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.
An Erratum to this paper has been published: https://doi.org/10.1134/S1064230723330018
The problem of constructing interval observers for discrete-time linear systems under external disturbances, measurement noise, and parametric uncertainties is studied. The relations allowing designing the interval observer of the minimal dimension that estimates the set of admissible values of the specified linear vector function of the system state are derived. The theoretical results are illustrated by an example.
We study a mechanical system with two degrees of freedom, consisting of two absolutely rigid bodies (material points) connected to each other by a weightless rectilinear viscoelastic rod that can be stretched or compressed. The bodies can move translationally along a fixed straight line. A control force limited in absolute value is applied to one of them, whose vector is directed along the rod. A continuous piecewise-linear control in time, which transfers the system from one equilibrium position to another in a length of time close to the minimum possible time, is constructed. In the absence of viscosity, with the constructed quasi time-optimal control, unwanted vibrations of the bodies are not excited either during the transition process or when it ends. In contrast to the time-optimal relay control, the constructed continuous control is also robust with respect to the uncertainty of the design parameters.
A numerical algorithm is developed for searching for an approximate solution to the optimal control problem in the presence of terminal-phase constraints. In general, the formulation of the optimal control problem with terminal-phase constraints is presented, in which the control is a limited piecewise constant function. To solve the problem, a step-by-step algorithm is formulated, which is based on the methods of penalties and differential evolution. Based on this algorithm, a program is created with the help of which a computational experiment is carried out for the catalytic reaction of the synthesis of benzylidenebenzylamine. The temperature profile of the process, which provides the highest concentration of the target substance with restrictions on the conversion of the starting substances, is determined.
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.
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.
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.
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