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Your search keyword '"Andrey Polyakov"' showing total 6 results
Start Over Author "Andrey Polyakov" Journal ieee transactions on automatic control
6 results on '"Andrey Polyakov"'

1. Hyperexponential and Fixed-Time Stability of Time-Delay Systems: Lyapunov–Razumikhin Method

Author

Artem N. Nekhoroshikh, Denis Efimov, Andrey Polyakov, Wilfrid Perruquetti, Igor B. Furtat, National Research University of Information Technologies, Mechanics and Optics [St. Petersburg] (ITMO), Finite-time control and estimation for distributed systems (VALSE), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Institute of Mechanical Engineering Problems [St. Petersburg] (IPME), Russian Academy of Sciences [Moscow] (RAS), and The results of Section IV are supported by the Russian Science Foundation under grant no. 18-79-10104 (https://rscf.ru/en/project/18-79-10104/) at IPME RAS. The results of Section V are supported by the Russian Science Foundation under grant no. 21-71-10032 at ITMO University.

Subjects
implicit theorem, Lyapunov-Razumikhin theorem, Control and Systems Engineering, Fixed-time and hyperexponential stability, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Electrical and Electronic Engineering, linear matrix inequalities, time-delay systems, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Computer Science Applications
Abstract

International audience; Razumikhin-like theorems on hyperexponential and fixed-time stability of time-delay systems are proposed for both explicitly and implicitly defined Lyapunov functions. While the former method is useful for stability analysis, the latter approach is more suitable for control synthesis. Examples of systems that can be stabilized hyperexponentially and in fixed time are given. The control parameters tuning algorithm is presented in the form of linear matrix inequalities. The numerical simulations illustrate the theoretical results.

Published
2023
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2. Energetically optimal finite-time stabilization of generalized homogeneous linear systems

Author

Andrey Polyakov, Denis Efimov, Xubin Ping, Finite-time control and estimation for distributed systems [VALSE], Xidian University, Finite-time control and estimation for distributed systems (VALSE), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), and Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)

Subjects
nonlinear control, stability of nonlinear systems, optimal control, Control and Systems Engineering, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Electrical and Electronic Engineering, Computer Science Applications
Abstract

International audience; The problem of finite-time stabilization of a linear plant with an optimization of both a settling time and an averaged/weighted control energy is studied using the concept of generalized homogeneity. It is shown that the optimal finite-time stabilizing control in this case can be designed by means of solving a simple linear algebraic equation. Robustness of the obtained control law is studied.

Published
2023
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3. A Switching Controller for a Class of MIMO Bilinear Systems With Time Delay

Author

Emilia Fridman, Tonametl Sanchez, Andrey Polyakov, Laurentiu Hetel, Universidad Nacional Autónoma de México (UNAM), Finite-time control and estimation for distributed systems (VALSE), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Department of Electrical Engineering, Tel Aviv University [Tel Aviv], Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Universidad Nacional Autónoma de México = National Autonomous University of Mexico (UNAM), Tel Aviv University (TAU), and ANR-18-CE40-0008,DIGITSLID,Différentiateurs et commandes homogènes par modes glissants multivalués en temps discret: l'approche implicite(2018)

Subjects
0209 industrial biotechnology, Computer science, switched control, MIMO, 02 engineering and technology, State (functional analysis), Stability (probability), Computer Science Applications, Nonlinear system, 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, bilinear systems, Trajectory, Electrical and Electronic Engineering, Constant (mathematics), Finite set, time-delay systems
Abstract

In this paper, we propose a state-dependent switching controller for multiple-input multiple-output (MIMO) bilinear systems with constant delays in both the state and the input. The control input is assumed to be restricted to take only a finite number of values. The stability analysis of the closed loop is based on a Lyapunov–Krasovskii functional, and the design is reduced to solve a system of linear matrix inequalities. The controller can be designed by considering (state) delay-dependent or delay-independent conditions.

