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Mathematics
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Analysis and Control of Nonlinear Dynamical System
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Analysis and Control of Nonlinear Dynamical System

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 6032

Special Issue Editor

Dr. Stepan Tkachev

E-Mail Website
Guest Editor
Keldysh Institute of Applied Mathematics, Miusskaya Sq. 4, 125047 Moscow, Russia
Interests: modeling; dynamics; small satellite; stability analysis; oscillation; asymptotic theory; satellite attitude dynamics

Special Issue Information

Dear Colleagues,

With the ever-increasing control performance requirements for nonlinear systems, the problem of new algorithms synthesis arises. The algorithm should satisfy accuracy, power or fuel consumption, time response and other constraints. In addition, the control system usually operates when there is a limit for computational capabilities while the information about the system itself and its state vector is inaccurate.

Another problem is the nonlinear system analysis. If the system is linear, there is a set of analytical and semi-analytical methods that can usually prove the control performance. In the case of a nonlinear system, usually only pure numerical methods of analysis are applied, which are not always effective. Therefore, the development of new methods and the adaptation of the existing ones is essential.

This Special Issue aims to demonstrate the modern control theory applied to real nonlinear systems and share examples of analytical and numerical analysis.

Dr. Stepan Tkachev
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • nonlinear control
  • dynamical system
  • dynamical system analysis
  • stability analysis
  • control synthesis
  • stabilization
  • optimal control
  • system identification
  • nonlinear analysis

Published Papers (6 papers)

