Nonlinear Analysis: Modelling and Control https://www.journals.vu.lt/nonlinear-analysis <p>Founded in 1997. Journal provides a multidisciplinary forum for scientists, researchers and engineers involved in research and design of nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature.&nbsp;</p> Vilnius University Press en-US Nonlinear Analysis: Modelling and Control 1392-5113 <p>Please read the Copyright Notice in&nbsp;<a href="http://www.zurnalai.vu.lt/acta-paedagogica-vilnensia/journalpolicy">Journal Policy</a>.&nbsp;</p> Finite-time control for uncertain systems and application to flight control https://www.journals.vu.lt/nonlinear-analysis/article/view/16510 <p>In this paper, the finite-time control design problem for a class of nonlinear systems with matched and mismatched uncertainty is addressed. The finite-time control scheme is designed by integrating multi power reaching (MPR) law and finite-time disturbance observer (FTDO) into integral sliding mode control, where a novel sliding surface is designed, and the FTDO is applied to estimate the uncertainty. Then the fixed-time reachability of the MPR law is analyzed, and the finite-time stability of the closed-loop system is proven in the framework of Lyapunov stability theory. Finally, numerical simulation and the application to the flight control of hypersonic vehicle (HSV) are provided to show the effectiveness of the designed controller.</p> Fang Wang Jianmei Wang Kun Wang Changchun Hua Qun Zong Copyright (c) 2020 Fang Wang | Jianmei Wang | Kun Wang | Changchun Hua | Qun Zong https://creativecommons.org/licenses/by/4.0 2020-03-02 2020-03-02 25 2 163–182 163–182 10.15388/namc.2020.25.16510 Synchronization of decentralized event-triggered uncertain switched neural networks with two additive time-varying delays https://www.journals.vu.lt/nonlinear-analysis/article/view/16512 <p>This paper addresses the problem of synchronization for decentralized event-triggered uncertain switched neural networks with two additive time-varying delays. A decentralized eventtriggered scheme is employed to determine the time instants of communication from the sensors to the central controller based on narrow possible information only. In addition, a class of switched neural networks is analyzed based on the Lyapunov–Krasovskii functional method and a combined linear matrix inequality (LMI) technique and average dwell time approach. Some sufficient conditions are derived to guarantee the exponential stability of neural networks under consideration in the presence of admissible parametric uncertainties. Numerical examples are provided to illustrate the effectiveness of the obtained results.&nbsp;</p> Rajarathinam Vadivel M. Syed Ali Faris Alzahrani Jinde Cao Young Hoon Joo Copyright (c) 2020 Rajarathinam Vadivel | M. Syed Ali | Faris Alzahrani | Jinde Cao | Young Hoon Joo https://creativecommons.org/licenses/by/4.0 2020-03-02 2020-03-02 25 2 183–205 183–205 10.15388/namc.2020.25.16512 Finite-time passivity for neutral-type neural networks with time-varying delays – via auxiliary function-based integral inequalities https://www.journals.vu.lt/nonlinear-analysis/article/view/16513 <p>In this paper, we investigated the problem of the finite-time boundedness and finitetime passivity for neural networks with time-varying delays. A triple, quadrable and five integral terms with the delay information are introduced in the new Lyapunov–Krasovskii functional (LKF). Based on the auxiliary integral inequality, Writinger integral inequality and Jensen’s inequality, several sufficient conditions are derived. Finally, numerical examples are provided to verify the effectiveness of the proposed criterion. There results are compared with the existing results.&nbsp;</p> Shanmugam Saravanan M. Syed Ali Ahmed Alsaedi Bashir Ahmad Copyright (c) 2020 Shanmugam Saravanan | M. Syed Ali | Ahmed Alsaedi | Bashir Ahmad https://creativecommons.org/licenses/by/4.0 2020-03-02 2020-03-02 25 2 206–224 206–224 10.15388/namc.2020.25.16513 Bifurcation on diffusive Holling–Tanner predator–prey model with stoichiometric density dependence https://www.journals.vu.lt/nonlinear-analysis/article/view/16514 <p>This paper studies a diffusive Holling–Tanner predator–prey system with stoichiometric density dependence. The local stability of positive equilibrium, the existence of Hopf bifurcation and stability of bifurcating periodic solutions have been obtained in the absence of diffusion. We also study the spatially homogeneous and nonhomogeneous periodic solutions through all parameters of the system, which are spatially homogeneous. In order to verify our theoretical results, some numerical simulations are carried out.&nbsp;</p> Maruthai Selvaraj Surendar Muniyagounder Sambath Krishnan Balachandran Copyright (c) 2020 Maruthai Selvaraj Surendar | Muniyagounder Sambath | Krishnan Balachandran https://creativecommons.org/licenses/by/4.0 2020-03-02 2020-03-02 25 2 225–244 225–244 10.15388/namc.2020.25.16514 Dynamic output nonfragile reliable control for nonlinear fractional-order glucose–insulin system https://www.journals.vu.lt/nonlinear-analysis/article/view/16515 <p>The main intention of this paper is to scrutinize the problem of internal model-based dynamic output feedback nonfragile reliable control problem for fractional-order glucose–insulin system. Specifically, a robust control law that represents the insulin injection rate is designed in order to regulate the level of glucose in diabetes treatment in the existence of meal disturbance or external glucose infusion due to improper diet. By the construction of suitable Lyapunov functional, a novel set of sufficient conditions is derived with the aid of linear matrix inequalities for obtaining the required dynamic output feedback control law. In particular, the designed controller ensures the robust stability and disturbance attenuation performance against meal disturbance of the glucose–insulin system. Numerical simulation results are performed to verify the advantage of the developed design technique. Specifically, the irregular blood glucose level can be brought down to normal level by injecting suitable rate of insulin to the patient. The result exposes that the level of blood glucose is sustained in the identified ranges via the proposed dynamic output feedback control law.