Published
2020
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4. Realization and Discretization of Asymptotically Stable Homogeneous Systems

Author

Wilfrid Perruquetti, Andrey Polyakov, Arie Levant, Denis Efimov, Non-Asymptotic estimation for online systems (NON-A-POST), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), School of Mathematical Sciences [Tel Aviv], Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University [Tel Aviv]-Tel Aviv University [Tel Aviv], Systèmes Non Linéaires et à Retards (SyNeR), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), This work was partially supported by ANR-15-CE23-0007 (Project Finite4SoS), the Government of Russian Federation (Grant 074-U01) andthe Ministry of Education and Science of Russian Federation (Project 14.Z50.31.0031)., ANR-15-CE23-0007,Finite4SoS,Commande et estimation en temps fini pour les Systèmes de Systèmes(2015), School of Mathematical Sciences [Tel Aviv] (TAU), Raymond and Beverly Sackler Faculty of Exact Sciences [Tel Aviv] (TAU), and Tel Aviv University (TAU)-Tel Aviv University (TAU)

Subjects
0209 industrial biotechnology, Discretization, Differential equation, 020208 electrical & electronic engineering, Mathematical analysis, Linear system, Explicit and implicit methods, 02 engineering and technology, Backward Euler method, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Computer Science Applications, Euler method, symbols.namesake, 020901 industrial engineering & automation, Exponential stability, Control and Systems Engineering, Stability theory, 0202 electrical engineering, electronic engineering, information engineering, symbols, Electrical and Electronic Engineering, Mathematics
Abstract

International audience; Sufficient conditions for the existence and convergence to zero of numeric approximations to solutions of asymptotically stable homogeneous systems are obtained for the explicit and implicit Euler integration schemes. It is shown that the explicit Euler method has certain drawbacks for the global approximation of homogeneous systems with non-zero degrees, whereas the implicit Euler scheme ensures convergence of the approximating solutions to zero. Properties of absolute and relative errors of the respective discretizations are investigated.

Published
2017
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5. Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems

Author

Andrey Polyakov, Non-Asymptotic estimation for online systems (NON-A), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), and Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Polynomial, Mathematical optimization, Variable structure control, Settling time, 02 engineering and technology, Nonlinear control, Sliding mode control, Stability (probability), Computer Science Applications, Nonlinear system, 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Convergence (routing), 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Electrical and Electronic Engineering, Mathematics
Abstract

International audience; Nonlinear control algorithms of two types are presented for uncertain linear plants. Controllers of the first type are stabilizing polynomial feedbacks that allow to adjust a guaranteed convergence time of system trajectories into selected neighborhood of the origin independently on initial conditions. The control design procedure uses block control principles and finite-time attractivity properties of polynomial feedbacks. Controllers of the second type are modifications of the second order sliding mode control algorithms. They provide global finite-time stability of the closed-loop system and allow to adjust a guaranteed settling time independently on initial conditions. Control algorithms are presented for both single-input and multi-input systems. Theoretical results are supported by numerical simulations.

Published
2012
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6. Reaching Time Estimation for 'Super-Twisting' Second Order Sliding Mode Controller via Lyapunov Function Designing

Author

Andrey Polyakov and Alexander S. Poznyak

Subjects
Lyapunov function, Partial differential equation, Differential equation, Order of accuracy, Sliding mode control, Computer Science Applications, symbols.namesake, Method of characteristics, Control and Systems Engineering, Control theory, Ordinary differential equation, symbols, Lyapunov equation, Electrical and Electronic Engineering, Mathematics
Abstract

A method of a Lyapunov functions design based on resolving of the first-order partial differential equation of a special type is presented. A successful resolution of this equation guaranties a finite-time convergence for the corresponding dynamics given by an ordinary differential equation with a discontinuous right-hand side. It is also provides an analytical formula for an upper bound of the corresponding reaching time. The suggested method is applied to the problem of a stability analysis and a reaching time estimation of the, so-called, ldquosuper-twistingrdquo controller. The estimation accuracy is confirmed by numerical example.

Published
2009
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