Science topics: Mathematical SciencesNonlinear Systems

Science topic

# Nonlinear Systems - Science topic

Theoretic and applied results in nonlinear system theory, non-linear models and nonlinear models.

Publications related to Nonlinear Systems (10,000)

Sorted by most recent

Much attention has been given to the study of nonlinear normal modes (NNMs), a nonlinear extension to the eminently useful framework for the analysis of linear dynamics provided by linear modal analysis (LMA). In the literature, several approaches have gained traction, with each able to preserve a subset of the useful properties of LMA. A recently-...

In this article, an adaptive neural fault‐tolerant decentralized tracking control problem is investigated for switched stochastic large‐scale uncertain nonlinear systems, in which time‐varying delay and unknown control coefficient are under consideration. By incorporating the quadratic Lyapunov function and Lyapunov Krasovskii function into the bac...

This article investigates the problem of finite-time stabilization for a class of interconnected switched nonlinear systems (ISNS) via sampled-data output feedback control. First, for each subsystem, the state observers and sampled-data output feedback controllers are constructed. Second, with a selected design parameter and a suitable sampling per...

The main goal of this paper is to study a class of differential nonlinear system involving parabolic variational and history-dependent hemivariational inequalities in Banach spaces by using the penalty method. We first construct a penalized problem for such a nonlinear system and then derive the existence and uniqueness of its solution to obtain an...

The present study introduces a novel design of Morlet wavelet neural network (MWNN) models to solve a class of a nonlinear nervous stomach system represented with governing ODEs systems via three categories, tension, food and medicine, i.e., TFM model. The comprehensive detail of each category is designated together with the sleep factor, food rate...

The aim of this paper is to investigate the possible treatment of a class of singular singularly perturbed fourth-order boundary value problems. We discretize the unknown solution using a truncated series based on Bernoulli polynomials with their differentiation matrix. Then, the resulting linear or nonlinear system in terms of the unknown coeffici...

This paper deals with the fault detection (FD) problem for uncertain time-delayed systems with nonlinearities satisfying incremental quadratic constraints. To begin with, an observer is designed to construct the residual system for FD purpose. Because the output disturbance is involved in the residual dynamics, this residual cannot be used for FD d...

The present study is made to develop the fractional model of non-Newtonian Casson and Williamson boundary layer flow in the fluid flow taking into account the heat flux and the slip velocity. The temperature and the velocity fields, of the steady boundary layer flow, are generated by a stretched sheet with a non-uniform thickness. The governing non...

The current article is concerned with a comprehensive investigation of achieving the simplest solution of non-conservative
coupled nonlinear forced oscillators. The article mainly depends on a non-perturbative method. It depends on yielding an
equivalent linear system. The advantage of this linear system is that its coefficients are easily computed...

The derivation of shaker profiles, based on vehicle measurements, needs manually adapted iterations due to different dynamical, nonlinear system behavior of components in vehicles or test benches. Targeting a similar dynamical behavior of the interesting component either mounted in a vehicle or on an assembly / component test, a representative exci...

Low-latency data processing is essential for wide-area monitoring of smart grids. Distributed and local data processing is a promising approach for enabling low-latency requirements and avoiding the large overhead of transferring large volumes of time-sensitive data to central processing units. State estimation in power systems is one of the key fu...

This paper is concerned with the large-time behavior of smooth solutions to the Cauchy problem for the three-dimensional bipolar quantum Navier–Stokes–Poisson equations. First, we show the existence of the stationary wave under the small assumption of the doping profile. Next, based on elaborate energy estimates, we prove that the smooth solutions...

In this paper, an adaptive tracking control scheme based on event-triggered strategy is developed for nonlinear non-strict-feedback systems with input saturation and incompletely known control gain function. The neural networks are utilized to deal with unknown nonlinearity and non-lower triangular structure of the systems. Then, the hyperbolic tan...

Conventional sliding mode controls (SMC) have always shown high robustness when applied to non‐linear systems. However, their applications are still limited due to their high‐frequency switching which could be a harmful phenomenon for different systems. As a solution, this paper proposes a high order SMC based drift algorithm. First, the algorithm...

