Nonlinear Systems: Dynamics, Control, Optimization and Applications in Science and Engineering, 3rd Edition

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

Deadline for manuscript submissions: 31 August 2024 | Viewed by 5904

Special Issue Editor

Special Issue Information

Dear Colleagues,

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields; this is because highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be it physical, biological, or financial, and technological complex systems and stochastic systems, such as mechanical or electronic devices, can be managed via the same conceptual approach, both analytically and through computer simulation using effective nonlinear dynamics methods.

The aim of this Special Issue is to highlight papers that present the dynamics, control, optimization and application of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and thus this Special Issue can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are particularly welcome. 

Potential topics include, but are not limited to, the following:

  • Stability analysis of discrete and continuous dynamical systems;
  • Nonlinear dynamics in biological complex systems;
  • Stability and stabilization of stochastic systems;
  • Mathematical models in statistics and probability;
  • Synchronization of oscillators and chaotic systems;
  • Optimization methods of complex systems;
  • Reliability modeling and system optimization;
  • Computation and control over networked systems.

Prof. Dr. Quanxin Zhu
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.

Related Special Issue

Published Papers (9 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

17 pages, 1961 KiB  
Article
Command-Filtered Nussbaum Design for Nonlinear Systems with Unknown Control Direction and Input Constraints
by Yuxuan Liu
Mathematics 2024, 12(14), 2167; https://doi.org/10.3390/math12142167 - 10 Jul 2024
Viewed by 243
Abstract
This paper studies the problem of adaptive fuzzy control based on command filtering for a class of nonlinear systems characterized by an input dead zone, input saturation, and unknown control direction. First, this paper proposes a novel equivalent transformation technique that simplifies the [...] Read more.
This paper studies the problem of adaptive fuzzy control based on command filtering for a class of nonlinear systems characterized by an input dead zone, input saturation, and unknown control direction. First, this paper proposes a novel equivalent transformation technique that simplifies the design complexity of multiple input constraints by converting the input dead zone and saturation nonlinearities into a unified functional form. Subsequently, a fuzzy logic system is utilized to handle the unknown nonlinear functions, and the command-filtering method is employed to address the issue of complexity explosion, while the Nussbaum function is utilized to resolve the challenge of an unknown control direction. Based on Lyapunov stability, it is proven that the tracking error converges to a small neighborhood around the origin, and all closed-loop signals are bounded. Finally, a numerical simulation result and an actual simulation result of a pendulum are presented to verify the feasibility and effectiveness of the proposed control strategy. Full article
22 pages, 477 KiB  
Article
Exponential Synchronization of Coupled Neural Networks with Hybrid Delays and Stochastic Distributed Delayed Impulses
by Gang Zhang, Yinfang Song and Xiaoyou Liu
Mathematics 2024, 12(13), 1995; https://doi.org/10.3390/math12131995 - 27 Jun 2024
Viewed by 296
Abstract
This paper is concerned with exponential synchronization for a class of coupled neural networks with hybrid delays and stochastic distributed delayed impulses. First of all, based on the average impulsive interval method, total probability formula and ergodic theory, several novel impulsive Halanay differential [...] Read more.
This paper is concerned with exponential synchronization for a class of coupled neural networks with hybrid delays and stochastic distributed delayed impulses. First of all, based on the average impulsive interval method, total probability formula and ergodic theory, several novel impulsive Halanay differential inequalities are established. Two types of stochastic impulses, i.e., stochastic distributed delayed impulses with dependent property and Markov property have been taken into account, respectively. Secondly, some criteria on exponential synchronization in the mean square of a class of coupled neural networks with stochastic distributed delayed impulses are acquired by combining the proposed lemmas and graph theory. The validity of the theoretical results is demonstrated by several numerical simulation examples. Full article
Show Figures

Figure 1

15 pages, 592 KiB  
Article
Stochastic Intermittent Control with Uncertainty
by Zhengqi Ma, Hongyin Jiang, Chun Li, Defei Zhang and Xiaoyou Liu
Mathematics 2024, 12(13), 1947; https://doi.org/10.3390/math12131947 - 23 Jun 2024
Viewed by 264
Abstract
In this article, we delve into the exponential stability of uncertainty systems characterized by stochastic differential equations driven by G-Brownian motion, where coefficient uncertainty exists. To stabilize the system when it is unstable, we consider incorporating a delayed stochastic term. By employing linear [...] Read more.
In this article, we delve into the exponential stability of uncertainty systems characterized by stochastic differential equations driven by G-Brownian motion, where coefficient uncertainty exists. To stabilize the system when it is unstable, we consider incorporating a delayed stochastic term. By employing linear matrix inequalities (LMI) and Lyapunov–Krasovskii functions, we derive a sufficient condition for stabilization. Our findings demonstrate that an unstable system can be stabilized with a control interval within (θ*,1). Some numerical examples are provided at the end to validate the correctness of our theoretical results. Full article
Show Figures

