No 2 (2023)

When studying complex optimization and control problems for systems described by polynomial and analytic functions, there is often a need to use necessary and sufficient optimality conditions. Moreover, if the known conditions turn out to be inapplicable, it is required to develop as subtle conditions as possible. This problem is studied in this article. The necessary and sufficient conditions for a local extremum are formulated for polynomials and power series. With a small number of variables, these conditions can be tested using practically implemented algorithms. The main ideas of the proposed methods involve using the Newton polytope for a polynomial (power series) and the expansion of a polynomial (power series) into a sum of quasi-homogeneous polynomial forms. The obtained results provide the practically applicable methods and algorithms necessary for solving complex problems of optimization and control of systems, which are described by polynomial and analytical functions. Specific examples of tasks in which the proposed technique can be used are given.

A problem of modal control by output for fourth-order dynamical systems with two inputs and two outputs is presented. For a certain class of such systems, an approach is proposed for reducing the problem under consideration to a control (direct version) or observation (dual version) problem for a system with a single input. The approach is based on two successive similarity transformations of the closed-loop system with a controller by output, which make it possible to reset one of the rows of the controller matrix by state or one of the columns of the observer matrix. The class of systems for which the condition of such zeroing is simultaneously a condition for the existence of an output controller is studied. Theorems on the inequality of the indices of controllability and observability in the system under the conditions presented are proved. A variant of using the well-known Bass–Gura and Ackermann formulas is proposed, which significantly simplifies the symbolic expressions for the controller (observer) in the transformed system. Examples of the application of the proposed approach, both in the direct and in the dual version, are considered. Symbolic calculations in MATLAB validate the results.

The problem of the feedback control of a system of ordinary differential equations, nonlinear in phase variables, subjected to the effect of an unknown nonsmooth disturbance is discussed. The problem consists of constructing a control action formation law that guarantees compensation for a nonsmooth disturbance; i.e., it guarantees that the phase trajectory (as well as the rate of its change) of the given system follows the prescribed phase trajectory (as well as the rate of its change) for any admissible realization of the disturbance. Two cases are considered. In the first case, admissible disturbances are constrained by instantaneous restrictions, and in the second case, any function that is an element of the space of Lebesgue measurable functions summable with the square of the Euclidean norm can be an admissible disturbance. The problem is solved under conditions of inaccurate measurement at discrete times of the phase states of both systems. In the presence of instantaneous restrictions on disturbances, the problem is also solved by measuring some of the phase states. Algorithms for solving this problem, oriented towards computer implementation, are designed that are resistant to information interference and computational errors. Estimates of the rate of convergence of the algorithms are given.

The use of the developed technology for solving inverse problems of parametric identification of the rotational motion of a spacecraft (SC) based on the accumulated sample of measurements of various compositions is expanded. On the example of processing telemetry data (measuring the direction vector to the Sun) of the BugSat-1 small spacecraft (SSC), the possibility of determining not only the characteristics of rotational motion but also its inertia coefficient is demonstrated. The rotational motion is determined based on the data obtained for five time intervals from January to May 2022, during which BugSat-1 made an uncontrolled movement around the direction vector toward the Sun. This type of motion does not allow applying traditional approaches to determine the dynamics of its rotation. In the process of data processing, a simplified model of the rotation of a SSC is used. At the same time, the initial conditions of rotational motion are estimated—the angular velocity vector and orientation angles, which made it possible to draw a conclusion about the precessional motion of a SSC. Using the analytical model of a regular precession, it is possible to estimate the inertia coefficient of a SSC. The results of flight information processing are presented and the errors of the obtained results are estimated.

The problem of the game-based control of a group of unmanned aerial vehicles (UAVs) in the conditions of informational counteraction by a group of stationary objects is considered. Two recurrent information-control algorithms are obtained: an algorithm for the interconnected control of a group of UAVs and a jammer control algorithm based on the theory of stochastic multistage games and the theory of systems with a random jump structure (RJS).

Four parallel algorithms are considered that implement the branch-and-bound method (BnB) for solving problems of finding a global minimum. The algorithms are designed for computing systems with shared memory. The BnB is based on two basic operations: branching and eliminating. To implement the elimination operation, interval arithmetic is used, which for real intervals defines operations similar to ordinary arithmetic. The main difference between the algorithms lies in the different implementation of storing the list of subproblems. In the process of testing on a representative set of test problems, the speed of the algorithms, their scalability, and their resistance to search anomalies are investigated.

A multilink pendulum located in a flow is considered. On the last link of the pendulum, a wing is installed, on which the interaction with the flow is concentrated. The dynamics of this system are studied as a potential working element of an oscillatory wind power plant. For different flow velocities, periodic modes are numerically investigated that occur under different numbers of links and different values of the external load. It is shown that the maximum power that can be obtained with a two-link pendulum is greater in a wide range of flow velocities than with pendulums with more than two links. At the same time, pendulums with a large number of links make it possible to obtain considerable power in a wider range of load values than a two-link one.

An automated control system for the technological process of applying galvanic coatings to a variety of cathode parts of various shapes and sizes is considered based on solving the problem of finding the optimal arrangement of the parts in a galvanic bath to obtain coatings with the minimum value of criterion R—the ratio of the number of rejected parts Nreject to the total number of parts N placed on the suspension device. To solve the problem, a calculation-logical system is developed that uses the exhaustive enumeration method, the Gomory algorithm modified by the authors, and the branch-and-bound method. When solving the problem, the Gomory algorithm is found to be the best algorithm among the three methods in terms of performance. A two-level control system for the galvanic process in a bath with a suspension device is developed.

Strategies are considered for the distribution of flows over various transmission routes in a multicommodity network model. Estimates of feasible network loads are formed based on the vector of jointly feasible internodal flows. Two distribution strategies are studied. When implementing the first one, the transmitted internodal flows are equal to each other. The second strategy assumes the search for a nondiscriminatory distribution of flows, during the transmission of which equal value resources are achieved. The load created by a certain pair of nodes is understood as the total capacity required to provide the given type of connection. To estimate the minimum specific resources for the transmission of a flow of a certain type, all the shortest paths between the corresponding pair of nodes are constructed. To obtain an upper estimate of resources when connecting each pair of nodes, the maximum single-product flow is calculated along all the network edges. Computational experiments were carried out for networks with different structures that make it possible to carry out a comparative analysis of equalizing distribution strategies when splitting internodal flows for transmission along different routes.