Nonlinear Analysis Modelling and Control
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Published By Vilnius University

1392-5113, 1392-5113
Updated Wednesday, 19 January 2022

2022 ◽  
Vol 27 ◽  
pp. 1-13
Author(s):  
Ganesan Arthi ◽  
Nallasamy Brindha ◽  
Dumitru Baleanu

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.


2022 ◽  
Vol 27 ◽  
pp. 1-22
Author(s):  
Yun-hua Weng ◽  
Tao Chen ◽  
Nan-jing Huang ◽  
Donal O'Regan

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.


2022 ◽  
Vol 27 ◽  
pp. 1-21
Author(s):  
Ranjit Kumar Upadhyay ◽  
Sattwika Acharya

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.


2022 ◽  
Vol 27 ◽  
pp. 1-20
Author(s):  
Yanfang Lei ◽  
Junmin Li ◽  
Ailiang Zhao

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.


2022 ◽  
Vol 27 ◽  
pp. 1-14
Author(s):  
Hemant Kumar Nashine ◽  
Anupam Das

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.


2022 ◽  
Vol 27 ◽  
pp. 1-23
Author(s):  
Rujda Parveen ◽  
Tapas Ray Mahapatra

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.


2022 ◽  
Vol 27 ◽  
pp. 1-19
Author(s):  
Yuanchao Si ◽  
JinRong Wang

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.


2022 ◽  
Vol 27 (1) ◽  
pp. 102-120
Author(s):  
Jin You ◽  
Shurong Sun

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


2022 ◽  
Vol 27 (1) ◽  
pp. 179-197
Author(s):  
Adolfas Dargys ◽  
Artūras Acus

Closed form expressions to calculate the exponential of a general multivector (MV) in Clifford geometric algebras (GAs) Clp;q are presented for n = p + q = 3. The obtained exponential formulas were applied to find exact GA trigonometric and hyperbolic functions of MV argument. We have verified that the presented exact formulas are in accord with series expansion of MV hyperbolic and trigonometric functions. The exponentials may be applied to solve GA differential equations, in signal and image processing, automatic control and robotics.


2022 ◽  
Vol 27 (1) ◽  
pp. 70-90
Author(s):  
Zhongli You ◽  
Michal Fečkan ◽  
JinRong Wang ◽  
Donal O’Regan

In this paper, relative controllability of impulsive multi-delay differential systems in finite dimensional space are studied. By introducing the impulsive multi-delay Gramian matrix, a necessary and sufficient condition, and the Gramian criteria, for the relative controllability of linear systems is given. Using Krasnoselskii’s fixed point theorem, a sufficient condition for controllability of semilinear systems is obtained. Numerically examples are given to illustrate our theoretically results.


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