Figure 1

14 pages, 387 KiB  
Article
Imputation-Based Variable Selection Method for Block-Wise Missing Data When Integrating Multiple Longitudinal Studies
by Zhongzhe Ouyang, Lu Wang and Alzheimer’s Disease Neuroimaging Initiative
Mathematics 2024, 12(7), 951; https://doi.org/10.3390/math12070951 - 23 Mar 2024
Viewed by 696
Abstract
When integrating data from multiple sources, a common challenge is block-wise missing. Most existing methods address this issue only in cross-sectional studies. In this paper, we propose a method for variable selection when combining datasets from multiple sources in longitudinal studies. To account [...] Read more.
When integrating data from multiple sources, a common challenge is block-wise missing. Most existing methods address this issue only in cross-sectional studies. In this paper, we propose a method for variable selection when combining datasets from multiple sources in longitudinal studies. To account for block-wise missing in covariates, we impute the missing values multiple times based on combinations of samples from different missing pattern and predictors from different data sources. We then use these imputed data to construct estimating equations, and aggregate the information across subjects and sources with the generalized method of moments. We employ the smoothly clipped absolute deviation penalty in variable selection and use the extended Bayesian Information Criterion criteria for tuning parameter selection. We establish the asymptotic properties of the proposed estimator, and demonstrate the superior performance of the proposed method through numerical experiments. Furthermore, we apply the proposed method in the Alzheimer’s Disease Neuroimaging Initiative study to identify sensitive early-stage biomarkers of Alzheimer’s Disease, which is crucial for early disease detection and personalized treatment. Full article
Show Figures

Figure 1

13 pages, 690 KiB  
Article
Fractional-Order Model-Free Adaptive Control with High Order Estimation
by Zhuo-Xuan Lv and Jian Liao
Mathematics 2024, 12(5), 784; https://doi.org/10.3390/math12050784 - 6 Mar 2024
Viewed by 715
Abstract
This paper concerns an improved model-free adaptive fractional-order control with a high-order pseudo-partial derivative for uncertain discrete-time nonlinear systems. Firstly, a new equivalent model is obtained by employing the Grünwald–Letnikov (G-L) fractional-order difference of the input in a compact-form dynamic linearization. Then, the [...] Read more.
This paper concerns an improved model-free adaptive fractional-order control with a high-order pseudo-partial derivative for uncertain discrete-time nonlinear systems. Firstly, a new equivalent model is obtained by employing the Grünwald–Letnikov (G-L) fractional-order difference of the input in a compact-form dynamic linearization. Then, the pseudo-partial derivative (PPD) is derived using a high-order estimation algorithm, which provides more PPD information than the previous time. A discrete-time model-free adaptive fractional-order controller is proposed, which utilizes more past input–output data information. The ultimate uniform boundedness of the tracking errors are demonstrated through formal analysis. Finally, the simulation results demonstrate the effectiveness of the proposed method. Full article
Show Figures

Figure 1

12 pages, 511 KiB  
Article
Synchronization for Reaction–Diffusion Switched Delayed Feedback Epidemic Systems via Impulsive Control
by Ruofeng Rao and Quanxin Zhu
Mathematics 2024, 12(3), 447; https://doi.org/10.3390/math12030447 - 30 Jan 2024
Cited by 3 | Viewed by 682
Abstract
Due to the facts that epidemic-related parameters vary significantly in different stages of infectious diseases and are relatively stable within the same stage, infectious disease models should be switch-type models. However, research on switch-type infectious disease models is scarce due to the complexity [...] Read more.
Due to the facts that epidemic-related parameters vary significantly in different stages of infectious diseases and are relatively stable within the same stage, infectious disease models should be switch-type models. However, research on switch-type infectious disease models is scarce due to the complexity and intricate design of switching rules. This scarcity has motivated the writing of this paper. By assuming that switching instants and impulse times occur at different moments, this paper proposes switch rules suitable for impulse control and derives synchronization criteria for reaction–diffusion switch-type infectious disease systems under impulse control. The effectiveness of this method is validated through numerical simulations. It is important to mention that, based on the information available to us, this paper is currently the sole study focusing on switch-type reaction–diffusion models for infectious diseases. Full article
Show Figures

