Science topics: MathematicsNonlinear 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
Dear Colleagues,
A nonlinear system with symmetry can be decomposed into interconnected lower-dimensional subsystems, where the subsystem architecture is determined by the symmetry group's structure. For general nonlinear control systems, the concept of symmetry can be used to analyze stability, design controllers, and construct observers. Further...
Understanding the intricate dynamics of complex nonlinear stochastic systems is pivotal in both scientific inquiry and engineering practice. These systems are fraught with uncertainties originating from diverse sources such as material properties, external excitations, and inherent nonlinear behaviors. Due to the coupling between nonlinearity and s...
This research introduces a novel and robust numerical approach, the stochastic improved Simpson Method, specifically developed to solve Itô and Stratonovich stochastic nonlinear system of differential equations with fractional order. By extending the classical Simpson’s one-third rule with the explicit product integration rectangle rule, the propos...
We study stability issues for a dynamical system consisting of a wave equation and a quasilinear parabolic equation. The nonlinearity involves the p-Laplacian, and the coupling involves a fractional Laplacian with exponent \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{...
This paper investigates the exponential stability of nonlinear singularly perturbed hybrid systems with non-uniform sampling. First of all, a hybrid sampling model is established for a class of nonlinear singularly perturbed hybrid systems with unstable subsystems through the design of a data-driven mechanism and sampling controller. Then, the expo...
Recently, the urge for renewable energy technologies has risen drastically as it emerges as a solution to severe environmental concerns such as global climate change, biodiversity loss, widespread pollution, and depletion of non-renewable resources. However, non-renewable resources serve as the backbone of global industrialization as they provide t...
Controlling nonlinear systems, such as the inverted pendulum on a moving cart, presents a well-known challenge due to the system’s nonlinearities and highly coupled states. This paper explores the control methodology of the system by linearizing the dynamics around the pendulum’s upright position. The primary objective of this review article is to...
Based on fuzzy sliding mode control, a control strategy is developed for the buckling suppression of a cantilever structure. Due to the laminated composite structure, shear effects on the dynamic behavior of the structure are incorporated into the development of the equations of motion. Subsequently, a second-order Galerkin discretization is applie...
An approximate analytical method is proposed to estimate the reliability of chain-like multi-degree-of-freedom nonlinear structural systems under Gaussian white noise, which combines the stochastic averaging method and the two-step generalized elliptical coordinate transformation to bypass the challenge of solving high-dimensional backward Kolmogor...
This paper investigates the tracking control problem for fractional-order (FO) nonlinear systems with model uncertainties and external disturbances under full-state constraints. An adaptive fuzzy control strategy based on a command filter is proposed, where the asymmetric Barrier Lyapunov Function is adopted to ensure that the states do not violate...
Earlier studies used classical time series models to forecast the nonlinear connectedness of conventional crypto-assets with CO2 emissions. For the first time, this study aims to provide a data-driven Nonlinear System Identification technique to study the nonlinear connectedness of crypto-assets with CO2 emissions. Using daily data from January 2,...
This study addresses why universal spherical multiplication, despite its intuitive and dimension-agnostic nature, remained elusive for so long. While spherical multiplication has emerged as a novel mathematical framework that enables norm-preserving operations in all dimensions, its delayed recognition is attributed to the dominance of traditional...
The idea of neural networks has emerged in recent times and has shown great results in complex and nonlinear systems. Many aerospace engineering areas like autonomous systems, adaptive control, and flight dynamics modeling can be better handled with neural networks. Selecting an orbit that consumes the fewest resources and reduces expenditure can b...
Recently, we considered the possibility of the maser output affecting the sample, emitting it. This effect is similar to the effect on the emitting sample of an electromagnetic field from an external source, leading to Stark dynamic frequency shift (SDS). To our mind, the similar absorption should exist at the inverted (operating) transition with t...
State estimation involves finding the states of a noisy dynamical system with a noisy initial condition using noisy measurements, given a model of the system. Many methods exist for state estimation of dynamical systems. For linear dynamical systems with white Gaussian noises of known mean and variance, Kalman filtering is an optimal state estimati...
State estimation of a dynamical system refers to estimating the state of a system given an imperfect model, noisy measurements and some or no information about the initial state. While Kalman filtering is optimal for estimation of linear systems with Gaussian noises, calculation of optimal estimators for nonlinear systems is challenging. We focus o...
Genetic algorithm (GA) is typically used to solve nonlinear model predictive control's optimisation problem. However, the size of the search space in which the GA searches for the optimal control inputs is crucial for its applicability to fast-response systems. This paper proposes accelerating the genetic optimisation of NMPC by learning optimal se...
