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Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science...
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Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering

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

Deadline for manuscript submissions: closed (31 May 2022) | Viewed by 25323

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Prof. Dr. Quanxin Zhu

grade E-Mail Website
Guest Editor
School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China
Interests: Markov processes; stochastic differential equations; stochastic partial differential equations; stochastic stability; stochastic neural networks
Special Issues, Collections and Topics in MDPI journals

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, as 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, technological complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from 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 show dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. 

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

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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.

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Published Papers (15 papers)

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Editorial

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2 pages, 172 KiB  
Editorial
Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering
by Quanxin Zhu
Mathematics 2022, 10(24), 4837; https://0-doi-org.brum.beds.ac.uk/10.3390/math10244837 - 19 Dec 2022
Cited by 2 | Viewed by 1185
Abstract
Nonlinear phenomena frequently occur in many fields, such as physics, biology, and engineering [...] Full article
(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering)

Research

Jump to: Editorial

12 pages, 395 KiB  
Article
Analysis of Equilibrium Points in Quantized Hill System
by Abdullah A. Ansari, Sawsan Alhowaity, Elbaz I. Abouelmagd and Shiv K. Sahdev
Mathematics 2022, 10(13), 2186; https://0-doi-org.brum.beds.ac.uk/10.3390/math10132186 - 23 Jun 2022
Cited by 6 | Viewed by 1157
Abstract
In this work, the quantized Hill problem is considered in order for us to study the existence and stability of equilibrium points. In particular, we have studied three different cases which give all whole possible locations in which two points are emerging from [...] Read more.
In this work, the quantized Hill problem is considered in order for us to study the existence and stability of equilibrium points. In particular, we have studied three different cases which give all whole possible locations in which two points are emerging from the first case and four points from the second case, while the third case does not provide a realistic locations. Hence, we have obtained four new equilibrium points related to the quantum perturbations. Furthermore, the allowed and forbidden regions of motion of the first case are investigated numerically. We demonstrate that the obtained result in the first case is a generalization to the classical one and it can be reduced to the classical result in the absence of quantum perturbation, while the four new points will disappear. The regions of allowed motions decrease as the value of the Jacobian constant increases, and these regions will form three separate areas. Thus, the infinitesimal body can never move from one allowed region to another, and it will be trapped inside one of the possible regions of motion with the relative large values of the Jacobian constant. Full article
(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering)
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10 pages, 386 KiB  
Article
Synchronization of Epidemic Systems with Neumann Boundary Value under Delayed Impulse
by Ruofeng Rao, Zhi Lin, Xiaoquan Ai and Jiarui Wu
Mathematics 2022, 10(12), 2064; https://0-doi-org.brum.beds.ac.uk/10.3390/math10122064 - 15 Jun 2022
Cited by 56 | Viewed by 1656
Abstract
This paper reports the construction of synchronization criteria for the delayed impulsive epidemic models with reaction–diffusion under the Neumann boundary value. Different from the previous literature, the reaction–diffusion epidemic model with a delayed impulse brings mathematical difficulties to this paper. In fact, due [...] Read more.
This paper reports the construction of synchronization criteria for the delayed impulsive epidemic models with reaction–diffusion under the Neumann boundary value. Different from the previous literature, the reaction–diffusion epidemic model with a delayed impulse brings mathematical difficulties to this paper. In fact, due to the existence of second-order partial derivatives in the reaction–diffusion model with a delayed impulse, the methods of first-order ordinary differential equations from the previous literature cannot be effectively applied in this paper. However, with the help of the variational method and an appropriate boundedness assumption, a new synchronization criterion is derived, and its effectiveness is illustrated by numerical examples. Full article
