Nonlinear Analysis: Modelling and Control

Journal Information
ISSN / EISSN : 1392-5113 / 1392-5113
Published by: Vilnius University Press (10.15388)
Total articles ≅ 877
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, Shuo Wang, Ruili Wang, Xingzhi Hu, Zhen Wang
Nonlinear Analysis: Modelling and Control, Volume 27, pp 1-19; https://doi.org/10.15388/namc.2022.27.25388

Abstract:
Synchronization of reaction–diffusion Hopfield neural networks with s-delays via sliding mode control (SMC) is investigated in this paper. To begin with, the system is studied in an abstract Hilbert space C([–r; 0];U) rather than usual Euclid space Rn. Then we prove that the state vector of the drive system synchronizes to that of the response system on the switching surface, which relies on equivalent control. Furthermore, we prove that switching surface is the sliding mode area under SMC. Moreover, SMC controller can also force with any initial state to reach the switching surface within finite time, and the approximating time estimate is given explicitly. These criteria are easy to check and have less restrictions, so they can provide solid theoretical guidance for practical design in the future. Three different novel Lyapunov–Krasovskii functionals are used in corresponding proofs. Meanwhile, some inequalities such as Young inequality, Cauchy inequality,Poincaré inequality, Hanalay inequality are applied in these proofs. Finally, an example is given to illustrate the availability of our theoretical result, and the simulation is also carried out based on Runge–Kutta–Chebyshev method through Matlab.
Ranjit Kumar Upadhyay, Sattwika Acharya
Nonlinear Analysis: Modelling and Control, Volume 27, pp 1-21; https://doi.org/10.15388/namc.2022.27.25197

Abstract:
The recent emergence of COVID-19 has drawn attention to the various methods of disease control. Since no proper treatment is available till date and the vaccination is restricted to certain age groups, also vaccine efficacy is still under progress, the emphasis has been given to the method of isolation and quarantine. This control is induced by tracing the contacts of the infectious individuals, putting them to the quarantine class and based on their symptoms, classifying them either as the susceptible or sick individuals and moving the sick individuals to the isolated class. To track the current pandemic situation of COVID-19 in India, we consider an extended Susceptible-Exposed-Quarantine-Infected-Isolated-Recovered (SEQ1IQ2R) compartmental model along with calculating its control reproductive number Rc. The disease can be kept in control if the value of Rc remains below one. This “threshold” value of Rc is used to optimize the period of quarantine, and isolation and have been calculated in order to eradicate the disease. The sensitivity analysis of Rc with respect to the quarantine and isolation period has also been done. Partial rank correlation coefficient method is applied to identify the most significant parameters involved in Rc. Based on the observed data, 7-days moving average curves are plotted for prelockdown, lockdown and unlock 1 phases. Following the trend of the curves for the infection, a generalized exponential function is used to estimate the data, and corresponding 95% confidence intervals are simulated to estimate the parameters. The effect of control measures such as quarantine and isolation are discussed. Following various mathematical and statistical tools, we systematically explore the impact of lockdown strategy in order to control the recent outbreak of COVID-19 transmission in India.
Yun-Hua Weng, Tao Chen, Nan-Jing Huang, Donal O'Regan
Nonlinear Analysis: Modelling and Control, Volume 27, pp 1-22; https://doi.org/10.15388/namc.2022.27.24649

Abstract:
We consider a new fractional impulsive differential hemivariational inequality, which captures the required characteristics of both the hemivariational inequality and the fractional impulsive differential equation within the same framework. By utilizing a surjectivity theorem and a fixed point theorem we establish an existence and uniqueness theorem for such a problem. Moreover, we investigate the perturbation problem of the fractional impulsive differential hemivariational inequality to prove a convergence result, which describes the stability of the solution in relation to perturbation data. Finally, our main results are applied to obtain some new results for a frictional contact problem with the surface traction driven by the fractional impulsive differential equation.
Rujda Parveen, Tapas Ray Mahapatra
Nonlinear Analysis: Modelling and Control, Volume 27, pp 1-23; https://doi.org/10.15388/namc.2022.27.25338

Abstract:
This paper examines the two-dimensional laminar steady magnetohydrodynamic doublediffusive mixed convection in a curved enclosure filled with different types of nanofluids. The enclosure is differentially heated and concentrated, and the heat and mass source are embedded in a part of the left wall having temperature Th (>Tc) and concentration ch (>cc). The right vertical wall is allowed to move with constant velocity in a vertically upward direction to cause a shear-driven flow. The governing equations along with the boundary conditions are transformed into a nondimensional form and are written in stream function-velocity formulation, which is then solved numerically using the Bi-CGStab method. Based on the numerical results, the effects of the dominant parameters such as Richardson number (1 ≤ Ri ≤ 50), Hartmann number (0 ≤ Ha ≤ 60), solid volume fraction of nanoparticles (0.0 ≤ ϕ ≤ 0.02), location and length of the heat and mass source are examined. Results indicate that the augmentation of Richardson number, heat and mass source length and location cause heat and mass transfer to increase, while it decreases when Hartmann number and volume fraction of the nanoparticles increase. The total entropy generation rises by 1.32 times with the growing Richardson number, decreases by 1.21 times and 1.02 times with the rise in Hartmann number and nanoparticles volume fraction, respectively.
Hemant Kumar Nashine, Anupam Das
Nonlinear Analysis: Modelling and Control, Volume 27, pp 1-14; https://doi.org/10.15388/namc.2022.27.25203