The multi-timestep command governor (MCG) is an add-on algorithm that enforces constraints by modifying, at each timestep, the reference command to a pre-stabilized control system. The MCG can be interpreted as a Model-Predictive Control scheme operating on the reference command. The implementation of MCG on nonlinear systems carries a heavy comput...
The magnetic levitation system (Maglev) is a nonlinear system by which an object is suspended with no support other than magnetic fields. The main control perspective of the Maglev system is to levitate a steel ball in air by the electromagnetic force. However, the Maglev system has highly nonlinear dynamics which is inconvenient in the sense of se...
The use of linear regression is ubiquitous across the social and behavioral sciences, and yet researchers rarely hold that the variables in their target systems are in fact linearly related. This raises the question of how to interpret linear regression coefficients when there is ‘functional misspecification’ and the target system exhibits nonlinea...
The present work investigates stochastic P-bifurcation phenomena in a Duffing–van der Pol vibro-impact oscillator containing a Bingham model under Gaussian white noise excitation. By employing non-smooth transformations and stochastic averaging techniques, an approximate analytical method is proposed to analyze the stochastic response and bifurcati...
Chaos is ubiquitous in nonlinear dynamical systems. It is a hidden state of deterministic disorder in certain regions of parameters and initial conditions of a nonlinear system. The path taken by the system to reach chaos is known as its route to chaos. The state of the system can drastically change from a stable fixed point or a periodic solution...
For the adaptive tracking control of a class of nonlinear systems with asymmetric input saturation and external disturbances, a novel dynamic event‐triggered neural network control scheme on the foundation of full‐state constraints is proposed. Firstly, by adding a compensation term into the traditional dynamic surface control framework, the filter...
This paper investigates the complex dynamics of the combined vibrations of the top-tensioned risers in in-line (IL) and cross-flow (CF) directions under the effects of vortices and time-varying tension. The study focuses on the 12 ODE equations for the first three order approximations, which are obtained by using the Galerkin projection method and...
This paper presents an initial exploration of stress-assisted diffusion problems in three dimensions within the framework of the virtual element method (VEM). Hilbert spaces enriched with parameter-weighted norms, the extended Babuška-Brezzi-Braess theory for perturbed saddle-point problems, and Banach fixed-point theory play a crucial role in perf...
Ultrafast fibre lasers, characterized by ultrashort pulse duration and broad spectral bandwidth, have drawn significant attention due to their vast potential across a wide range of applications, from fundamental scientific to industrial processing and beyond. As dissipative nonlinear systems, ultrafast fibre lasers not only generate single solitons...
This article deals with systems of ordinary differential equations (ODEs). New differential integrals are found for general ODEs systems. With the help of them, the Cauchy problem for an ODEs system is reduced to a Cauchy problem for a single linear PDE of the first order, and as well transformed to a Cauchy problem for an overdetermined universal...
Conventional methods for estimating the residual capacity of lead-acid batteries often overlook the variations in available capacity across different environments and usage scenarios throughout the life cycle of batteries, as well as the natural aging and degradation processes. The oversight results in inaccurate capacity estimations, subsequently...
We obtain a two-dimensional (2D) nonlinear system of equations for the electrostatic potential envelope and the low-frequency magnetic field perturbation to describe the interaction of the upper hybrid wave propagating perpendicular to an external magnetic field with the dust-ion-magnetoacoustic (DIMA) wave in a magnetized dusty plasma. The equatio...
This paper presents the synthesis of a hybrid control scheme of proportional integral derivative (PID) and sliding mode (SM) controllers for stabilizing the class of underactuated nonlinear systems described in the cascaded form. The PID controller performs well when the controller parameters are optimally tuned using standard methods, but its perf...
System stability control in resource allocation is a critical issue in group robot systems. Against this backdrop, this study investigates the nonlinear dynamics and chaotic phenomena that arise during pricing games among finitely rational group robots and proposes control strategies to mitigate chaotic behaviors. A system model and a business mode...
Linear Parameter Varying (LPV) Systems are a well-established class of nonlinear systems with a rich theory for stability analysis, control, and analytical response finding, among other aspects. Although there are works on data-driven identification of such systems, the literature is quite scarce in terms of works that tackle the identification of...
The parameter convergence relies on a stringent persistent excitation (PE) condition in adaptive control. Several works have proposed a memory term in the last decade to translate the PE condition to a feasible finite excitation (FE) condition. This work proposes a combined model reference adaptive control for a class of uncertain nonlinear systems...
In this paper, we explore the dynamical properties of a class of nonlinear systems governed by delay differential equations with multitime periodic switching. The systems incorporate piecewise-smooth birth and death functions to capture complex population dynamics under seasonal variations. Assuming monotonicity for both birth and death functions,...
