Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be very simple...
Non-standard Lagrangians do not display any discernible energy-like terms, yet they give the same equations of motion as standard Lagrangians, which have easily identifiable energy-like terms. A new method to derive non-standard Lagrangians for secon...
This is the first on a series of articles that deal with nonlinear dynamical systems under oscillatory input that may exhibit harmonic and non-harmonic frequencies and possibly complex behavior in the form of chaos. Frequency response techniques of n...
The present study investigates non-fragile H∞ state estimation based on a dynamic event-triggered mechanism for a class of discrete time-varying nonlinear systems subject to dynamical bias and fading measurements. The dynamic deviation caused b...
This work is the second in a series of articles that deal with analytical solutions of nonlinear dynamical systems under oscillatory input that may exhibit harmonic frequencies. Frequency response techniques of nonlinear dynamical systems are usually...
Best proximity point theorem furnishes sufficient conditions for the existence and computation of an approximate solution
Fractional differential problems are widely used in applied sciences. For this reason, there is a great interest in the construction of efficient numerical methods to approximate their solution. The aim of this paper is to describe in detail a colloc...
This paper focuses on the modification of the large parameter approach (LPA), a novelty procedure, for estimating the periodic solutions of two degrees-of-freedom (DOF) autonomous quasi-linear systems with a first integral. This strategy is crucial b...
Electric motors and Internal Combustion Engine test benches allow for testing, under various conditions, the behavior of the Electric Vehicles and they are essential in the automotive field development. In this paper, we introduce the state-of-art of...
We study an interesting superization problem of integrable nonlinear dynamical systems on functional manifolds. As an example, we considered a quantum many-particle Schrödinger–Davydov model on the axis, whose quasi-classical reduction pro...
This paper presents a comprehensive framework addressing optimal nonlinear analysis and feedback control synthesis for nonlinear stochastic dynamical systems. The focus lies on establishing connections between stochastic Lyapunov theory and stochasti...
In previous studies, information dynamics methods such as Von Neumann entropy and Rényi entropy played an important role in many fields, covering both macroscopic and microscopic studies. They have a solid theoretical foundation, but there are...
Electromechanical equipment is indispensable in the modernization. The motions of electromechanical systems are becoming increasingly complex, which inevitably involves nonlinearity. The recent advances in design, analysis and control are to improve...
This paper is concerned with controllability of nonlinear fractional dynamical systems with a Mittag–Leffler kernel. First, the solution of fractional dynamical systems with a Mittag–Leffler kernel is given by Laplace transform. In additi...
In this paper, a nonlinear dynamic model of a parallel shaft gear system consisting of two involute spur gears is developed to investigate the coupling effect between the gradual surface wear of gear teeth over time and nonlinear dynamic characterist...
In this paper, the non-linear dynamical behavior of a 3D autonomous dissipative system of Hopf–Langford type is investigated. Through the help of a mode transformation (as the system’s energy is included) it is shown that the 3D nonlinear system can...
The problem of virtual sensor design for nonlinear systems under the disturbance is investigated. Two different mathematical techniques are used to solve the problem: the algebra of functions and the logic-dynamic approach. The first one allows obtai...
The paper considers the problem of invariance with respect to the unknown input for discrete-time nonlinear dynamic systems. To solve the problem, the algebraic approaches, called algebra of functions and logic–dynamic approach, are used. Such...
A systematic identification approach for the rotor/radial active magnetic bearing (rotor/RAMB) system is presented in this study. First, the system identification of the controller of commercial TMP is undertaken, and the corresponding linear dynamic...
Dynamics of arable and pastoral farming systems in Scotland over the period 1867–2020 are documented using time series analysis methods, including for nonlinear dynamical systems. Results show arable and pastoral farming, at a national scale, are dyn...
In this paper, the adaptive control problem of a type of uncertain nonlinear system is addressed. The system discussed includes unknown nonlinear functions, uncertain nonlinear dynamics, and unknown actuator faults. Based on the fuzzy logic systems a...
Networked nonlinear systems (NNSs) have great potential security threats because of malicious attacks. These attacks will destabilize the networked systems and disrupt the communication to the networked systems, which will affect the stability and pe...
In previous studies, the meshing force of a gear system is usually treated as being uniformly distributed for the convenience of analysis. In practical applications, however, it is nonuniformly distributed along the line of action due to machining er...
