
Main / Konstantin Valerievich Pakhomov
Author: "Konstantin Valerievich Pakhomov"
Olga Alekseevna Peregudova, Ulyanovsk State University, Doctor of Physics and Mathematics, Associate Professor, graduated from the Mechanics and Mathematics Department of Ulyanovsk State University; Professor at the Department of Information Security and Control Theory of Ulyanovsk State University; an author of articles, textbooks, and a monograph on the theory of stability and motion control of mechanical systems. [email: peregudovaoa@sv.ulsu.ru]O. Peregudova, Konstantin Valerievich Pakhomov, Ulyanovsk State University, Postgraduate student; graduated from the Faculty of Mathematics and Information Technologies of Ulyanovsk State University; Junior Researcher of the Research Department of Ulyanovsk State University; an author of articles in the field of motion control of mechanical systems. [email: pakhomovkv@yandex.ru]K. Pakhomov


Constructing of Piecewise Constant Control in the Problem of Dynamic Positioning of Ship
The paper deals with the results of solving the problem of control synthesis performing dynamic positioning of ship in a point. The problem of simple dynamic positioning, which is in alignment with the center of mass of the vessel with given point waters (center position) for the given requirements for the orientation course is considered. The solution of this problem is provided by use of control on the basis of feedback that asymptotically stabilizes the position and orientation of the ship. To justify the control law, which is based in a discrete form, Euler discrete approximation of the original continuous system is constructed and the method of recursive procedure of backstepping is applied. This procedure allows to build a controlled system that can be represented as a cascade connection of several subsystems. For each subsystem, the stabilizing control and the Lyapunov function are built. At the final step of the recursive procedure, a control law for the entire system and the corresponding Lyapunov function is constructed. Thus, the structure of the found control law essentially depends on the Lyapunov function used at each stage of the procedure. We justify the use of a new class of Lyapunov functions in the form of vector norms for solving this problem, which is used in comparison to previously known works with class of quadratic Lyapunov functions and allows us to simplify the control structure and improve its properties, such as the speed of convergence of the process at a given position. The results of numerical simulations, confirming a higher effectiveness of the proposed control law in comparison with the known results are obtained. Dynamic positioning, piecewise constant control, backstepping technique, lyapunov function.



Sections: Automated control systems
Subjects: Automated control systems, Architecture of ship's system. 
Olga Alekseevna Peregudova, Ulyanovsk State University, Doctor of Physics and Mathematics, Associate Professor, graduated from the Faculty of Mechanics and Mathematics at Ulyanovsk State University; Professor of the Department of Information Security and Control Theory at Ulyanovsk State University; an author of articles, textbooks, and a monograph in the field of the theory of stability and motion control of mechanical systems. [email: peregudovaoa@sv.ulsu.ru]O. Peregudova, Konstantin Valerevich Pakhomov, Ulyanovsk State University, Postgraduate student, graduated from the Faculty of Mathematics and Information Technologies at Ulyanovsk State University; a research assistant at the Office of Scientific Research of Ulyanovsk State University; an author of articles in the field of motion control of mechanical systems. [email: pakhomovkv@yandex.ru]K. Pakhomov


On the Stabilization of Nonlinear Systems With Piecewise Constant Control Using a Back Stepping Method
A method of solving a stabilization problem of nonlinear systems with piecewise constant control on the basis of a sampling system using a back stepping method and Lyapunov’s functions of vector norms type is proved in the paper. Sufficient stabilization conditions with the initial deviations estimation are obtained. A specific example illustrates the effectiveness of the results in comparison with the known ones. Nonlinear system, piecewise constant control, back stepping, lyapunov’s function, matrix norm.



Sections: Mathematical modeling, calculi of approximation and software systems
Subjects: Mathematical modeling, Operational research. 