Figure 1

19 pages, 475 KiB  
Article
Generalized Halanay Inequalities and Asymptotic Behavior of Nonautonomous Neural Networks with Infinite Delays
by Dehao Ruan and Yao Lu
Mathematics 2024, 12(1), 155; https://doi.org/10.3390/math12010155 - 3 Jan 2024
Viewed by 691
Abstract
This paper focuses on the asymptotic behavior of nonautonomous neural networks with delays. We establish criteria for analyzing the asymptotic behavior of nonautonomous recurrent neural networks with delays by means of constructing some new generalized Halanay inequalities. We do not require to constructi [...] Read more.
This paper focuses on the asymptotic behavior of nonautonomous neural networks with delays. We establish criteria for analyzing the asymptotic behavior of nonautonomous recurrent neural networks with delays by means of constructing some new generalized Halanay inequalities. We do not require to constructi any complicated Lyapunov function and our results improve some existing works. Lastly, we provide some illustrative examples to demonstrate the effectiveness of the obtained results. Full article
Show Figures

Figure 1

17 pages, 3234 KiB  
Article
Optimal Control of SLBRS with Recovery Rates
by Xiangqing Zhao and Wanmei Hou
Mathematics 2024, 12(1), 132; https://doi.org/10.3390/math12010132 - 30 Dec 2023
Viewed by 734
Abstract
In the information age, frequent information exchange has provided a breeding ground for the spread of computer viruses. The significant losses caused by computer virus attacks have long rung the alarm for information security. From academia to businesses, and even to government, everyone [...] Read more.
In the information age, frequent information exchange has provided a breeding ground for the spread of computer viruses. The significant losses caused by computer virus attacks have long rung the alarm for information security. From academia to businesses, and even to government, everyone remains highly vigilant about information security. Researchers have put forward various approaches to combat computer viruses, involving innovative efforts in both the hardware and software aspects, as well as theoretical innovation and practical exploration. This article is dedicated to theoretical exploration, specifically investigating the stability of a computer virus model, known as SLBRS, from the perspective of optimal control. Firstly, a control system is introduced with the aim of minimizing the costs related to network detoxification and diminishing the percentage of computers impacted by the virus. Secondly, we employ the Pontryagin maximum principle to analyze the optimality of a control strategy for the proposed system. Thirdly, we validate the effectiveness of our theoretical analysis through numerical simulation. In conclusion, both theoretical analysis and numerical simulation reveal that the utilization of optimal control analysis to stabilize the SLBRS has been demonstrated to be advantageous in restoring contaminated computer network environments. Full article
Show Figures

Figure 1

24 pages, 506 KiB  
Article
Discounted Risk-Sensitive Optimal Control of Switching Diffusions: Viscosity Solution and Numerical Approximation
by Xianggang Lu and Lin Sun
Mathematics 2024, 12(1), 38; https://doi.org/10.3390/math12010038 - 22 Dec 2023
Viewed by 624
Abstract
This work considers the infinite horizon discounted risk-sensitive optimal control problem for the switching diffusions with a compact control space and controlled through the drift; thus, the the generator of the switching diffusions also depends on the controls. Note that the running cost [...] Read more.
This work considers the infinite horizon discounted risk-sensitive optimal control problem for the switching diffusions with a compact control space and controlled through the drift; thus, the the generator of the switching diffusions also depends on the controls. Note that the running cost of interest can be unbounded, so a decent estimation on the value function is obtained, under suitable conditions. To solve such a risk-sensitive optimal control problem, we adopt the viscosity solution methods and propose a numerical approximation scheme. We can verify that the value function of the optimal control problem solves the optimality equation as the unique viscosity solution. The optimality equation is also called the Hamilton–Jacobi–Bellman (HJB) equation, which is a second-order partial differential equation (PDE). Since, the explicit solutions to such PDEs are usually difficult to obtain, the finite difference approximation scheme is derived to approximate the value function. As a byproduct, the ϵ-optimal control of finite difference type is also obtained. Full article
Show Figures

Figure 1

Back to TopTop