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Mathematics
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Impulsive Control Systems and Complexity II
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Impulsive Control Systems and Complexity II

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

Deadline for manuscript submissions: closed (15 August 2022) | Viewed by 8964

Special Issue Editors

Prof. Dr. Xiaodi Li

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Guest Editor
School of Mathematics and Statistics, Shandong Normal University, Ji'nan 250014, China
Interests: impulsive control theory; hybrid systems; time-delay systems; neural networks and applied mathematics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Jinde Cao

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Guest Editor
School of Mathematics, Southeast University, Nanjing 210096, China
Interests: complex networks; neural networks; multi-agent systems engineering; stability dynamics; control time delay systems; computational intelligence; complex systems; intelligent control; nonlinear systems; applied mathematics
Prof. Dr. Wei Zhu

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Guest Editor
School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
Interests: functional differential equations; qualitative theory of impulsive differential equations; analysis and control of complex dynamical systems
Prof. Dr. Gani Stamov

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Guest Editor
1. Department of Mathematical Physics, Technical University of Sofia, Sliven, Bulgaria
2. Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
Interests: nonlinear analysis; control theory; mathematical modeling; differential equations; fractional calculus
Special Issues, Collections and Topics in MDPI journals
Dr. Ivanka Stamova

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Guest Editor
Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
Interests: nonlinear analysis; mathematical modeling; fractional order systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues, 

Many complex real word phenomena exist under the conditions of disorder, chaos, randomness, uncertainty, or in general, under the conditions of entropy. The design of efficient impulsive controllers for such chaotic systems is the main objective of numerous researchers. The impulsive control of complex phenomena arises naturally in a wide variety of applications. Indeed, impulsive control dynamical systems are used for the mathematical simulation of processes which are subject to impulses during their evolution. Such types of processes are observed in numerous fields of science and technology: Control theory, population dynamics, biotechnologies, industrial robotics, etc.

The dynamic of impulsive control dynamical systems has long been and will continue to be one of the dominant themes in mathematics and mathematics applications due to its theoretical and practical significance. During the last couple of decades, the analysis of impulsive control complex systems and related models has attracted the attention of a wide audience of professionals, such as mathematicians, applied researchers, and practitioners. For example, impulsive control and synchronization are the most interesting and important collective behaviors of complex networking systems and have aroused great interest in researchers in fields such as secure communication and information processing. There are many cases where impulsive control can give a better performance than continuous control. Sometimes even only impulsive control can be used for control purposes. Impulsive control methodology is very effective and allows synchronization of a complex system using only small control impulses, even though the system’s behavior may follow unpredictable patterns.

In spite of the amount of published results recently focused on impulsive control complex systems, there remain many challenging open questions. The theory and applications of these systems are still very active areas of research.

In this Special Issue, we provide an international forum for researchers to contribute with original research as well as review papers focusing on the latest achievements in the theory and applications of impulsive control complex dynamical systems.

Prof. Dr. Xiaodi Li
Prof. Dr. Jinde Cao
Prof. Dr. Wei Zhu
Prof. Dr. Gani Stamov
Dr. Ivanka Stamova
Guest Editors

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

  • complex dynamical systems
  • impulsive control
  • synchronization
  • stability
  • impulsive state feedback control
  • chaos control
  • complex networks
  • cluster synchronization
  • hybrid control
  • time-varying delays
  • finite-time synchronization

Published Papers (6 papers)