Abstract:
In this paper, we discuss solvability of infinite system of fractional integral equations (FIE) of mixed type. To achieve this goal, we first use shifting distance function to establish a new generalization of Darbo’s fixed point theorem, and then apply it to the FIEs to establish the existence of solution on tempered sequence space. Finally, we verify our results by considering a suitable example.
Ganesan Arthi, Nallasamy Brindha, Dumitru Baleanu
Nonlinear Analysis: Modelling and Control, Volume 27, pp 1-13; https://doi.org/10.15388/namc.2022.27.25194

Abstract:
This paper is explored with the stability procedure for linear nonautonomous multiterm fractional damped systems involving time delay. Finite-time stability (FTS) criteria have been developed based on the extended form of Gronwall inequality. Also, the result is deduced to a linear autonomous case. Two examples of applications of stability analysis in numerical formulation are described showing the expertise of theoretical prediction.
Yanfang Lei, Junmin Li, Ailiang Zhao
Nonlinear Analysis: Modelling and Control, Volume 27, pp 1-20; https://doi.org/10.15388/namc.2022.27.25195

Abstract:
In this study, we focus on designing a robust piecewise adaptive controller to globally asymptotically stabilize a semilinear parabolic distributed parameter systems (DPSs) with external disturbance, whose nonlinearities are bounded by unknown functions. Firstly, a robust piecewise adaptive control is designed against the unknown nonlinearity and the external disturbance. Then, by constructing an appropriate Lyapunov–Krasovskii functional candidate (LKFC) and using the Wiritinger’s inequality and a variant of the Agmon’s inequality, it is shown that the proposed robust piecewise adaptive controller not only ensures the globally asymptotic stability of the closed-loop system, but also guarantees a given performance. Finally, two simulation examples are given to verify the validity of the design method.
, Jinrong Wang
Nonlinear Analysis: Modelling and Control, Volume 27, pp 1-19; https://doi.org/10.15388/namc.2022.27.25333

Abstract:
In this manuscript, relative controllability of leader–follower multiagent systems with pairwise different delays in states and fixed interaction topology is considered. The interaction topology of the group of agents is modeled by a directed graph. The agents with unidirectional information flows are selected as leaders, and the others are followers. Dynamics of each follower obeys a generic time-invariant delay differential equation, and the delays of agents, which satisfy a specified condition, are different one another because of the degeneration or burn-in of sensors. With a neighbor-based protocol steering, the dynamics of followers become a compact form with multiple delays. Solution of the multidelayed system without pairwise matrices permutation is obtained by improving the method in the references, and relative controllability is established via Gramian criterion. Further rank criterion of a single delay system is dealt with. Simulation illustrates the theoretical deduction.
, , Stojan Radenović
Nonlinear Analysis: Modelling and Control, Volume 27, pp 163-178; https://doi.org/10.15388/namc.2022.27.25193

Abstract:
In this manuscript, we generalize, improve, and enrich recent results established by Budhia et al. [L. Budhia, H. Aydi, A.H. Ansari, D. Gopal, Some new fixed point results in rectangular metric spaces with application to fractional-order functional differential equations, Nonlinear Anal. Model. Control, 25(4):580–597, 2020]. This paper aims to provide much simpler and shorter proofs of some results in rectangular metric spaces. According to one of our recent lemmas, we show that the given contractive condition yields Cauchyness of the corresponding Picard sequence. The obtained results improve well-known comparable results in the literature. Using our new approach, we prove that a Picard sequence is Cauchy in the framework of rectangular metric spaces. Our obtained results complement and enrich several methods in the existing state-ofart. Endorsing the materiality of the presented results, we also propound an application to dynamic programming associated with the multistage process.
Jin You, Shurong Sun
Nonlinear Analysis: Modelling and Control, Volume 27, pp 102-120; https://doi.org/10.15388/namc.2022.27.25204

Abstract:
This paper investigates practical stability for a class of fractional-order impulsive control coupled systems with noninstantaneous impulses on networks. Using graph theory and Lyapunov method, new criteria for practical stability, uniform practical stability as well as practical asymptotic stability are established. In this paper, we extend graph theory to fractional-order system via piecewise Lyapunov-like functions in each vertex system to construct global Lyapunov-like functions. Our results are generalization of some known results of practical stability in the literature and provide a new method of impulsive control law for impulsive control systems with noninstantaneous impulses. Examples are given to illustrate the effectiveness of our results
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