The estimates of the complexity are oriented on the synthesis of combinational circuits based on the programmed logical arrays and the library’s logical elements.

The concepts of step graphs and networks in which the edges are divided into ordered classes (shortage classes) are introduced. Each path in such graphs is assigned a tuple (an ordered sequence of nonnegative integers). The tuples are compared lexicographically. The problem of finding the path with the minimum tuple according to this ordering is stated. Functionals are compared using the lexicographic rule. An algorithm for finding the optimal path is described, and the relationship between step networks and weighted networks is investigated. The proposed formalism is applied to the problem of filling a network subject to constraints imposed on communication line capacities with communication flows under the condition that requests for the organization of such flows arrive to the network sequentially in time and the filling strategy must maximize the number of satisfied requests. The idea of an algorithm for the approximate solution of the integer multicommodity problem that uses the concepts of step networks and sequential algorithms is proposed.

Two techniques for approximating the tails of the probability distribution of automatic aircraft landing characteristics are considered: an approximation technique based on the Pareto distribution and a spline approximation technique. Computational algorithms designed based on these techniques allow assessing ultra-low risks (on the order of 10^–6–10^–8) under the confirmed compliance of aircraft landing characteristics with airworthiness requirements. The modeling shows good agreement between the results obtained by these techniques, which makes it possible to implement a simpler technique based on the Pareto distribution. This technique reduces the amount of statistical modeling by predicting accuracy characteristics in the unobservable range of their variation.

Algorithms are proposed for the detection, localization (i.e., position determination in the observed scene), and recognition of optoelectronic images of a group of plants with a contrasting image background intended for use in inertial sighting systems for the navigation and guidance of aircraft [1, 2]. The structure and parameters of the developed algorithms are presented. The parameters of the quality of the processes of detection, localization, and recognition of halftone electro-optical images of a group of ground objects are given.

An algorithm is developed for terminal guidance during the main deceleration section of the lunar landing trajectory of a spacecraft with an integrated propulsion system, which has a main engine with variable thrust and four auxiliary nonthrottleable engines. A method of guidance adaptation to the actual motion conditions by measuring the thrust acceleration with jumps in time is proposed.

The paper is devoted to the problem of estimating the parameters of two maneuvers performed by an active space object between two successive sessions of measurements, which is very important for the maintenance of the catalog of space objects. The parameters of coplanar and noncoplanar impulse and long-duration maneuvers are determined. An advantage of the proposed method is the high speed of estimation, unattainable in traditional approaches, and simplicity of program implementation, because the solution of each problem depends upon the solution of the preceding, simpler problems.

The problem of the optimal control of a spacecraft reorientation from an arbitrary initial position into a prescribed final angular position is studied. For optimization, we use a generalized integral index characterizing the complexity of the rotation trajectory from the viewpoint of the “distance covered,” which is the generalized rotation angle that takes into account the different weights of the spacecraft axes in the sense of expenditures (of fuel, time, or another irreplaceable resource) needed to rotate the spacecraft by the same angle. An analytical solution of this problem is obtained. Two versions of the optimal spacecraft slew maneuver problem (using the shortest trajectory) are considered—the quickest maneuver and a maneuver in the prescribed time. The optimal control problem is solved for several types of constraints on the control variables. The time of starting the deceleration is determined based on the actual motion parameters (mismatch angle and angular velocity) using the terminal control principles (based on the angular position and angular velocity measurements). An example and simulation results of the spacecraft dynamics under the optimal control are presented, which demonstrate the practical usefulness of the proposed control algorithms.