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Research

14 pages, 1430 KiB  
Article
Lyapunov-Based Control via Atmospheric Drag for Tetrahedral Satellite Formation
by Mikhail Ovchinnikov, Yaroslav Mashtakov and Sergey Shestakov
Mathematics 2024, 12(2), 189; https://doi.org/10.3390/math12020189 - 6 Jan 2024
Viewed by 458
Abstract
The problem of small tetrahedral satellite formation maintenance in a Low Earth Orbit is being considered. The main purpose is to develop a simple algorithm for tetrahedron control via atmospheric drag. To design a controller, the direct Lyapunov method is used. The control [...] Read more.
The problem of small tetrahedral satellite formation maintenance in a Low Earth Orbit is being considered. The main purpose is to develop a simple algorithm for tetrahedron control via atmospheric drag. To design a controller, the direct Lyapunov method is used. The control obtained is suitable for tetrahedral formation maintenance, with an average distance of about 1 km. During the controlled motion, the geometric characteristics of the tetrahedron are preserved. Full article
(This article belongs to the Special Issue Analysis and Control of Nonlinear Dynamical System)
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24 pages, 2066 KiB  
Article
Attitude Stabilization of a Satellite with Large Flexible Elements Using On-Board Actuators Only
by Stepan Tkachev, Alexey Shestoperov, Anna Okhitina and Anna Nuralieva
Mathematics 2023, 11(24), 4928; https://doi.org/10.3390/math11244928 - 11 Dec 2023
Viewed by 660
Abstract
Attitude control of a satellite with three flexible elements is considered. Control torque is developed by a set of reaction wheels, which are installed on the central hub of the satellite. The flexible elements are large, so the control torque constraints must be [...] Read more.
Attitude control of a satellite with three flexible elements is considered. Control torque is developed by a set of reaction wheels, which are installed on the central hub of the satellite. The flexible elements are large, so the control torque constraints must be taken into account. In the paper, a control algorithm based on a linear-quadratic regulator is studied. The asymptotic stability of this control is shown. The choice of the control parameters is based on the closed form solution of the corresponding algebraic Riccati equation, which is supplemented by the linear matrix inequality. To increase the convergence rate, particle swarm optimization is used to tune the control parameters. Full article
(This article belongs to the Special Issue Analysis and Control of Nonlinear Dynamical System)
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13 pages, 1165 KiB  
Article
Multivariate Forecasting Model for COVID-19 Spread Based on Possible Scenarios in Ecuador
by Juan Guamán, Karen Portilla, Paúl Arias-Muñoz, Gabriel Jácome, Santiago Cabrera, Luis Álvarez, Bolívar Batallas, Hernán Cadena and Juan Carlos García
Mathematics 2023, 11(23), 4721; https://doi.org/10.3390/math11234721 - 22 Nov 2023
Viewed by 652
Abstract
So far, about 770.1 million confirmed cases of COVID-19 have been counted by August 2023, and around 7 million deaths have been reported from these cases to the World Health Organization. In Ecuador, the first confirmed COVID-19 case was registered on 19 February [...] Read more.
So far, about 770.1 million confirmed cases of COVID-19 have been counted by August 2023, and around 7 million deaths have been reported from these cases to the World Health Organization. In Ecuador, the first confirmed COVID-19 case was registered on 19 February 2020, and the country’s mortality rate reached 0.43% with 12986 deaths, suggesting the need to establish a mechanism to show the virus spread in advance. This study aims to build a dynamic model adapted to health and socio-environmental variables as a multivariate model to understand the virus expansion among the population. The model is based on Susceptible-Infected-Recovered (SIR), which is a standard model in which the population is divided into six groups with parameters such as susceptible S(t), transit stage E(t), infected I(t), recovered R(t), deceased Me(t), infected asymptomatic Ia(t), infected symptomatic Is(t) and deceased by other causes M(t) to be considered and adapted. The model was validated by using consistent data from Chile and run by inconsistent data from Ecuador. The forecast error was analyzed based on the mean absolute error between real data and model forecast, showing errors within a range from 6.33% to 8.41% for Chile, with confidence a interval of 6.17%, then 3.87% to 4.70% range for Ecuador with a confidence interval of 2.59% until 23rd December 2020 of the database. The model forecasts exponential variations in biosecurity measures, exposed population, and vaccination. Full article
(This article belongs to the Special Issue Analysis and Control of Nonlinear Dynamical System)
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16 pages, 1480 KiB  
Article
Observer-Based Dynamic Event-Triggered Tracking Consensus for Switched Multi-Agent Systems
by Xiaoli Ruan, Jiayi Cai, Zhaojing Wang, Chen Wang and Huali Yang
Mathematics 2023, 11(13), 2861; https://doi.org/10.3390/math11132861 - 26 Jun 2023
Cited by 1 | Viewed by 935
Abstract
This article discusses the event-triggered consensus problem for a switched multi-agent system (MASs) with switching topologies. An observer-based dynamic event-triggered (DET) controller with a discontinuous nonlinear term is designed to reduce arduous communication. With the designed approach, the error system can reach a [...] Read more.
This article discusses the event-triggered consensus problem for a switched multi-agent system (MASs) with switching topologies. An observer-based dynamic event-triggered (DET) controller with a discontinuous nonlinear term is designed to reduce arduous communication. With the designed approach, the error system can reach a tracking consensus. Then, a continuous observer-based DET protocol is created using the boundary layer method to prevent chattering effects. Moreover, by employing the Riccati equation and the switched Lyapunov function method, some sufficient criteria are put forward to guarantee the tracking consensus of the systems. The suggested observer-based DET protocol can also exclude the Zeno behavior. Finally, two examples verify the validity of the analysis. Full article
(This article belongs to the Special Issue Analysis and Control of Nonlinear Dynamical System)
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17 pages, 1057 KiB  
Article
Output Feedback Control for Spacecraft Attitude System with Practical Predefined-Time Stability Based on Anti-Windup Compensator
by Nguyen Xuan-Mung, Mehdi Golestani, Huu Tiep Nguyen, Ngoc Anh Nguyen and Afef Fekih
Mathematics 2023, 11(9), 2149; https://doi.org/10.3390/math11092149 - 4 May 2023
Cited by 3 | Viewed by 1285
Abstract
This paper investigates the problem of output feedback attitude control for rigid spacecraft subject to inertia matrix uncertainty, space disturbance, and input saturation. Firstly, a model transformation is adopted to convert an attitude system with immeasurable angular velocity into a new system. All [...] Read more.
This paper investigates the problem of output feedback attitude control for rigid spacecraft subject to inertia matrix uncertainty, space disturbance, and input saturation. Firstly, a model transformation is adopted to convert an attitude system with immeasurable angular velocity into a new system. All states of the new converted system are measurable and available for feedback; however, the system contains mismatched uncertainty resulting from the coordinate transformation. Then, an adaptive nonsingular back-stepping control with practical predefined-time convergence is designed. To resolve the problem of input saturation, an anti-windup compensator is developed. It is analytically proved that the spacecraft attitude and angular velocity are practical predefined-time stable, such that the convergence time is a given tunable constant. The simulation results reveal that the proposed control framework provides rapid attitude maneuver and actuator saturation elimination. Full article
(This article belongs to the Special Issue Analysis and Control of Nonlinear Dynamical System)
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14 pages, 1366 KiB  
Article
Terminal One Axis Stabilization Properties of a Spinning Satellite Employing Simple Magnetic Attitude Control
by Dmitry Roldugin and Mikhail Ovchinnikov
Mathematics 2023, 11(6), 1530; https://doi.org/10.3390/math11061530 - 21 Mar 2023
Cited by 1 | Viewed by 1410
Abstract
A spin stabilized satellite reorientation maneuver in the inertial space is investigated. Spin axis pointing and nutation damping magnetic attitude control algorithms are utilized. Evolutionary equations for the oscillations of a symmetrical satellite near the required position are derived. The exact solution for [...] Read more.
A spin stabilized satellite reorientation maneuver in the inertial space is investigated. Spin axis pointing and nutation damping magnetic attitude control algorithms are utilized. Evolutionary equations for the oscillations of a symmetrical satellite near the required position are derived. The exact solution for the wobble amplitude is obtained for the averaged equations of motion. Spin axis attitude angles relative to the required direction are analyzed. Optimal control gain is found for the reorientation maneuver. Theoretical results are verified with numerical simulation. Full article
(This article belongs to the Special Issue Analysis and Control of Nonlinear Dynamical System)
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