Prescribed Performance Neural Control of Strict-Feedback Systems via Disturbance Observers by Wei Xiang, Guangkui Xu, Fang Zhu, Chunzhi Yang

“…And radial basis function neural networks (RBFNNs) are used to approximate nonlinear functions, while second-order filters are employed to eliminate the “explosion-complexity” problem inherent in the existing method. …”
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A second-order resolvent formulation for the analysis of turbulent flow structures by Chevalier, Quentin, Lutz, Lesshafft, Cavalieri, André V. G.

“…Closure assumptions for unresolved nonlinearities are thus pushed back to a higher order. …”
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Modeling and analysis of a simple manufacturing-oriented multi-agent system by P. Levi, M. Schanz, V. Avrutin

“…In order to develop appropriate tools for this task, the dynamic behaviour of the system is investigated using concepts and methods of synergetics and the theory of nonlinear dynamical systems.…”
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Extraction of individual Pockels coefficients of thin films via interferometric reflection measurements by Kobe De Geest, Enes Lievens, Ewout Picavet, Klaartje De Buysser, Dries Van Thourhout, Jeroen Beeckman

“…Ferroelectric thin films integrated on passive photonic platforms offer ways to achieve functionalities that are otherwise impossible or inefficient, such as electro-optic (EO) modulation, acousto-optic modulation or optical nonlinear conversion. Characterization methods of the EO properties of thin films are often only able to extract an effective EO response, while in many integrated photonic circuits it is one of the Pockels coefficients that determines the strength of the modulation. …”
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Modeling and Analysis of Energy/Exergy for Absorber Pipes of Linear Parabolic Concentrating Systems by Reza Alayi, Mahdi Mohkam, Hossein Monfared, Alibek Issakhov, Nima Khalilpoor

“…The results show that increasing the length of the absorber pipe causes a nonlinear decrease in the efficiency of the absorber pipe. …”
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Novel Analytical and Numerical Approximations to the Forced Damped Parametric Driven Pendulum Oscillator: Chebyshev Collocation Method by M.R. Alharthi, Alvaro H. Salas, Wedad Albalawi, S.A. El-Tantawy

“…In this work, some novel approximate analytical and numerical solutions to the forced damped driven nonlinear (FDDN) pendulum equation and some relation equations of motion on the pivot vertically for arbitrary angles are obtained. …”
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Robust Control of Wind Turbines by Using Singular Perturbation Method and Linear Parameter Varying Model by Yan Zhang, Zhengfan Liu, Zhong Yang, Haifei Si

“…A linear parameter varying (LPV) model is developed to approximate the nonlinear singularly perturbed model. Then stability and robust properties of the open-loop linear singularly perturbed system are analyzed using linear matrix inequalities (LMIs). …”
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A Novel Algorithm for Studying the Effects of Squeezing Flow of a Casson Fluid between Parallel Plates on Magnetic Field by Abdul-Sattar J. A. Al-Saif, Abeer Majeed Jasim

“…The suitable one of similarity transformation conversion laws is proposed to obtain the governing MHD flow nonlinear ordinary differential equation. The resulting equation has been solved by a novel algorithm. …”
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Additive contribution of multiferroic film and semiconductor substrate from nanotube array to resistive switching, topographic features by Shikhgasan Ramazanov, Gaji Gajiev, Daud Selimov, Sadrudin Gadzhimuradov, Sagim Suleymanov, Ştefan Ţălu, Robert S. Matos, Henrique D. da Fonseca Filho

“…Studies of the resistive switching effect showed nonlinear current-voltage characteristics. The negative differential resistance probably arises from the oxide dielectric layer of BFO, thin regions of which participate in the tunneling process. …”
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Residual Symmetry, Bäcklund Transformation, and Soliton Solutions of the Higher-Order Broer-Kaup System by Yarong Xia, Ruoxia Yao, Xiangpeng Xin

“…In order to find more general solution of HBK system, we further generalize the residual symmetry method to the consistent tanh expansion (CTE) method and prove that the HBK system is CTE solvable, then the resonant soliton solutions and interaction solutions among different nonlinear excitations are obtained by the CET method.…”
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Adaptive Neural Sliding Mode Control of Active Power Filter by Juntao Fei, Zhe Wang

