Vol 57, No 6 (2018)

The new results associated with properties of the controllability of discrete-time bilinear systems are presented. The properties of the controllability of a class of bilinear systems with block-triangular matrices are discussed. As a consequence, systems with permutation matrices and scalar bounded control are investigated. A series of necessary controllability conditions related to the dimension of the state vector and spectral properties of systems’ matrices are established and proved.

This paper extends anisotropy-based control theory methods to the class of linear discrete-time systems with multiplicative noise, which involves an informational criterion to describe the stochastic uncertainty of an external disturbance. An approximate calculation method for the anisotropic norm of such systems using decomposition into linear subsystems without multiplicative noise is suggested. The cases of perfect and imperfect state measurements are considered. The existence criterion for anisotropy-based controllers in form of special matrix inequalities is established.

The estimates for the power spectrum of multidimensional uniform random fields in the form of models of finite mixtures of standard spectra are proposed. The learning algorithm of the models demonstrates improved convergence properties for degenerate spectra and small interclass distances in the frequency space, as well as for small volumes of the experimental data. Based on this, the noncanonical models of uniform random fields are presented as a sum of statistically independent spatial harmonics with random amplitudes and frequencies. The alternative representation of a multidimensional spectrum as a sample of random frequencies allowed us to propose computationally efficient algorithms of digital synthesis of background and underlying surface images with the topology of spectral estimates that are adequate for the experimental data. The algorithms are free from simplifying assumptions regarding the method of discretization of the field and functional form of the power spectral density.

The first part of the paper is devoted to justifying the possibility of the correct description of a controllable stochastic observation system. The state is a Markov jump process, and the observations are a combination of continuous, discrete, and counting processes. A martingale problem of the system under study is solved: it is shown that there exists a canonical probability space with filtration such that under any admissible control, this system is stochastic differential with the martingales on the right-hand side. Further, for this system there exists a solution of the optimal in the mean square sense filtering problem given the compound observations. The filtering estimate is presented in the form of a continuous-discrete stochastic system with the martingales on the right-hand side. The article contains a description of a numerical algorithm implementing both process modeling in the considered observation system and the proposed solution for the filtering problem.

A method for selecting the working conditions affecting the probability of human errors is proposed. The problem is reduced to comparing alternative scenarios each of which determines a set of concrete working conditions. The method is based on the idea of evaluating each working condition by the criterion of fuzzy perfection, i.e., the degree of proximity to a certain perfect condition, and on an integral evaluation of the scenario as a whole by intersecting fuzzy perfection sets of individual conditions. Fuzzy perfection membership functions, an algorithm for comparing alternative scenarios, and an example illustrating a comparison of the different working conditions of the crew of a vehicle are considered.

Recommender systems provide recommendations for users. In this paper, we train and test some algorithms for recommender systems on a certain dataset, as well as analyze their strengths and weaknesses. Based on this information, we construct a system that yields a better solution.

This goal of this article is a more accurate theoretical description of the dynamic movement of a valve ensuring better efficiency of controlling the liquid flow in pipes. The computer-modeled functional diagram of the control system proves that the further issues of improvement of the control system are associated with refining the mathematical description of the valve with respect to its dynamic parameters. Our studies allowed determining the admissible parameters of other elements of the control system.

The problem of the optimal stabilization of a vertical rigid rotor rotating in two electromagnetic bearings is considered. A quantitative estimate of transient processes is based on the maximal deviation of the rotor from the equilibrium state and the maximal value of the current intensity in the windings of electromagnets. The use of linear matrix inequalities allow synthesizing the Pareto optimal control laws in the form of linear state-feedback, as well as decentralized control laws, which are defined by the displacements of the rotor in each electromagnetic bearing. The Pareto optimal criteria for centralized and decentralized control laws are compared. It is shown that utilization of simple easily realizable decentralized control laws only slightly worsens transient processes.

In connection with the planned increase in the intensity of air traffic worldwide, air traffic management systems need to be modernized. As aviation safety is a priority in the development of civil aviation, any changes to these systems have to be accompanied by an assessment of the aviation safety level. The estimates can be obtained by simulation modeling (SM). In the paper, the problem of the assessment of the aviation safety level using a simulation model of the controlled air traffic is formulated. Further, the authors consider the applicability of this model to formulate the reliability requirements for the radio communication, navigation, and surveillance systems that would assure an acceptable aviation safety level in prospective air traffic management systems. The methods and the model developed for the solution of these problems, as well as the calculated aviation safety estimates for the air traffic service sector are described.

Direct low thrust trajectory optimization techniques that reduce the optimization problem in the class of continuous functions to a nonlinear programming problem are described. Two direct low thrust trajectory optimization methods are implemented; one of them is based on the optimization of thrust acceleration and the other optimizes the impulses approximating the thrust arcs. These methods are compared using a sample problem of transfer from Earth to Mars in terms of runtime, the number of iterations, and the size of the convergence domains. The computations are performed on a personal computer using MATLAB and on a multiprocessor computer.