(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering)
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16 pages, 585 KiB  
Article
Optimal Timing Fault Tolerant Control for Switched Stochastic Systems with Switched Drift Fault
by Chenglong Zhu, Li He, Kanjian Zhang, Wei Sun and Zengxiang He
Mathematics 2022, 10(11), 1880; https://0-doi-org.brum.beds.ac.uk/10.3390/math10111880 - 30 May 2022
Cited by 3 | Viewed by 1295
Abstract
In this article, an optimal timing fault tolerant control strategy is addressed for switched stochastic systems with unknown drift fault for each switching point. The proposed controllers in existing optimal timing control schemes are not directly aimed at the switched drift fault system, [...] Read more.
In this article, an optimal timing fault tolerant control strategy is addressed for switched stochastic systems with unknown drift fault for each switching point. The proposed controllers in existing optimal timing control schemes are not directly aimed at the switched drift fault system, which affects the optimal control performance. A cost functional with system state information and fault variable is constructed. By solving the optimal switching time criterion, the switched stochastic system can accommodate switching drift fault. The variational technique is presented for the proposed cost function in deriving the gradient formula. Then, the optimal fault tolerant switching time is calculated by combining the Armijo step-size gradient descent algorithm. Finally, the effectiveness of the proposed controller design scheme is proved by the safe trajectory planning for a four wheel drive mobile robot and numerical example. Full article
(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering)
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17 pages, 3261 KiB  
Article
Neural Adaptive Fixed-Time Attitude Stabilization and Vibration Suppression of Flexible Spacecraft
by Qijia Yao, Hadi Jahanshahi, Irene Moroz, Naif D. Alotaibi and Stelios Bekiros
Mathematics 2022, 10(10), 1667; https://0-doi-org.brum.beds.ac.uk/10.3390/math10101667 - 12 May 2022
Cited by 21 | Viewed by 1557
Abstract
This paper proposes a novel neural adaptive fixed-time control approach for the attitude stabilization and vibration suppression of flexible spacecraft. First, the neural network (NN) was introduced to identify the lumped unknown term involving uncertain inertia, external disturbance, torque saturation, and elastic vibrations. [...] Read more.
This paper proposes a novel neural adaptive fixed-time control approach for the attitude stabilization and vibration suppression of flexible spacecraft. First, the neural network (NN) was introduced to identify the lumped unknown term involving uncertain inertia, external disturbance, torque saturation, and elastic vibrations. Then, the proposed controller was synthesized by embedding the NN compensation into the fixed-time backstepping control framework. Lyapunov analysis showed that the proposed controller guaranteed the stabilization of attitude and angular velocity to the adjustable small neighborhoods of zero in fixed time. The proposed controller is not only robust against uncertain inertia and external disturbance, but also insensitive to elastic vibrations of the flexible appendages. At last, the excellent stabilization performance and good vibration suppression capability of the proposed control approach were verified through simulations and detailed comparisons. Full article
(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering)
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12 pages, 275 KiB  
Article
Stability of Impulsive Stochastic Delay Systems with Markovian Switched Delay Effects
by Wei Hu
Mathematics 2022, 10(7), 1110; https://0-doi-org.brum.beds.ac.uk/10.3390/math10071110 - 30 Mar 2022
Cited by 3 | Viewed by 1297
Abstract
In this paper, we investigate the pth moment exponential stability of impulsive stochastic delay systems with Markovian switched delay effects. The model we consider here is rather different from the models in the existing literature. In particular, the delay is a Markov [...] Read more.
In this paper, we investigate the pth moment exponential stability of impulsive stochastic delay systems with Markovian switched delay effects. The model we consider here is rather different from the models in the existing literature. In particular, the delay is a Markov chain, which is quite different from the traditional deterministic delay. By using the Markov chain theory, stochastic analysis theory, Razumikhin technology and the Lyaponov method, we derive a criterion of pth moment exponential stability for the suggested system. Finally, an example is provided to illustrate the effectiveness of the obtained result. Full article
(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering)
20 pages, 4308 KiB  
Article
Adaptive Evolutionary Computation for Nonlinear Hammerstein Control Autoregressive Systems with Key Term Separation Principle
by Faisal Altaf, Ching-Lung Chang, Naveed Ishtiaq Chaudhary, Muhammad Asif Zahoor Raja, Khalid Mehmood Cheema, Chi-Min Shu and Ahmad H. Milyani