“…The advantages of the adaptive control, neural network control, and sliding mode control are combined together to achieve the control task; that is, the harmonic current of nonlinear load can be eliminated and the quality of power system can be well improved. …”
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A Dynamic Motion Tracking Control Approach for a Quadrotor Aerial Mechanical System by Hugo Yañez-Badillo, Francisco Beltran-Carbajal, Ruben Tapia-Olvera, Antonio Valderrabano-Gonzalez, Antonio Favela-Contreras, Julio C. Rosas-Caro

“…Thus, differentiation of signals and real-time estimation of disturbances affecting the multi-input multioutput, underactuated nonlinear dynamic system are unnecessary. The presented active control approach can be directly extended for a class of vibrating mechanical systems. …”
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Further Application of H-Differentiability to Generalized Complementarity Problems Based on Generalized Fisher-Burmeister Functions by Wei-Zhe Gu, Mohamed A. Tawhid

“…When specializing GCP(f,g) to the nonlinear complementarity problems, our results not only give new results but also extend/unify various similar results proved for C1, semismooth, and locally Lipschitzian.…”
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Multiobjective Location Routing Problem considering Uncertain Data after Disasters by Keliang Chang, Hong Zhou, Guijing Chen, Huiqin Chen

“…This paper proposes a nonlinear location routing problem with half-time windows and with three objectives. …”
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Designing the Adaptive Tracking Controller for Uncertain Fully Actuated Dynamical Systems with Additive Disturbances Based on Sliding Mode by Chi Nguyen Van

“…This control method is applied to the angles tracking control of the twin rotor multi-input multi-output system (TRMS) which have nonlinear characteristics, the input torque disturbances and the coupling between the horizontal and vertical movements. …”
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Positive Solutions for Second-Order Singular Semipositone Differential Equations Involving Stieltjes Integral Conditions by Jiqiang Jiang, Lishan Liu, Yonghong Wu

“…By means of the fixed point theory in cones, we investigate the existence of positive solutions for the following second-order singular differential equations with a negatively perturbed term: −u′′(t)=λ[f(t,u(t))−q(t)], 0<t<1, αu(0)−βu′(0)=∫01u(s)dξ(s), γu(1)+δu′(1)=∫01u(s)dη(s), where λ>0 is a parameter; f:(0,1)×(0,∞)→[0,∞) is continuous; f(t,x) may be singular at t=0, t=1, and x=0, and the perturbed term q:(0,1)→[0,+∞) is Lebesgue integrable and may have finitely many singularities in (0,1), which implies that the nonlinear term may change sign.…”
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An Intelligence Optimized Rolling Grey Forecasting Model Fitting to Small Economic Dataset by Li Liu, Qianru Wang, Ming Liu, Lian Li

“…Grey system theory has been widely used to forecast the economic data that are often highly nonlinear, irregular, and nonstationary. The size of these economic datasets is often very small. …”
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Moving mesh simulations of pitting corrosion by Abu Naser Sarker, Ronald D. Haynes, Michael D. Robertson

“…The adaptive mesh is generated automatically by solving a mesh PDE coupled to the nonlinear potential problem. The moving mesh approach is shown to enable initial mesh generation, provide automatic mesh adjustment (or recovery) and is able to smoothly tackle changing pit geometry. …”
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The Application of the Homotopy Perturbation Method and the Homotopy Analysis Method to the Generalized Zakharov Equations by Hassan A. Zedan, Eman El Adrous

“…HAM is a strong and easy-to-use analytic tool for nonlinear problems. Computation of the absolute errors between the exact solutions of the GZE equations and the approximate solutions, comparison of the HPM results with those of Adomian’s decomposition method and the HAM results, and computation the absolute errors between the exact solutions of the GZE equations with the HPM solutions and HAM solutions are presented.…”
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The role of multiple modeling perspectives in students' learning of exponential growth by Carlos Castillo-Garsow

“…In order to investigate these issues, I preformed a teaching experiment with two high school students, which focused on building understandings of exponential growth leading up to the (nonlinear) logistic differential equation model. In this paper, I highlight some of the ways of thinking used by participants in this teaching experiment. …”
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