Teoriâ i sistemy upravleniâ

We consider the problem of constructing reachable sets, i.e., sets of terminal states into which a system can be transferred from the origin in a fixed time, and 0-controllability sets, i.e., sets of initial states, from which a system can be transferred to the origin in a fixed time, for stationary linear discrete systems with a total control constraint. The representation of reachable and 0-controllable sets as linear transformations of superellipsoidal sets of finite and infinite dimensions is proved. A constructive method for describing the desired sets based on the apparatus of supporting half-planes is proposed, including for the limit sets of reachability and controllability. In the case of Euclidean spaces, the description is obtained explicitly. Examples are given. For a three-dimensional satellite motion control system in a near-circular orbit, reachability sets are modeled.

This paper presents a nonlinear discontinuous control law that allows stabilizing the output voltage of a step-down voltage converter in conditions when the input voltage and load current are unknown. The main idea is based on the use of the so-called vortex algorithms, which ensure invariance with respect to external unmatched disturbances. The efficiency of the developed algorithms is shown by numerical simulation.

The problem of constructing an algorithm for automatic tracking of a ground object for a guidance system (GS) for an unmanned aerial vehicle (UAV) is considered. The guidance system includes a thermal imaging target coordinator with a combined correlation-contrast direction finding algorithm and a strapdown inertial navigation system. Guidance takes place under conditions of information counteraction, which causes random interruptions in information and random changes in the power of interference, which are recorded by the corresponding indicators. A combined noise-resistant automatic tracking algorithm is obtained, using the readings of information interruption indicators, interference power, and measuring bearing angles, based on the theory of systems with a random jump structure. An example is given that illustrates the operation of the algorithm and demonstrates the satisfactory accuracy of automatic tracking.

We consider a controlled mechanical system of many bodies, consisting of a load-bearing disk that rotates around its axis fixed in space, and a carried disk attached to it using weightless elastic elements. The presented bodies are in the same plane. The problem of minimizing the amplitude of radial oscillations is studied. To solve this problem over a sufficiently large interval, two numerical methods are used: the method of successive approximations in the control space and Newton’s method. The properties of the phase trajectories of the system are studied depending on the initial states of the disks. Various disk spin-up modes are detected. Using the smoothing procedure for optimal control, a continuous control is constructed that reduces the amplitude of radial oscillations.

The longitudinal vibrations of an elastic rod controlled by a distributed force, which is applied to individual sections of the rod, are studied. It is assumed that the force varies in space in a piecewise constant manner. Such a mechanical system can be implemented using piezoactuators attached along the rod. The dynamics of the system is determined from the solution of the variational problem following the method of integrodifferential relations. The variational problem is solved analytically. To do this, traveling waves of the d’Alembert type are introduced on the space-time mesh, which determine continuous displacements and a dynamic potential. The latter relates the momentum density and stresses. A control problem is posed under the condition of the weighted minimization of the vibrational energy stored by the rod at the terminal time instant, and the mean potential energy generated by the control actions. The extremal motion and the corresponding control law are found explicitly by solving the Euler–Lagrange equations. As an example, the control capabilities for certain configurations of piezoelectric elements are studied.

Fault detection is an important task in the design of fault-tolerant state machines. Structural models of Moore finite-state machines are proposed to detect multiple faults in various elements of the finite-state machine and prevent their negative impact on the controlled object. The structural models under consideration make it possible to detect invalid input and output vectors both in each state and for the entire automaton, invalid code of the current and next state of the automaton, and invalid transitions between states. The costs of implementing the proposed structures by area range on average from 3 to 26%, and the speed of the machine either does not change or even increases by an average of 24–30%. Estimates of the area and performance of the proposed structural models of finite-state machines are given, and recommendations for their practical use are given. It is shown that the choice of a suitable structure allows us not to increase the area, and in some cases even leads to an increase in the performance of the finite-state machine.

We consider the problem of developing and optimizing the rules of the spectrum auction. One-sided sealed-bid spectrum auctions are studied. Two types of pricing are compared theoretically: the first-price and the second-price. А game model of the auction with free riders is constructed. A free rider uses frequencies purchased by another such participant for free. All Nash equilibria of the obtained games are found and represented in an analytical form. The significant difference between games with all free riders and games with at least one ordinary player is shown. It is proved that when players eliminate their dominated strategies, the resulting auction price of the lot is determined by its value for ordinary players. In the case when all players are free riders, the price is equal to the minimal bid price. The influence of the information the participants have about their partners’ values of a lot on the outcome of the game is discussed. The theoretically obtained properties are in agreement with the results of the experiments presented for spectrum auctions in the scientific literature.

Recommender systems are special algorithms that allow users to receive personalized recommendations on topics that interest them. Systems of this kind are widely used in various fields, for example, in e-commerce, provider services, social networks, etc. Together with classical approaches, neural networks have also become popular in recommender systems in recent years, which are gradually replacing traditional methods of collaborative filtering and content-based algorithms. However, neural networks require large computing resources, which often raises questions on whether an increase in quality will be justified and whether there be one at all. The neural network approach in recommender systems—the self-attentive sequential recommendation (SASRec) transformer model from Microsoft Recommenders—is studied and compared with the classic algorithm, the LightFM hybrid model. For training and validation, the data taken from a housing search application are used. It is proposed to use the hit rate as the main metric for comparison. The results of the experiments will help to understand which algorithms have higher accuracy in terms of predictions and recommendations. As an additional part, the clustering of user and object embeddings is considered.

The existing experience of the design of aviation technology proves that in a number of cases a promising aircraft (AC) that satisfies the set of requirements cannot be created within the framework of the accumulated scientific and technical groundwork in the field of AC manufacturing. As a result, there is a need to determine priority scientific and technical solutions, whose implementation, under time and financial constraints, will ensure the creation of an AC that meets the stated requirements. It is shown that such a problem can be interpreted as a so-called generalized optimization problem, whose difference from the classical mathematical programming problem lies in the fact that the set of permissible values of flight performance characteristics (FPC) is an additional object of optimization. A constructive algorithm for solving such a problem is proposed, whose capabilities are illustrated using the example of designing a transport ramp aircraft