Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 

Saved Queries

Sign in to use this feature.

Search Filter Reset All

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
Add Subjects Reset
Select Subjects

Journals

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
Add Journals Reset
Select Journals

Article Types

remove_circle_outline
Add Article Types Reset
Select Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
Add Countries / Regions Reset
Select Countries / Regions
Update Search
share announcement

Search Results (7)

Search Parameters:
Keywords = discontinuous piecewise differential systems

Order results
Result details
Results per page
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
18 pages, 6607 KiB  
Article
Total Model-Free Robust Control of Non-Affine Nonlinear Systems with Discontinuous Inputs
by Quanmin Zhu, Jing Na, Weicun Zhang and Qiang Chen
Processes 2025, 13(5), 1315; https://doi.org/10.3390/pr13051315 - 25 Apr 2025
Cited by 2 | Viewed by 425
Abstract
Taking the plant as a total uncertainty in a black box with measurable inputs and attainable outputs, this paper presents a constructive control design of agnostic nonlinear dynamic systems with discontinuous input (such as hard nonlinearities in the forms of dead zones, friction, [...] Read more.
Taking the plant as a total uncertainty in a black box with measurable inputs and attainable outputs, this paper presents a constructive control design of agnostic nonlinear dynamic systems with discontinuous input (such as hard nonlinearities in the forms of dead zones, friction, and backlashes). This study expands the model-free sliding mode control (MFSMC), based on the Lyapunov differential inequality, to a total model-free robust control (TMFRC) for this class of piecewise systems, which does not use extra adaptive online data fitting modelling to deal with plant uncertainties and input discontinuities. The associated properties are analysed to justify the constraints and provide assurance for system stability analysis. Numerical examples in control of a non-affine nonlinear plant with three hard nonlinear inputs—a dead zone, Coulomb and viscous friction, and backlash—are used to test the feasibility of the TMFRC. Furthermore, real experimental tests on a permanent magnet synchronous motor (PMSM) are also given to showcase the control’s applicability and offer guidance for implementation. Full article
(This article belongs to the Special Issue Design and Analysis of Adaptive Identification and Control)
►▼ Show Figures

Figure 1

22 pages, 648 KiB  
Article
Synchronization Analysis for Quaternion-Valued Delayed Neural Networks with Impulse and Inertia via a Direct Technique
by Juan Yu, Kailong Xiong and Cheng Hu
Mathematics 2024, 12(7), 949; https://doi.org/10.3390/math12070949 - 23 Mar 2024
Cited by 1 | Viewed by 1129
Abstract
The asymptotic synchronization of quaternion-valued delayed neural networks with impulses and inertia is studied in this article. Firstly, a convergence result on piecewise differentiable functions is developed, which is a generalization of the Barbalat lemma and provides a powerful tool for the convergence [...] Read more.
The asymptotic synchronization of quaternion-valued delayed neural networks with impulses and inertia is studied in this article. Firstly, a convergence result on piecewise differentiable functions is developed, which is a generalization of the Barbalat lemma and provides a powerful tool for the convergence analysis of discontinuous systems. To achieve synchronization, a constant gain-based control scheme and an adaptive gain-based control strategy are directly proposed for response quaternion-valued models. In the convergence analysis, a direct analysis method is developed to discuss the synchronization without using the separation technique or reduced-order transformation. In particular, some Lyapunov functionals, composed of the state variables and their derivatives, are directly constructed and some synchronization criteria represented by matrix inequalities are obtained based on quaternion theory. Some numerical results are shown to further confirm the theoretical analysis. Full article
(This article belongs to the Topic Advances in Artificial Neural Networks)
►▼ Show Figures

Figure 1

7 pages, 242 KiB  
Article
Limit Cycles of Discontinuous Piecewise Differential Hamiltonian Systems Separated by a Straight Line
by Joyce A. Casimiro and Jaume Llibre
Axioms 2024, 13(3), 161; https://doi.org/10.3390/axioms13030161 - 29 Feb 2024
Cited by 1 | Viewed by 1668
Abstract
In this article, we study the maximum number of limit cycles of discontinuous piecewise differential systems, formed by two Hamiltonians systems separated by a straight line. We consider three cases, when both Hamiltonians systems in each side of the discontinuity line have simultaneously [...] Read more.
In this article, we study the maximum number of limit cycles of discontinuous piecewise differential systems, formed by two Hamiltonians systems separated by a straight line. We consider three cases, when both Hamiltonians systems in each side of the discontinuity line have simultaneously degree one, two or three. We obtain that in these three cases, this maximum number is zero, one and three, respectively. Moreover, we prove that there are discontinuous piecewise differential systems realizing these maximum number of limit cycles. Note that we have solved the extension of the 16th Hilbert problem about the maximum number of limit cycles that these three classes of discontinuous piecewise differential systems separated by one straight line and formed by two Hamiltonian systems with a degree either one, two, or three, which such systems can exhibit. Full article
(This article belongs to the Topic Advances in Nonlinear Dynamics: Methods and Applications)
►▼ Show Figures