&nbsp;</p> Rathinasamy Sakthivel Hari Hara Subramanian Divya Saminathan Mohanapriya Yong Ren Copyright (c) 2020 Rathinasamy Sakthivel | Hari Hara Subramanian Divya | Saminathan Mohanapriya | Yong Ren https://creativecommons.org/licenses/by/4.0 2020-03-02 2020-03-02 25 2 245–256 245–256 10.15388/namc.2020.25.16515 Some Krasnosel’skii-type fixed point theorems for Meir–Keeler-type mappings https://www.journals.vu.lt/nonlinear-analysis/article/view/16516 <p>In this paper, inspired by the idea of Meir–Keeler contractive mappings, we introduce Meir–Keeler expansive mappings, say MKE, in order to obtain Krasnosel’skii-type fixed point theorems in Banach spaces. The idea of the paper is to combine the notion of Meir–Keeler mapping and expansive Krasnosel’skii fixed point theorem. We replace the expansion condition by the weakened MKE condition in some variants of Krasnosel’skii fixed point theorems that appear in the literature, e.g., in [T. Xiang, R. Yuan, A class of expansive-type Krasnosel’skii fixed point theorems, <em>Nonlinear Anal., Theory Methods Appl</em>., 71(7–8):3229–3239, 2009].</p> Ehsan Pourhadi Reza Saadati Zoran Kadelburg Copyright (c) 2020 Ehsan Pourhadi | Reza Saadati | Zoran Kadelburg https://creativecommons.org/licenses/by/4.0 2020-03-02 2020-03-02 25 2 257–265 257–265 10.15388/namc.2020.25.16516 Support vector machine parameter tuning based on particle swarm optimization metaheuristic https://www.journals.vu.lt/nonlinear-analysis/article/view/16517 <p>This paper introduces a method for linear support vector machine parameter tuning based on particle swarm optimization metaheuristic, which is used to find the best cost (penalty) parameter for a linear support vector machine to increase textual data classification accuracy. Additionally, majority voting based ensembling is applied to increase the efficiency of the proposed method. The results were compared with results from our previous research and other authors’ works. They indicate that the proposed method can improve classification performance for a sentiment recognition task.<br><br></p> Konstantinas Korovkinas Paulius Danėnas Gintautas Garšva Copyright (c) 2020 Konstantinas Korovkinas | Paulius Danėnas | Gintautas Garšva https://creativecommons.org/licenses/by/4.0 2020-03-02 2020-03-02 25 2 266–281 266–281 10.15388/namc.2020.25.16517 Modeling the Dirichlet distribution using multiplicative functions https://www.journals.vu.lt/nonlinear-analysis/article/view/16518 <p>For <em>q</em>,<em>m</em>,<em>n</em>,<em>d</em> ∈ N and some multiplicative function <em>f</em> &gt; 0, we denote by <em>T</em><sub>3</sub>(<em>n</em>) the sum of <em>f</em>(<em>d</em>) over the ordered triples (<em>q</em>,<em>m</em>,<em>d</em>) with <em>qmd</em> = <em>n</em>. We prove that Cesaro mean of distribution functions defined by means of <em>T</em><sub>3</sub> uniformly converges to the one-parameter Dirichlet distribution function. The parameter of the limit distribution depends on the values of <em>f</em> on primes. The remainder term is estimated as well.&nbsp;</p> Gintautas Bareikis Algirdas Mačiulis Copyright (c) 2020 Gintautas Bareikis | Algirdas Mačiulis https://creativecommons.org/licenses/by/4.0 2020-03-02 2020-03-02 25 2 282–300 282–300 10.15388/namc.2020.25.16518 Square root of a multivector in 3D Clifford algebras https://www.journals.vu.lt/nonlinear-analysis/article/view/16519 <p>The problem of square root of multivector (MV) in real 3D (<em>n</em> = 3) Clifford algebras <em>Cl</em><sub>3;0</sub>, <em>Cl</em><sub>2;1</sub>, <em>Cl</em><sub>1;2</sub> and <em>Cl</em><sub>0;3</sub> is considered. It is shown that the square root of general 3D MV can be extracted in radicals. Also, the article presents basis-free roots of MV grades such as scalars, vectors, bivectors, pseudoscalars and their combinations, which may be useful in applied Clifford algebras. It is shown that in mentioned Clifford algebras, there appear isolated square roots and continuum of roots on hypersurfaces (infinitely many roots). Possible numerical methods to extract square root from the MV are discussed too. As an illustration, the Riccati equation formulated in terms of Clifford algebra is solved.&nbsp;</p> Adolfas Dargys Artūras Acus Copyright (c) 2020 Adolfas Dargys | Artūras Acus https://creativecommons.org/licenses/by/4.0 2020-03-02 2020-03-02 25 2 301–320 301–320 10.15388/namc.2020.25.16519 Lagrange problem for fractional ordinary elliptic system via Dubovitskii–Milyutin method https://www.journals.vu.lt/nonlinear-analysis/article/view/16520 <p>In the paper, we investigate a weak maximum principle for Lagrange problem described by a fractional ordinary elliptic system with Dirichlet boundary conditions. The Dubovitskii–Milyutin approach is used to find the necessary conditions. The fractional Laplacian is understood in the sense of Stone–von Neumann operator calculus.</p> Dariusz Idczak Stanisław Walczak Copyright (c) 2020 Dariusz Idczak | Stanisław Walczak https://creativecommons.org/licenses/by/4.0 2020-03-02 2020-03-02 25 2 321–340 321–340 10.15388/namc.2020.25.16520