This research focuses on controlling a class of MIMO state‐delayed nonlinear systems with switching conditions that depend on the delayed states. The key concept is to consider the dynamic changes brought by switching between sub‐systems as an uncertainty bounded by a certain polynomial of the delayed states norm. The challenge of managing a delaye...

The nonlinear limit-cycle oscillations induced by aileron rotational freeplay are investigated by numerical simulation and flutter wind tunnel tests. An integrated nonlinear aeroelastic analysis method and procedure based on the nonlinear system identification technology is proposed. Based on the characteristics of the structure, a low-speed nonlin...

The prediction of accurate singlet triplet (ST) gaps of polyaromatic hydrocarbons has been challenging due to the differential multireference character of the two states. The ST gaps of linear polyacenes have shown an exponential decay with system size due to the decreasing stability and increasing multireference nature of the singlet state. These...

Treating specific tissues without affecting other regions is a difficult task. It is desirable to target the particular tissue where the chemical has its biological effect. To study this phenomenon computationally, in this work we numerically study a mathematical model which is written as a nonlinear system composed by three parabolic partial diffe...

This paper studies the controller design of sampled data robust adaptive control (RAC) with control update strategy for a class of networked uncertain nonlinear systems under random denial-of-service (DoS) attacks with frequency and duration constraints. Two switching-type robust adaptive controllers with corresponding update strategies based on ce...

The prediction of accurate singlet triplet (ST) gaps of polyaromatic hydrocarbons has been challenging due to the differential multireference character of the two states. The ST gaps of linear polyacenes have shown an exponential decay with system size due to the decreasing stability and increasing multireference nature of the singlet state. These...

Tea is the national drink of the Chinese nation. It combines the thoughts of various Chinese schools and has experienced the changes and baptism of successive dynasties and has been spread to this day. It is difficult to achieve the inheritance of tea culture by relying on ordinary display methods. In order to better display the digital effect of t...

Providing formal safety and performance guarantees for autonomous systems is becoming increasingly important as they are integrated in our society. Hamilton-Jacobi (HJ) reachability analysis is a popular formal verification tool for providing these guarantees, since it can handle general nonlinear system dynamics, bounded adversarial system disturb...

The sliding-mode control (SMC) has been used successfully to stabilize nonlinear systems, yet a side effect of SMC is chattering, an undesired phenomenon. Researchers have then introduced the so-called integral-type approach to diminish chattering. Additional studies have shown that SMC with the so-called barrier function can drive the system state...

Artificial neural networks (ANNs), one of the most important artificial intelligence techniques, are used extensively in modeling many types of problems. A successful training process is required to create effective models with ANN. An effective training algorithm is essential for a successful training process. In this study, a new neural network t...

A system with multiple controllers and a multiple-model architecture is one of the most effective solutions for the real-time control of nonlinear systems. The employment of these structures necessitates the resolution of certain difficulties, such as selecting the optimal algorithm or switching control algorithms. Based on the concepts of auto-tra...

The Davydov–Kyslukha nonlinear exciton–phonon model on a regular one-dimensional lattice is asserted to be the driving force for the development of integrable multi-component nonlinear dynamical systems encompassing excitonic, vibrational and orientational degrees of freedom. The two most representative quasi-one-dimensional integrable multi-compon...

In this paper, considering the simultaneous influence of multi-source disturbances, system modeling uncertainties and input–output constraints, an adaptive robust attitude tracking control scheme is proposed for near space vehicles (NSVs) which is expressed as a stochastic nonlinear system. A multi-dimensional Taylor polynomial network (MTPN) is ut...

In this paper, we study the existence of a Nash‐type equilibrium for a non‐potential nonlinear system by combining variational methods with the monotonicity approach. The advance over existing research is that we can consider systems of Dirichlet problems in which the operator is not necessarily linear.

We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid. We prove local existence of strong solutions and global existence and uniqueness for small data. The main result is the characterization of long-time behaviour of the elastic displacement. We show convergence either to a re...

Qualitative methods have been the basis for the study of nonlinear systems since the beginning of the 20th century, highlighting their key concepts allows a better understanding of the evolution of these methods and their role in mathematics. To fulfill this task, specific features inherent in nonlinear systems were identified and the corresponding...