Figure 1

29 pages, 757 KiB  
Article
The Solution of the Extended 16th Hilbert Problem for Some Classes of Piecewise Differential Systems
by Louiza Baymout, Rebiha Benterki and Jaume Llibre
Mathematics 2024, 12(3), 464; https://doi.org/10.3390/math12030464 - 31 Jan 2024
Viewed by 1587
Abstract
The limit cycles have a main role in understanding the dynamics of planar differential systems, but their study is generally challenging. In the last few years, there has been a growing interest in researching the limit cycles of certain classes of piecewise differential [...] Read more.
The limit cycles have a main role in understanding the dynamics of planar differential systems, but their study is generally challenging. In the last few years, there has been a growing interest in researching the limit cycles of certain classes of piecewise differential systems due to their wide uses in modeling many natural phenomena. In this paper, we provide the upper bounds for the maximum number of crossing limit cycles of certain classes of discontinuous piecewise differential systems (simply PDS) separated by a straight line and consequently formed by two differential systems. A linear plus cubic polynomial forms six families of Hamiltonian nilpotent centers. First, we study the crossing limit cycles of the PDS formed by a linear center and one arbitrary of the six Hamiltonian nilpotent centers. These six classes of PDS have at most one crossing limit cycle, and there are systems in each class with precisely one limit cycle. Second, we study the crossing limit cycles of the PDS formed by two of the six Hamiltonian nilpotent centers. There are systems in each of these 21 classes of PDS that have exactly four crossing limit cycles. Full article
(This article belongs to the Special Issue Advances in Chaos Theory and Dynamical Systems)
►▼ Show Figures

Figure 1

19 pages, 398 KiB  
Article
Limit Cycles of Polynomially Integrable Piecewise Differential Systems
by Belén García, Jaume Llibre, Jesús S. Pérez del Río and Set Pérez-González
Axioms 2023, 12(4), 342; https://doi.org/10.3390/axioms12040342 - 31 Mar 2023
Cited by 2 | Viewed by 1760
Abstract
In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides. We assume that at least one of the systems is Hamiltonian. Under this assumption, [...] Read more.
In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides. We assume that at least one of the systems is Hamiltonian. Under this assumption, piecewise differential systems have no more than one limit cycle. This study characterizes linear differential systems with polynomial first integrals. Full article
(This article belongs to the Special Issue Differential Equations and Dynamical Systems—Theory and Applications)
►▼ Show Figures

Figure 1

10 pages, 294 KiB  
Article
Limit Cycles of Planar Piecewise Differential Systems with Linear Hamiltonian Saddles
by Jaume Llibre and Claudia Valls
Symmetry 2021, 13(7), 1128; https://doi.org/10.3390/sym13071128 - 24 Jun 2021
Cited by 14 | Viewed by 2422
Abstract
We provide the maximum number of limit cycles for continuous and discontinuous planar piecewise differential systems formed by linear Hamiltonian saddles and separated either by one or two parallel straight lines. We show that when these piecewise differential systems are either continuous or [...] Read more.
We provide the maximum number of limit cycles for continuous and discontinuous planar piecewise differential systems formed by linear Hamiltonian saddles and separated either by one or two parallel straight lines. We show that when these piecewise differential systems are either continuous or discontinuous and are separated by one straight line, or are continuous and are separated by two parallel straight lines, they do not have limit cycles. On the other hand, when these systems are discontinuous and separated by two parallel straight lines, we prove that the maximum number of limit cycles that they can have is one and that this maximum is reached by providing an example of such a system with one limit cycle. When the line of discontinuity of the piecewise differential system is formed by one straight line, the symmetry of the problem allows to take this straight line without loss of generality as the line x=0. Similarly, when the line of discontinuity of the piecewise differential system is formed by two parallel straight lines due to the symmetry of the problem, we can assume without loss of generality that these two straight lines are x=±1. Full article
(This article belongs to the Special Issue Qualitative Theory and Symmetries of Ordinary Differential Equations)
►▼ Show Figures

Figure 1

16 pages, 516 KiB  
Article
Unpredictable Solutions of Linear Impulsive Systems
by Marat Akhmet, Madina Tleubergenova, Mehmet Onur Fen and Zakhira Nugayeva
Mathematics 2020, 8(10), 1798; https://doi.org/10.3390/math8101798 - 16 Oct 2020
Cited by 8 | Viewed by 3283
Abstract
We consider a new type of oscillations of discontinuous unpredictable solutions for linear impulsive nonhomogeneous systems. The models under investigation are with unpredictable perturbations. The definition of a piecewise continuous unpredictable function is provided. The moments of impulses constitute a newly determined unpredictable [...] Read more.
We consider a new type of oscillations of discontinuous unpredictable solutions for linear impulsive nonhomogeneous systems. The models under investigation are with unpredictable perturbations. The definition of a piecewise continuous unpredictable function is provided. The moments of impulses constitute a newly determined unpredictable discrete set. Theoretical results on the existence, uniqueness, and stability of discontinuous unpredictable solutions for linear impulsive differential equations are provided. We benefit from the B-topology in the space of discontinuous functions on the purpose of proving the presence of unpredictable solutions. For constructive definitions of unpredictable components in examples, randomly determined unpredictable sequences are newly utilized. Namely, the construction of a discontinuous unpredictable function is based on an unpredictable sequence determined by a discrete random process, and the set of discontinuity moments is realized by the logistic map. Examples with numerical simulations are presented to illustrate the theoretical results. Full article
(This article belongs to the Special Issue Nonlinear Dynamics)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying article 1-50 on page 1 of 1.
Back to TopTop