We investigate traveling wave solutions for a nonlinear system of two coupled reaction-diffusion equations characterized by double degenerate diffusivity: nt=−f(n,b),bt=[g(n)h(b)bx]x+f(n,b). These systems mainly appear in modeling spatio-temporal patterns during bacterial growth. Central to our study is the diffusion term g(n)h(b), which degenerate...
Bioprocesses are often characterised by nonlinear and uncertain dynamics, posing particular challenges for model predictive control (MPC) algorithms due to their computational demands when applied to nonlinear systems. Recent advances in optimal control theory have demonstrated that concepts from convex optimisation, tube MPC, and differences of co...
Hamilton-Jacobi (HJ) reachability is a rigorous mathematical framework that enables robots to simultaneously detect unsafe states and generate actions that prevent future failures. While in theory, HJ reachability can synthesize safe controllers for nonlinear systems and nonconvex constraints, in practice, it has been limited to hand-engineered col...
Civilizations evolve through complex, nonlinear processes shaped by economic, political, cultural, and technological forces. Traditional historical analysis often relies on reductionist models that focus on isolated causes, failing to capture the emergent, self-organizing nature of societal dynamics. In this paper, we introduce a Homotopy Type Theo...
This work presents a mathematical framework based on uncertain numbers to address the inherent uncertainty in nonlinear systems, a challenge that traditional mathematical frameworks often struggle to fully capture. By establishing five axioms, a formal system of uncertain numbers is developed and embedded within set theory, providing a comprehensiv...
In this paper, an adaptive control strategy is developed for discrete-time switched nonlinear systems with actuator faults and dead-zone input under arbitrary switching conditions. The actuator faults considered include loss-of-effectiveness and bias faults, which are unknown but bounded. The complex structure of these systems, combined with actuat...
This study aimed to analyze methods for modeling and controlling the output of nonlinear systems using feedback, analytical methods, mathematical modeling, and differential equation theory. Key findings include the mathematical characterization of equations and the analysis of system stability and asymptotic behavior. The study explored various met...
This paper presents the so-called shifted Jacobi method, an efficient numerical technique to solve second-order periodic boundary value problems with finitely many singularities involving nonlinear systems of two points. The method relies on the Jacobi polynomials used as natural basis functions in the conformable sense of fractional derivative. A...
This study investigates the stability of nonlinear systems, particularly those characterized by eigenvalues. We introduce dynamic Lyapunov functions as a mechanism for stability analysis, especially when explicit solutions are not available. The authors provide stability criteria at the equilibrium point, demonstrating exponential stability and ens...
This study addresses the critical issue of understanding the numerical relevance of cubic-quartic solitonic expressions in birefringent fibers, a topic of increasing significance in the field of nonlinear optics due to its implications for optical communication and signal propagation. The research employs the improved Adomian decomposition scheme,...
We perform an investigation using numerical simulations to examine the influence of magnetohydrodynamics and thermal radiation on the mass transport and thermal energy properties of non-Newtonian Reiner-Philippoff nanofluids. We thoroughly examine the species response concerning activation energy, thermal radiation at the surface, viscous dissipati...
In recent years, Neural Networks (NNs) have been employed to control nonlinear systems due to their potential capability in dealing with situations that might be difficult for conventional nonlinear control schemes. However, to the best of our knowledge, the current literature on NN-based control lacks theoretical guarantees for stability and track...
In this manuscript, we introduce a novel system of fractional differential equations incorporating both Caputo and conformable derivatives. We delve into the existence and uniqueness of solutions for this system, employing fixed-point techniques under appropriate conditions. To illustrate the practical applications of our theoretical findings, we i...
The time-delayed (TD) of velocity and position are employed throughout this investigation to lessen the nonlinear vibration of an exciting Van der Pol-Duffing oscillator (VdPD). The issue encompasses multiple real-world elements such as feedback lags, signal transmission delays, and delayed responses in mechanical, electrical, or biological systems...
A power amplifier (PA) modeling method based on the time delay deep neural network (TDDNN) is proposed in this paper. By integrating time-delay units with a multi-layer hidden neural network structure, the TDDNN enhances the modeling capability for dynamic nonlinear systems. Time-delay information and a multi-layer network architecture are incorpor...
This paper is devoted to the static bifurcation of a nonlinear elastic chain with softening and both direct and indirect interactions. This system is also known as a generalized softening FPU system (Fermi–Pasta–lam nonlinear lattice) with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amss...
Understanding the interplay between spatial and kinematic properties in chaotic systems is crucial for advancing nonlinear dynamics, yet remains a challenging problem. The double pendulum, as a classic example of deterministic chaos, provides a rich platform for exploring these dynamics, making its study highly relevant to researchers in nonlinear...