Mathematics 2022, 10(6), 1001; https://0-doi-org.brum.beds.ac.uk/10.3390/math10061001 - 21 Mar 2022
Cited by 16 | Viewed by 1553
Abstract
The knacks of evolutionary and swarm computing paradigms have been exploited to solve complex engineering and applied science problems, including parameter estimation for nonlinear systems. The population-based computational heuristics applied for parameter identification of nonlinear systems estimate the redundant parameters due to an [...] Read more.
The knacks of evolutionary and swarm computing paradigms have been exploited to solve complex engineering and applied science problems, including parameter estimation for nonlinear systems. The population-based computational heuristics applied for parameter identification of nonlinear systems estimate the redundant parameters due to an overparameterization problem. The aim of this study was to exploit the key term separation (KTS) principle-based identification model with adaptive evolutionary computing to overcome the overparameterization issue. The parameter estimation of Hammerstein control autoregressive (HC-AR) systems was conducted through integration of the KTS idea with the global optimization efficacy of genetic algorithms (GAs). The proposed approach effectively estimated the actual parameters of the HC-AR system for noiseless as well as noisy scenarios. The simulation results verified the accuracy, convergence, and robustness of the proposed scheme. While consistent accuracy and reliability of the designed approach was validated through statistical assessments on multiple independent trials. Full article
(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering)
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16 pages, 314 KiB  
Article
Uniform Persistence and Global Attractivity in a Delayed Virus Dynamic Model with Apoptosis and Both Virus-to-Cell and Cell-to-Cell Infections
by Meng Li, Ke Guo and Wanbiao Ma
Mathematics 2022, 10(6), 975; https://0-doi-org.brum.beds.ac.uk/10.3390/math10060975 - 18 Mar 2022
Cited by 1 | Viewed by 1141
Abstract
In this paper, we study the global dynamics of a delayed virus dynamics model with apoptosis and both virus-to-cell and cell-to-cell infections. When the basic reproduction number R0>1, we obtain the uniform persistence of the model, and give some [...] Read more.
In this paper, we study the global dynamics of a delayed virus dynamics model with apoptosis and both virus-to-cell and cell-to-cell infections. When the basic reproduction number R0>1, we obtain the uniform persistence of the model, and give some explicit expressions of the ultimate upper and lower bounds of any positive solution of the model. In addition, by constructing the appropriate Lyapunov functionals, we obtain some sufficient conditions for the global attractivity of the disease-free equilibrium and the chronic infection equilibrium of the model. Our results extend existing related works. Full article
(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering)
14 pages, 794 KiB  
Article
Operator Methods of the Maximum Principle in Problems of Optimization of Quantum Systems
by Alexander Buldaev and Ivan Kazmin
Mathematics 2022, 10(3), 507; https://0-doi-org.brum.beds.ac.uk/10.3390/math10030507 - 05 Feb 2022
Cited by 5 | Viewed by 1467
Abstract
In the class of optimal control problems for quantum systems, operator optimality conditions for control are constructed in the form of fixed-point problems in the control space. The equivalence of the obtained operator optimality conditions to the well-known Pontryagin maximum principle is shown. [...] Read more.
In the class of optimal control problems for quantum systems, operator optimality conditions for control are constructed in the form of fixed-point problems in the control space. The equivalence of the obtained operator optimality conditions to the well-known Pontryagin maximum principle is shown. Based on the obtained operator forms of optimality conditions, new iterative methods for finding extreme equations satisfying the maximum principle are developed. A comparative analysis of the effectiveness of the proposed operator methods of the maximum principle with known methods is carried out on model examples of optimization of quantum systems. Full article
(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering)
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14 pages, 2311 KiB  
Article
Symbolic Regulator Sets for a Weakly Nonlinear Discrete Control System with a Small Step
by Yulia Danik and Mikhail Dmitriev
Mathematics 2022, 10(3), 487; https://0-doi-org.brum.beds.ac.uk/10.3390/math10030487 - 02 Feb 2022
Cited by 7 | Viewed by 983
Abstract
For a class of discrete weakly nonlinear state-dependent coefficient (SDC) control systems, a suboptimal synthesis is constructed over a finite interval with a large number of steps. A one-point matrix Padé approximation (PA) of the solution of the initial problem for [...] Read more.
