scholarly journals Robust Stabilization via Super-Stable Systems Techniques

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 98
Author(s):  
Svetlana A. Krasnova ◽  
Yulia G. Kokunko ◽  
Victor A. Utkin ◽  
Anton V. Utkin
Keyword(s):  
Direct Method ◽  
Robust Stabilization ◽  
Control Plant ◽  
Parametric Uncertainty ◽  
Parametric Uncertainties ◽  
Regular Form ◽  
The Matrix ◽  
Degree Of Stability ◽  
Control Procedures ◽  
Robust Systems

In this paper, we propose a direct method for the synthesis of robust systems operating under parametric uncertainty of the control plant model. The developed robust control procedures are based on the assumption that the structural properties of the nominal system are conservated over the entire range of parameter changes. The invariant-to-parametric-uncertainties transformation of the initial model to a regular form makes it possible to use the concept of super-stable systems for the synthesis of a stabilizing feedback. It is essential that the synthesis of super-stable systems is carried out not on the basis of assigning eigenvalues to the matrix of the close-loop system, but in terms of its elements. The proposed approach is applicable to a wide class of linear systems with parametric uncertainties and provides a given degree of stability.

scholarly journals Robust Stabilization of Interval Plants with Uncertain Time-Delay Using the Value Set Concept

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 429
Author(s):  
Pedro Zamora ◽  
Alejandro Arceo ◽  
Noé Martínez ◽  
Gerardo Romero ◽  
Luis E. Garza
Keyword(s):  
Time Delay ◽  
Robust Stabilization ◽  
Parametric Uncertainty ◽  
Exclusion Principle ◽  
Control Synthesis ◽  
Classical Orthogonal Polynomials ◽  
Loop Control ◽  
Value Set ◽  
Interval Plants ◽  
Uncertain Time

This paper considers the robust stabilization problem for interval plants with parametric uncertainty and uncertain time-delay based on the value set characterization of closed-loop control systems and the zero exclusion principle. Using Kharitonov’s polynomials, it is possible to establish a sufficient condition to guarantee the robust stability property. This condition allows us to solve the control synthesis problem using conditions similar to those established in the loopshaping technique and to parameterize the controllers using stable polynomials constructed from classical orthogonal polynomials.

DMRG Approach to Fast Linear Algebra in the TT-Format

2011 ◽  
Vol 11 (3) ◽  
pp. 382-393 ◽  
Author(s):  
Ivan Oseledets
Keyword(s):  
Linear Systems ◽  
Linear Algebra ◽  
Direct Method ◽  
Fast Algorithms ◽  
Approximate Solutions ◽  
Vector Product ◽  
The Matrix ◽  
Minimization Scheme

AbstractIn this paper, the concept of the DMRG minimization scheme is extended to several important operations in the TT-format, like the matrix-by-vector product and the conversion from the canonical format to the TT-format. Fast algorithms are implemented and a stabilization scheme based on randomization is proposed. The comparison with the direct method is performed on a sequence of matrices and vectors coming as approximate solutions of linear systems in the TT-format. A generated example is provided to show that randomization is really needed in some cases. The matrices and vectors used are available from the author or at http://spring.inm.ras.ru/osel

scholarly journals Solvency control of the enterprise in the bankruptcy prevention system

2020 ◽  
Vol 4 (2) ◽  
pp. 14-23
Author(s):  
Hanna Sytnyk ◽  
Inna Olesenko
Keyword(s):  
Control System ◽  
Financial Management ◽  
Financial Responsibility ◽  
Coverage Ratio ◽  
Total Capital ◽  
Logical Sequence ◽  
The Matrix ◽  
Control Procedures ◽  
Recent Trends ◽  
Control Circuits

Introduction. Recent trends in the economy, in particular the situation with COVID-19 epidemic, will contribute to the deterioration of the level of solvency, financial security of enterprises, and, as consequence, increasing the number of bankruptcies. Constant monitoring of the solvency level is a necessary element of anti-crisis financial management and a tool to prevent bankruptcy. That is why the development of methodological bases and methodological approaches to solvency control is an important area of research. Aim and tasks. The aim of the article is to substantiate the solvency control system of the enterprise, which would cover the identification of the main control indicators, methods of control over individual control circuits, the formation of a clear structural and logical sequence of this process. Results. The tendency of increasing the share of current liabilities in the total capital of the enterprise, decreasing the value of the financial autonomy ratio and total coverage ratio, which indicates a problematic state of solvency of Ukrainian enterprises was investigated. The solvency control system elements of the enterprise were determined: objects, subject, purpose, functions, functional directions, components of the control according to the management contours. The characteristic of solvency control according to the management contours (strategic, current, operational) was described more detailed. The gradation of the deviation scales in a solvency condition of the enterprise was improved and the matrix of decisions in which directions of the reaction on type and scale of deviations were defined was composed. Conclusions. In order to avoid bankruptcy, the enterprise must adhere to the financial discipline, be aware of financial responsibility and constantly improve management mechanisms, especially preventive anti-crisis methods, which should include a solvency control. The proposed approach to controlling is expected to provide a comprehensive nature of solvency control as an important component of preventive anti-crisis management aimed at preventing bankruptcy. Complexity is achieved by the consistency of the control procedures on the control contours, differentiation of the control tools, identification of possible deviations and ways to respond to them.

Automated System of Stabilization and Position Control of Aviation Equipment

2019 ◽  
pp. 297-330
Author(s):  
Olha Sushchenko
Keyword(s):  
Position Control ◽  
Transfer Functions ◽  
Controller Design ◽  
Robust Stabilization ◽  
Automated System ◽  
Simulink Model ◽  
The Matrix ◽  
Stabilized Platform ◽  
And Control ◽  
The Mathematical Model

In this chapter, the author presents the problems of design of the robust automated system for stabilization and control of platforms with aircraft observation equipment. The mathematical model of the triaxial stabilized platform is developed. The procedure of synthesis of robust stabilization system based on robust structural synthesis is represented. The above-mentioned procedure uses loop-shaping approach and method of the mixed sensitivity. The matrix weighting transfer functions are obtained. The optimization programs in MatLab are developed. The developed procedures are approved based on the results of simulation by means of the appropriate Simulink model. The obtained results can be useful for unmanned aerial vehicles and aircraft of special aviation, which are used for monitoring technical objects and aerial photography. The technical contributions are procedures of the robust controller design represented as the flowchart. The proposed approach is validated by application of the theoretical suppositions to the concrete example and appropriate simulation results.

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