Flexure-based Stirling cryocooler compressors are a critical technology in providing cryogenic temperatures in various advanced engineering fields, such as aerospace, defense, and medical imaging. The most challenging problem in the design of this type of compressor is achieving a precise alignment that preserves small gaps between the components m...
In this work, we address the challenge of approximating unknown system dynamics and costs by representing them as a bilinear system using Koopman-based Inverse Optimal Control (IOC). Using optimal trajectories, we construct a bilinear control system in transformed state variables through a modified Extended Dynamic Mode Decomposition with control (...
In this paper, we develop novel accuracy and performance guarantees for optimal state estimation of general nonlinear systems (in particular, moving horizon estimation, MHE). Our results rely on a turnpike property of the optimal state estimation problem, which essentially states that the omniscient infinite-horizon solution involving all past and...
In this research paper, beginning with the Lagrangian and generalized velocity proportional (Rayleigh) dissipation function of a physical/engineering system, the Lagrange-dissipative model ( {L,D}-model briefly) of the system is initially developed. Upon satisfying the prerequisite condition for a Legendre transform, the Hamiltonian function can be...
Autonomous flight control systems have become an important technology for safety flight. The control problem of autonomous flight aircraft is challenging due to the nonlinearity and uncertain disturbances such as the external forces generated by the air flow. Model predictive control is a kind of optimal feedback control in which the control perfor...
The interplay between entropy and fractal dimensions within nonlinear systems offers profound insights into the intricate behaviors exhibited near critical transitions. This study investigates the dynamic relationship between entropy fluctuations and fractal structures in the logistic map, a quintessential model for chaos theory. By analyzing the e...
In this paper, we propose an economic nonlinear model predictive control (MPC) algorithm for district heating networks (DHNs). The proposed method features prosumers, multiple producers, and storage systems, which are essential components of 4th generation DHNs. These networks are characterized by their ability to optimize their operations, aiming...
This paper introduces a novel wavelet-based method utilizing the Tricomi–Carlitz orthogonal polynomials for solving the challenging coupled Lane–Emden–Fowler equations, which are prevalent in astrophysics and various physical sciences. These equations are notoriously difficult to solve numerically due to their singularity and nonlinearity, particul...
The construction and enhancement of chaotic systems are the research hotspot, especially in the secure communication applications fields. By applying Hamiltonian energy function to differential dynamical system, a dissipative nonlinear system is constructed based on generalized Hamiltonian system and Hamiltonian energy function, which enlarge the r...
The increasing deployment of offshore wind farms necessitates robust and stable high‐voltage direct current networks. Achieving optimal stability, especially in damping oscillations on the DC side, remains a significant challenge. This study focuses on mitigating post‐fault converter de‐blocking oscillations, a critical issue exacerbated by complex...
This paper considers the design of nonlinear data-enabled predictive control (DeePC) using kernel functions. Compared with existing methods that use kernels to parameterize multi-step predictors for nonlinear DeePC, we adopt a novel, operator-based approach. More specifically, we employ a universal product kernel parameterization of nonlinear syste...
Motores de indução trifásicos (MIT) são amplamente utilizados em aplicações industriais devido à sua robustez, baixo custo e construção simples. No entanto, estão sujeitos a perturbações externas e variações paramétricas, que podem comprometer seu desempenho em sistemas críticos. Este estudo propõe uma estratégia de controle que vai além do control...
In this paper, we study nonlinear systems of fractional differential equations with a Caputo fractional derivative with respect to another function (CFDF) and we define the strict stability of the zero solution of the considered nonlinear system. As an auxiliary system, we consider a system of two scalar fractional equations with CFDF and define a...
In this study, we explore the bifurcation of chirped waves in a nonlinear lattice incorporating the Morse potential. By applying the reductive perturbation method, we derive the generalized Kaup-Newell equation, representing the nonlinear system in a planar framework. Through qualitative analysis, homoclinic and heteroclinic orbits are revealed, co...
The study of high-dimensional solitons will bring great interest and new opportunities for understanding three-dimensional nonlinear physical phenomena and the design of complex nonlinear systems. The development of spatiotemporal mode-locked (STML) lasers has enabled the exploration of high-dimensional soliton dynamics. In this study, an STML lase...
This study delves into the synchronization issues of the impulsive fractional-order, mainly the Caputo derivative of the order between 0 and 1, bidirectional associative memory (BAM) neural networks incorporating the diffusion term at a fixed time (FXT) and a predefined time (PDT). Initially, this study presents certain characteristics of fractiona...
The regular decoding problem asks for (the existence of) regular solutions to a syndrome decoding problem (SDP). This problem has increased applications in post-quantum cryptography and cryptanalysis. Recently, Esser and Santini explored in depth the connection between the regular (RSD) and classical syndrome decoding problems. They have observed t...