For a class of discrete weakly nonlinear state-dependent coefficient (SDC) control systems, a suboptimal synthesis is constructed over a finite interval with a large number of steps. A one-point matrix Padé approximation (PA) of the solution of the initial problem for the discrete matrix Riccati equation is constructed based on the state-dependent Riccati equation (SDRE) approach and the asymptotics by the small-step of the boundary layer functions method. The symmetric gain coefficients matrix for Padé control synthesis is constructed based on the one-point PA. As a result, the parametric closed-loop control is obtained. The results of numerical experiments illustrate, in particular, the improved extrapolation properties of the constructed regulator, which makes the algorithm applicable in control systems for a wider range of parameter variation. Full article
(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering)
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18 pages, 7386 KiB  
Article
Research on Intellectualized Location of Coal Gangue Logistics Nodes Based on Particle Swarm Optimization and Quasi-Newton Algorithm
by Shengli Yang, Junjie Wang, Ming Li and Hao Yue
Mathematics 2022, 10(1), 162; https://0-doi-org.brum.beds.ac.uk/10.3390/math10010162 - 05 Jan 2022
Cited by 6 | Viewed by 1829
Abstract
The optimization of an integrated coal gangue system of mining, dressing, and backfilling in deep underground mining is a multi-objective and complex decision-making process, and the factors such as spatial layout, node location, and transportation equipment need to be considered comprehensively. In order [...] Read more.
The optimization of an integrated coal gangue system of mining, dressing, and backfilling in deep underground mining is a multi-objective and complex decision-making process, and the factors such as spatial layout, node location, and transportation equipment need to be considered comprehensively. In order to realize the intellectualized location of the nodes for the logistics and transportation system of underground mining and dressing coal and gangue, this paper establishes the model of the logistics and transportation system of underground mining and dressing coal gangue, and analyzes the key factors of the intellectualized location for the logistics and transportation system of coal and gangue, and the objective function of the node transportation model is deduced. The PSO–QNMs algorithm is proposed for the solution of the objective function, which improves the accuracy and stability of the location selection and effectively avoids the shortcomings of the PSO algorithm with its poor local detailed search ability and the quasi-Newton algorithm with its sensitivity to the initial value. Comparison of the particle swarm and PSO–QNMs algorithm outputs for the specific conditions of the New Julong coal mine, as an example, shows that the PSO–QNMs algorithm reduces the complexity of the calculation, increases the calculation efficiency by eight times, saves 42.8% of the cost value, and improves the efficiency of the node selection of mining–dressing–backfilling systems in a complex underground mining environment. The results confirm that the method has high convergence speed and solution accuracy, and provides a fundamental basis for optimizing the underground coal mine logistics system. Based on the research results, a node siting system for an integrated underground mining, dressing, and backfilling system in coal mines (referred to as MSBPS) was developed. Full article
(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering)
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26 pages, 398 KiB  
Article
Finite-Time Passivity Analysis of Neutral-Type Neural Networks with Mixed Time-Varying Delays
by Issaraporn Khonchaiyaphum, Nayika Samorn, Thongchai Botmart and Kanit Mukdasai
Mathematics 2021, 9(24), 3321; https://0-doi-org.brum.beds.ac.uk/10.3390/math9243321 - 20 Dec 2021
Cited by 6 | Viewed by 2128
Abstract
This research study investigates the issue of finite-time passivity analysis of neutral-type neural networks with mixed time-varying delays. The time-varying delays are distributed, discrete and neutral in that the upper bounds for the delays are available. We are investigating the creation of sufficient [...] Read more.
This research study investigates the issue of finite-time passivity analysis of neutral-type neural networks with mixed time-varying delays. The time-varying delays are distributed, discrete and neutral in that the upper bounds for the delays are available. We are investigating the creation of sufficient conditions for finite boundness, finite-time stability and finite-time passivity, which has never been performed before. First, we create a new Lyapunov–Krasovskii functional, Peng–Park’s integral inequality, descriptor model transformation and zero equation use, and then we use Wirtinger’s integral inequality technique. New finite-time stability necessary conditions are constructed in terms of linear matrix inequalities in order to guarantee finite-time stability for the system. Finally, numerical examples are presented to demonstrate the result’s effectiveness. Moreover, our proposed criteria are less conservative than prior studies in terms of larger time-delay bounds. Full article