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Research

13 pages, 1862 KiB  
Article
Impulsive Control and Synchronization for Fractional-Order Hyper-Chaotic Financial System
by Xinggui Li, Ruofeng Rao, Shouming Zhong, Xinsong Yang, Hu Li and Yulin Zhang
Mathematics 2022, 10(15), 2737; https://doi.org/10.3390/math10152737 - 02 Aug 2022
Cited by 5 | Viewed by 999
Abstract
This paper reports a new global Mittag-Leffler synchronization criterion with regard to fractional-order hyper-chaotic financial systems by designing the suitable impulsive control and the state feedback controller. The significance of this impulsive synchronization lies in the fact that the backward economic system can [...] Read more.
This paper reports a new global Mittag-Leffler synchronization criterion with regard to fractional-order hyper-chaotic financial systems by designing the suitable impulsive control and the state feedback controller. The significance of this impulsive synchronization lies in the fact that the backward economic system can synchronize asymptotically with the advanced economic system under effective impulse macroeconomic management means. Matlab’s LMI toolbox is utilized to deduce the feasible solution in a numerical example, which shows the effectiveness of the proposed methods. It is worth mentioning that the LMI-based criterion usually requires the activation function of the system to be Lipschitz, but the activation function in this paper is fixed and truly nonlinear, which cannot be assumed to be Lipschitz continuous. This is another mathematical difficulty overcome in this paper. Full article
(This article belongs to the Special Issue Impulsive Control Systems and Complexity II)
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16 pages, 977 KiB  
Article
Quantitative Mean Square Exponential Stability and Stabilization of Linear Itô Stochastic Markovian Jump Systems Driven by Both Brownian and Poisson Noises
by Gaizhen Chang, Tingkun Sun, Zhiguo Yan, Min Zhang and Xiaomin Zhou
Mathematics 2022, 10(13), 2330; https://doi.org/10.3390/math10132330 - 03 Jul 2022
Viewed by 1003
Abstract
In this paper, quantitative mean square exponential stability and stabilization of Itô-type linear stochastic Markovian jump systems with Brownian and Poisson noises are investigated. First, the definition of quantitative mean square exponential stability, which takes into account the transient and steady behaviors of [...] Read more.
In this paper, quantitative mean square exponential stability and stabilization of Itô-type linear stochastic Markovian jump systems with Brownian and Poisson noises are investigated. First, the definition of quantitative mean square exponential stability, which takes into account the transient and steady behaviors of the system, is presented. Second, the relationship between general finite-time mean square stability, finite-time stochastic stability, and quantitative mean square exponential stability is proposed. Subsequently, some sufficient conditions for the existence of state feedback and observer-based controllers are derived, and an algorithm is offered to solve the matrix inequalities resulting from quantitative mean square exponential stabilization. Finally, the effectiveness of the proposed results is illustrated with the numerical example and the practical example. Full article
(This article belongs to the Special Issue Impulsive Control Systems and Complexity II)
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16 pages, 418 KiB  
Article
Mean-Square Strong Stability and Stabilization of Discrete-Time Markov Jump Systems with Multiplicative Noises
by Zhiguo Yan and Fangxu Su
Mathematics 2022, 10(6), 979; https://doi.org/10.3390/math10060979 - 18 Mar 2022
Viewed by 1313
Abstract
In this paper, the mean-square strong stability and stabilization of discrete-time Markov jump systems are studied. Firstly, the definition of mean-square strong stability is given, and the necessary and sufficient conditions for mean-square strong stability are derived. Secondly, several necessary and sufficient conditions [...] Read more.
In this paper, the mean-square strong stability and stabilization of discrete-time Markov jump systems are studied. Firstly, the definition of mean-square strong stability is given, and the necessary and sufficient conditions for mean-square strong stability are derived. Secondly, several necessary and sufficient conditions for mean-square strong stabilization via a state feedback controller and an output feedback controller are obtained. Furthermore, explicit expressions for the state feedback controller and static output feedback controller are obtained. Finally, two examples are given to illustrate the validity of the above results. Full article
(This article belongs to the Special Issue Impulsive Control Systems and Complexity II)
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12 pages, 406 KiB  
Article
Event-Triggered Extended Kalman Filtering Analysis for Networked Systems
by Huijuan Zhao, Jiapeng Xu and Fangfei Li
Mathematics 2022, 10(6), 927; https://doi.org/10.3390/math10060927 - 14 Mar 2022
Cited by 2 | Viewed by 1454
Abstract
In this paper, the filtering problem of nonlinear networked systems with event-triggered data transmission tasks is studied. To reduce the transmission of excessive measurement data in the bandwidth-limited network, a data transmission mechanism with event trigger is introduced to analyze the error behavior [...] Read more.
In this paper, the filtering problem of nonlinear networked systems with event-triggered data transmission tasks is studied. To reduce the transmission of excessive measurement data in the bandwidth-limited network, a data transmission mechanism with event trigger is introduced to analyze the error behavior of the extended Kalman filter. We prove that the real estimation error and error covariance matrices can be determined by restricting the initial conditions appropriately. Finally, the effectiveness of the filtering algorithm is verified by simulation. Full article
(This article belongs to the Special Issue Impulsive Control Systems and Complexity II)
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14 pages, 428 KiB  
Article
Impulsive Control of Complex-Valued Neural Networks with Mixed Time Delays and Uncertainties
by Yujuan Tian, Yuhan Yin, Fei Wang and Kening Wang
Mathematics 2022, 10(3), 526; https://doi.org/10.3390/math10030526 - 08 Feb 2022
Cited by 1 | Viewed by 1287
Abstract
This paper investigates the global exponential stability of uncertain delayed complex-valued neural networks (CVNNs) under an impulsive controller. Both discrete and distributed time-varying delays are considered, which makes our model more general than previous works. Unlike most existing research methods of decomposing CVNNs [...] Read more.
This paper investigates the global exponential stability of uncertain delayed complex-valued neural networks (CVNNs) under an impulsive controller. Both discrete and distributed time-varying delays are considered, which makes our model more general than previous works. Unlike most existing research methods of decomposing CVNNs into real and imaginary parts, some stability criteria in terms of complex-valued linear matrix inequalities (LMIs) are obtained by employing the complex Lyapunov function method, which is valid regardless of whether the activation functions can be decomposed. Moreover, a new impulsive differential inequality is applied to resolve the difficulties caused by the mixed time delays and delayed impulse effects. Finally, an illustrative example is provided to back up our theoretical results. Full article
(This article belongs to the Special Issue Impulsive Control Systems and Complexity II)
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16 pages, 345 KiB  
Article
Parameter Estimation Algorithms for Hammerstein Finite Impulse Response Moving Average Systems Using the Data Filtering Theory
by Yan Ji and Jinde Cao
Mathematics 2022, 10(3), 438; https://doi.org/10.3390/math10030438 - 29 Jan 2022
Cited by 4 | Viewed by 1595
Abstract
This paper considers the parameter estimation problems of Hammerstein finite impulse response moving average (FIR–MA) systems. Based on the matrix transformation and the hierarchical identification principle, the Hammerstein FIR–MA system is recast into two models, and a decomposition-based recursive least-squares algorithm is deduced [...] Read more.
This paper considers the parameter estimation problems of Hammerstein finite impulse response moving average (FIR–MA) systems. Based on the matrix transformation and the hierarchical identification principle, the Hammerstein FIR–MA system is recast into two models, and a decomposition-based recursive least-squares algorithm is deduced for estimating the parameters of these two models. In order to further improve the accuracy of the parameter estimation, a multi-innovation hierarchical least-squares algorithm based on the data filtering theory proposed. Finally, a simulation example demonstrates the effectiveness of the proposed scheme. Full article
(This article belongs to the Special Issue Impulsive Control Systems and Complexity II)
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