Том 57, № 6 (2018)
- Год: 2018
- Статей: 13
- URL: https://journals.rcsi.science/1064-2307/issue/view/13645
Systems Theory and General Control Theory
On the Properties of Controllability of Discrete-Time Bilinear Systems Associated with Block-Triangular and Permutation Matrices
Аннотация
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.
On the Asymptotic Stability of Nonlinear Time-Varying Switched Systems
Аннотация
This paper considers a class of nonlinear systems with switching from one nonstationary Lienard-type equation to another. For such a system, the asymptotic stability of a given equilibrium is studied using the method of Lyapunov functions and theory of differential inequalities. The switching law constraints that guarantee the desired property of the system are established. As shown below, these constraints generally depend on the rate of change of time-varying system parameters. Some illustrative examples are also given.
Control in Stochastic Systems and Under Uncertainty Conditions
Anisotropy-Based Controller Design for Linear Discrete-Time Systems with Multiplicative Noise
Аннотация
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.
Computer Methods
Noncanonical Spectral Model of Multidimensional Uniform Random Fields
Аннотация
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.
Systems Analysis and Operations Research
Controllable Markov Jump Processes. I. Optimum Filtering Based on Complex Observations
Аннотация
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.
Fuel and Energy System Control at Large-Scale Damages. IV. A Priori Estimates of Structural and Functional Vulnerability
Аннотация
The paper continues the study of the possibilities of a multiparametric model that provides an aggregated description of the operation of spatially distributed fuel and energy systems using a single-commodity network. An approach to obtaining the characteristics of the simulated system that reflect possible changes in the supply of energy resources after large-scale accidents is proposed. Scenarios involving the simultaneous failure of a set of arcs corresponding to the minimum cut for an arbitrary sink vertex, where each sink vertex simulates the regional consumption of some commodity, are considered. The maximum energy flows for all sink vertices are calculated to determine the damage caused in these scenario assumptions. Different damage indices are computed and the expected damage diagrams are constructed based on them. A comparison of the introduced damage characteristics and the structure of the indicated sets makes it possible to trace the changes in the quantity and trace of energy flows with the change in the localization, severity, and type of damage. Postoptimal analysis makes it possible to identify spatial interdependence and mutual influence, as well as the technological features of the interchange and interconnection of energy resource production. The computational problems arising in the model calculations are solved effectively by flow methods.
Selection of Human Working Conditions Based on Fuzzy Perfection
Аннотация
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.
Discrete Systems
Constructing a Hybrid Recommender System
Аннотация
Control Systems for Technological Processes
Imitation Modeling of a Control System Regulating the Viscous Flow Movement for Applying Coatings on Pipe Inner Surfaces
Аннотация
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.
Control in Deterministic Systems
Pareto Optimal Decentralized Control of a Rotor in Electromagnetic Bearings
Аннотация
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.
Control Systems of Moving Objects
A Solution to the Problem of Assessing Aviation Safety by Simulation Modeling
Аннотация
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.
Mission Design of Multipurpose Flights to Venus
Аннотация
The results of applying the efficient methods developed by the authors of this paper for designing interplanetary flight missions to Venus in the near future with the purpose of either executing gravity assist maneuvers (GAMs) around it or being injected into an orbit of Venus and descending onto its surface are presented. The focus is on calculating the launch times and methods for constructing and calculating the reachability regions of the descent module on the surface of Venus.
Two Direct Low Thrust Trajectory Optimization Techniques
Аннотация
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.