In order to compare different solvers for systems of nonlinear equations, some novel goodness and qualification criteria are defined in this paper. These use all parameters of a nonlinear solver such as convergence order, number of function evaluations, number of iterations, CPU time, etc. To achieve the criteria, different algorithms to solve nonl...

The aim of this study is controlling of spurious oscillations developing around discontinuous solutions of both linear and non-linear wave equations or hyperbolic partial differential equations (PDEs). The equations include both first-order and second-order (wave) hyperbolic systems. In these systems even smooth initial conditions, or smoothly vary...

This work is aimed at presenting a new numerical scheme for COVID-19 epidemic model based on Atangana-Baleanu fractional order derivative in Caputo sense (ABC) to investigate the vaccine efficiency. Our construction of the model is based on the classical SEIR, four compartmental models with an additional compartment V of vaccinated people extending...

This article focuses on the issue of adaptive memory-event-triggered control for a class of interval type-2 Takagi–Sugeno fuzzy system (IT-2 TSFS) subjected to network-induced delays. Firstly, the IT-2 TSFS is established to effectively describe the nonlinearities and parameter uncertainties. Secondly, in order to decrease the burden of network tra...

The present paper focuses on the effects of Arrhenius activation energy on the hydromagnetic rotating flow of Casson nanofluid. Entropy production, viscous dissipation Brownian dispersion, porous medium, velocity slip, magnetic field, convective heat, and mass conditions are taken into consideration. Transformation schemes are used to extract a non...

Complex neural network structures may not be appropriate for adaptive control applications, as large number of variable adaptive parameters have to be updated in each time step, thus increasing the computational burden, which makes the real-time implementation of the controller difficult. In this study, the ability of the neural networks to approxi...

In this paper, we studied the Drinfel'd-Sokolov-Wilson equation (DSWE) and Boiti Leon Pempinelli equation (BLPE) in the conformable sense. The sine-cosine method is utilized to achieve various traveling wave solutions to the suggested nonlinear systems. It is an easy approach to use and does not require sophisticated mathematical software or a know...

In this paper, a new model based nonlinear control technique, called PID (Proportional-Integral-Derivative) type sliding surface based sliding mode control is designed using improved reaching law. To improve the performance of the second order nonlinear differential equations with unknown parameters modified particle swarm intelligent optimization...

Model Predictive Control (MPC) is a state-of-the-art (SOTA) control technique which requires solving hard constrained optimization problems iteratively. For uncertain dynamics, analytical model based robust MPC imposes additional constraints, increasing the hardness of the problem. The problem exacerbates in performance-critical applications, when...

A stochastic computing approach is implemented in the present work to solve the nonlinear nanofluidics system that occurs in the model of atomic physics. The process converts the partial differential nanofluidics system with suitable level of similarities transformation into nonlinear systems of differential equations. For the construction of datas...

We construct quantum algorithms to compute the solution and/or physical observables of nonlinear ordinary differential equations (ODEs) and nonlinear Hamilton-Jacobi equations (HJE) via linear representations or exact mappings between nonlinear ODEs/HJE and linear partial differential equations (the Liouville equation and the Koopman-von Neumann eq...

This article investigates different nonlinear systems of fractional partial differential equations analytically using an attractive modified method known as the Laplace residual power series technique. Based on a combination of the Laplace transformation and the residual power series technique, we achieve analytic and approximation results in rapid...

A class of nonlinear systems with unknown input power is discussed about their tracking control problem in this paper. To guarantee that the output of this system can converge asymptotically to the reference signal, a robust adaptive control method is proposed. Based on Lyapunov stability theory, it is proven that the tracking error asymptotically...

This paper concentrates on necessary conditions for properly efficient solutions in nonsmooth multiobjective optimization problems. We first present a generalization of Tucker’s alternative theorem for conic nonlinear systems, provided that a closedness condition holds. Some sufficient conditions for the validity of such a closedness condition are...

In this work, our motivation is to design a new collocation method based on Müntz–Legendre polynomial involving operational matrices to solve variable‐order stochastic fractional integro‐differential equation. We first prove the existence and uniqueness result for the solution of considered problem. The operational matrices are used to convert the...