(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering)
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16 pages, 2742 KiB  
Article
Improved Rotor Flux and Torque Control Based on the Third-Order Sliding Mode Scheme Applied to the Asynchronous Generator for the Single-Rotor Wind Turbine
by Habib Benbouhenni and Nicu Bizon
Mathematics 2021, 9(18), 2297; https://0-doi-org.brum.beds.ac.uk/10.3390/math9182297 - 17 Sep 2021
Cited by 39 | Viewed by 2313
Abstract
In this work, a third-order sliding mode controller-based direct flux and torque control (DFTC-TOSMC) for an asynchronous generator (AG) based single-rotor wind turbine (SRWT) is proposed. The traditional direct flux and torque control (DFTC) technology or direct torque control (DTC) with integral proportional [...] Read more.
In this work, a third-order sliding mode controller-based direct flux and torque control (DFTC-TOSMC) for an asynchronous generator (AG) based single-rotor wind turbine (SRWT) is proposed. The traditional direct flux and torque control (DFTC) technology or direct torque control (DTC) with integral proportional (PI) regulator (DFTC-PI) has been widely used in asynchronous generators in recent years due to its higher efficiency compared with the traditional DFTC switching strategy. At the same time, one of its main disadvantages is the significant ripples of magnetic flux and torque that are produced by the classical PI regulator. In order to solve these drawbacks, this work was designed to improve the strategy by removing these regulators. The designed strategy was based on replacing the PI regulators with a TOSMC method that will have the same inputs as these regulators. The numerical simulation was carried out in MATLAB software, and the results obtained can evaluate the effectiveness of the designed strategy relative to the traditional strategy. Full article
(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering)
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11 pages, 289 KiB  
Article
Global Stability of Delayed Ecosystem via Impulsive Differential Inequality and Minimax Principle
by Ruofeng Rao
Mathematics 2021, 9(16), 1943; https://0-doi-org.brum.beds.ac.uk/10.3390/math9161943 - 14 Aug 2021
Cited by 3 | Viewed by 1141
Abstract
This paper reports applying Minimax principle and impulsive differential inequality to derive the existence of multiple stationary solutions and the global stability of a positive stationary solution for a delayed feedback Gilpin–Ayala competition model with impulsive disturbance. The conclusion obtained in this paper [...] Read more.
This paper reports applying Minimax principle and impulsive differential inequality to derive the existence of multiple stationary solutions and the global stability of a positive stationary solution for a delayed feedback Gilpin–Ayala competition model with impulsive disturbance. The conclusion obtained in this paper reduces the conservatism of the algorithm compared with the known literature, for the impulsive disturbance is not limited to impulsive control. Full article
(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering)
16 pages, 1217 KiB  
Article
Eliminating Stick-Slip Vibrations in Drill-Strings with a Dual-Loop Control Strategy Optimised by the CRO-SL Algorithm
by Jorge Pérez-Aracil, Carlos Camacho-Gómez, Emiliano Pereira, Vahid Vaziri, Sumeet S. Aphale and Sancho Salcedo-Sanz
Mathematics 2021, 9(13), 1526; https://0-doi-org.brum.beds.ac.uk/10.3390/math9131526 - 29 Jun 2021
Cited by 9 | Viewed by 2235
Abstract
Friction-induced stick-slip vibrations are one of the major causes for down-hole drill-string failures. Consequently, several nonlinear models and control approaches have been proposed to solve this problem. This work proposes a dual-loop control strategy. The inner loop damps the vibration of the system, [...] Read more.
Friction-induced stick-slip vibrations are one of the major causes for down-hole drill-string failures. Consequently, several nonlinear models and control approaches have been proposed to solve this problem. This work proposes a dual-loop control strategy. The inner loop damps the vibration of the system, eliminating the limit cycle due to nonlinear friction. The outer loop achieves the desired velocity with a fast time response. The optimal tuning of the control parameters is carried out with a multi-method ensemble meta-heuristic, the Coral Reefs Optimisation algorithm with Substrate Layer (CRO-SL). It is an evolutionary-type algorithm that combines different search strategies within a single population, obtaining a robust, high-performance algorithm to tackle hard optimisation problems. An application example based on a real nonlinear dynamics model of a drill-string illustrates that the controller optimised by the CRO-SL achieves excellent performance in terms of stick-slip vibrations cancellation, fast time response, robustness to system parameter uncertainties and chattering phenomenon prevention. Full article
(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering)
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