Vol 55, No 5 (2016)

The procedures of structural parametric synthesis of reduced controllers of automatic control systems are simplified. Methods for reducing controllers based on the physical features of the controlled plants, on completing the definition of “small parameters” of the plant, on the technical feasibility of differentiating controllers, and on a modification of the classical modal control techniques are developed. Examples of effective control of plants of various complexity based on the use of the reduced controllers are discussed.

The problem of optimal boundary-control with nonseparated boundary conditions is considered in the case where the motion of a plant is described by a system of nonlinear ordinary differential equations with a corresponding initial condition, which thereafter is taken as a control action. First, the system of corresponding nonlinear Euler–Lagrange equations is described and in order to solve it, the quasi-linearization method (the first method) is taken. After that, the quasi-linearization method is used with the aim to solve just the optimization problem with boundary control and the nonseparated boundary condition; as a result, the initial nonlinear problem is reduced to the solution of a corresponding linearly quadratic optimization problem (the second method). By the particular example (of oil production) we demonstrate that the second method converges considerably faster and its accuracy is five times higher than the accuracy of the first method. The numerical results reinforce the compliance of the constructed mathematical model with practice.

A dynamic system that models the operation of a switching device (switch) is considered. During the operation, the system changes its state a finite number of times. The change of state (switching) is described by a recurrent inclusion, which corresponds to the representation of the switch by a dynamic finite state machine with memory; instantaneous multiple switchings are admitted. The instants of time at which switchings are made and the number of switchings are not given in advance. They are found by optimizing a functional in which the number of switchings and the cost of each of them are taken into account. Necessary optimality conditions for such systems are proved. Different versions of the optimality conditions for different types of constraints are given. In particular, under additional convexity conditions, conditions that are similar to the maximum principle for discrete systems are obtained. The application of the optimality conditions is illustrated by examples.

Methods for the evaluation of spline functions for digital filtering in data processing systems are developed. Basis polynomials of general form and basis discrete orthogonal polynomials are considered. Computations are organized by solving constrained optimization problems. Recurrences for the system of normalized discrete orthogonal polynomials and their derivatives are obtained. The proposed spline functions on discrete orthogonal polynomials reduce the computational cost and approximation errors compared with the case of general polynomials. The results of the statistical simulation of the application of spline functions based on discrete orthogonal polynomials in digital filtering problems are presented.

This paper presents a method for the impartial assessment of the quality of scientific and technological natural language documents and their collections by using bibliometric and scientometric indicators. The method of computational document search and design of document collections that are adequate for calculating reference values to assess the quality of the documents and document collections is formulated. This method is based on the mathematical modeling of natural language texts. Examples of the obtained assessments are presented.

The limitations of the control principle currently used in air conditioning systems are analyzed. It is proposed to consider the principles of deviation and disturbance control in order to address these limitations. The contents of the used concepts are revealed. The structure of the air conditioning system control algorithm based on this principle is presented. The problems solved at the higher and local control levels, as well as the interaction condition between them, are investigated.

This study continues the series of papers devoted to the approach to solving the problem of autonomous navigation of a spacecraft (SC) in a geostationary orbit at all stages of its lifecycle: final ascent, transfer to the operating longitude, remaining at the operating longitude, removal from the orbit, and burial. In [1], we formulated the concept of autonomous navigation of a spacecraft at the stage of its final ascent to a geostationary orbit. This stage is most complicated from the technical point of view, taking into account the nonlinearity of the applied mathematical models, the influence of uncontrollable factors of various physical nature, and the necessity of the application of promising hardware (electric low-thrust engine, onboard receiver of signals from global navigation satellite systems, intersatellite communication channels, etc.). Taking this into account, the only constructive method for proving the viability and efficiency (taking into account the requirements formulated by the customer who placed the order) of the developed concept of the autonomous navigation at the final ascent stage in the mathematical simulation of this process. The subject of this study is to demonstrate the capabilities of the developed concept of autonomous navigation from the point of view of achieving the required level of reliability and accuracy in solving the navigation problem at the final ascent stage. This demonstration is based on the analysis of the results of imitating the simulation of the process of a spacecraft’s final ascent to a geostationary orbit obtained using the specially developed software complex.

The possibility of the development of a distributed navigation system for the efficient estimation of the navigation parameters of a group of ground mobile modules is considered. A distinctive feature of the proposed system is that only a small part of the modules is equipped with precise navigation equipment. The problem is solved in a nonlinear formulation for nonholonomic wheeled modules using the Bayesian filter in the form of a particle filter. The consistency of the estimation of navigation parameters in the distributed system of modules is provided by the covariance intersection algorithm.

The solvability conditions and just the solution of the problem of the regular and irregular proportional-integral (PI) control are found in accordance with the properties of invariant zeros of a multi-input multioutput (MIMO) system. It is proved that the problem of synthesizing the control of the MIMO system is solvable if and only if the pair of matrices (A, B) that describes a control plant is controllable and the matrix B_L^⊥AC_R^⊥ (where B_L^⊥ is the left zero divisor of the matrix B and C_R^⊥ is the right zero divisor of the output matrix C) has a complete row rank.