This paper considers the stabilization problem for a class of nonlinear systems in the presence of mismatched disturbances. For this purpose, a differentiator is employed such that by using newly defined virtual controls and the modified error compensation signals, the command-filter backstepping approach combined with a mismatched finite-time dist...

The properties of the convergence region of the estimation error of a robust observer for second-order systems are determined, and a new algorithm is proposed for setting the observer parameters, considering persistent but bounded disturbances in the two observation error dynamics. The main contributions over closely related studies of the stabilit...

This study explores the flow irreversibility of the Ellis hybrid nanofluid (containing C o F e 2 O 4 − T i O 2 nanoparticles) with homogeneous and heterogeneous reactions to a horizontal porous stretching cylinder. The energy transportation aspects are investigated in terms of the influence of joule heating and viscous dissipation. The slip and con...

Unmanned aerial vehicles (UAVs), particularly quadrotor, have seen steady growth in use over the last several decades. The quadrotor is an under-actuated nonlinear system with few actuators in comparison to the degree of freedom (DOF); hence, stabilizing its attitude and positions is a significant challenge. Furthermore, the inclusion of nonlinear...

Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. Two computational challenges have so far prevented its deployment on large-scale systems: (a) the energy functions requi...

We consider the problem of synthesis of safe controllers for nonlinear systems with unknown dynamics using Control Barrier Functions (CBF). We utilize Koopman operator theory (KOT) to associate the (unknown) nonlinear system with a higher dimensional bilinear system and propose a data-driven learning framework that uses a learner and a falsifier to...

This paper investigates the event-triggered model predictive control (ETMPC) problem for nonlinear systems with the bounded disturbance. First, a novel adaptive event-triggered mechanism without Zeno behaviors, in which the triggering threshold can constantly be adjusted with the change of the system state, is proposed for computational load reduct...

In this work, we investigate the existence and nonexistence of nonnegative solutions to a class of nonlocal elliptic systems set in a bounded open subset of
R
N
, where the gradients of the unknowns act as source terms (see \((S)\) below). Our approach can be also used to treat other nonlinear systems with different structures. This work extends pr...

The article describes the solution to the problem of stabilizing a nonlinear system using machine learning methods. Neural networks are one of the promising directions in this area. The article describes a model of spiking neural network, which differs from previous generations of networks by its similarity to biological neurons. A pendulum on an e...

Very high dimensional nonlinear systems arise in many engineering problems due to semi-discretization of the governing partial differential equations, e.g. through finite element methods. The complexity of these systems present computational challenges for direct application to automatic control. While model reduction has seen ubiquitous applicatio...

Reference governors are add-on predictive safety supervision algorithms that monitor and modify, if it becomes necessary, commands passed to a nominal system to ensure that pointwise-in-time state and input constraints are satisfied. After briefly surveying the basics of the reference governor schemes, this paper discusses several more recent exten...

An innovative numerical algorithm for solving infinite-horizon optimal control problems is introduced in this paper, using the IsoCost-HyperSurface (ICHS) concept. In the state space of an optimal control system, an ICHS is defined as a set of state points having a certain amount of the cost value. In this paper, it is proved that for a certain cos...

A cohesive dual boundary element formulation is presented for crack propagation analysis and a path-following method is proposed to solve the nonlinear system of equations by the direct control of one of the known degrees of freedom. The simple linear cohesive model is introduced into the algebraic boundary element equations by local stiffness matr...

Although constructing a dam can bring significant economic and social benefits to a region, it can be catastrophic for the population living downstream when it breaks. Given the dynamic and nonlinear characteristics of dam deformation, the traditional dam prediction model has been unable to meet the actual engineering demands. Consequently, this pa...

This paper extends previous studies work on the application of Machine Learning (ML) to distortion compensation in optical communication systems with optical fibers nonlinear coefficients (γ) that exceed current industry standards e.g. \(\gamma > 1.4W^{ - 1} km^{ - 1}\). To quantify the improvement afforded by ML methods under different transmissio...

The estimation of weather forecast uncertainty with ensemble systems requires a careful selection of perturbations to establish a reliable sampling of the error growth potential in the phase space of the model. Usually, the singular vectors of the tangent linear model propagator are used to identify the fastest growing modes (classical singular vec...