Load shedding processes are widespread in hydropower stations, which has great influence on the safe and stable operation of the hydro–turbine governing system. In order to study the dynamic characteristics of the hydro–turbine governing system durin...
In this article, we present a new accurate iterative and asymptotic method to construct analytical periodic solutions for a strongly nonlinear system, even if it is not Z2-symmetric. This method is applicable not only to a conservative system but als...
The Gaussian process is gaining increasing importance in different areas such as signal processing, machine learning, robotics, control and aerospace and electronic systems, since it can represent unknown system functions by posterior probability. Th...
In this paper we have established the sufficient conditions for asymptotic convergence of all solutions of nonlinear dynamical system (with potentially unknown and unbounded external disturbances) to zero with time
This paper deals with the leader-following consensus of multi-agent systems with matched nonlinear dynamics. Compared with previous works, the major difficulty here is caused by the simultaneous existence of nonidentical agent dynamics and unknown sy...
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 robo...
In the article, the semi-global finite-time control strategy for stochastic nonlinear systems is studied. Firstly, the general stochastic nonlinear system is considered and the required conditions are provided. An important theorem that helps to cons...
Based on the statics and quasi-statics analysis methods, the thermal deformation calculation model of a deep-groove ball bearing was constructed for the helical gear transmission system of a high speed electric drive, and the radial and axial bearing...
In this paper, the dynamic event-triggered tracking control issue is studied for a class of unknown stochastic nonlinear systems with strict-feedback form. At first, neural networks (NNs) are used to approximate the unknown nonlinear functions. Then,...
We present a novel and completely deterministic method to model chaotic orbits in nonlinear discrete dynamics, taking the quadratic map as an example. This method is based on the resurgent analysis developed by Écalle to perform the resummatio...
In this paper, four fractional-order memristor-based Lorenz systems with the flux-controlled memristor characterized by a monotone-increasing piecewise linear function, a quadratic nonlinearity, a smooth continuous cubic nonlinearity and a quartic no...
This paper presents a novel nonlinear piezoelectric energy harvesting system which consists of linear piezoelectric energy harvesters connected by linear springs. In principle, the presented nonlinear system can improve broadband energy harvesting ef...
System identification (SI) is the discipline of inferring mathematical models from unknown dynamic systems using the input/output observations of such systems with or without prior knowledge of some of the system parameters. Many valid algorithms are...
The Nonlinear Frequency Response (NFR) method is a useful Process Systems Engineering tool for developing experimental techniques and periodic processes that exploit the system nonlinearity. The basic and most time-consuming step of the NFR method is...
In recent years, applications of inverse model-based control techniques have experienced significant growth in popularity and have been widely used in engineering applications, mainly in nonlinear control system design problems. In this study, a nove...
The elastic support structure is widely employed in rotor systems and has an important influence on the nonlinear vibration of such systems. Nevertheless, coupled motion between elastic supports and bearings has not been taken into account, and the c...
This work addresses the tracking control problem of nonstrict-feedback nonlinear systems affected by unmodeled dynamics and input delays, which significantly complicate controller design and degrade system performance. To overcome these challenges, a...
This paper focuses on the parameter identification problem for Wiener nonlinear dynamic systems with moving average noises. In order to improve the convergence rate, the gradient-based iterative algorithm is presented by replacing the unmeasurable va...
Complex nonlinear turbulent dynamical systems are ubiquitous in many areas. Quantifying the model error and model uncertainty plays an important role in understanding and predicting complex dynamical systems. In the first part of this article, a simp...
This work addresses the design of a predefined-time adaptive fuzzy control scheme for high-order nonlinear systems with nonstrict-feedback structures, subject to unmodeled dynamics and input time delay. To mitigate the influence of unmodeled dynamics...
An adaptive fixed-time dynamic surface tracking control scheme is developed in this paper for a class of strict-feedback nonlinear systems, where the control input is subject to hysteresis dynamics. To deal with the input hysteresis, a compensation f...
Numerical estimation of Lyapunov exponents in non-linear dynamical systems results in a very high computational cost. This is due to the large-scale computational cost of several Runge–Kutta problems that need to be calculated. In this work we introd...
Brain-inspired intelligence using the cognitive dynamic system (CDS) concept is proposed to control the quality-of-service (QoS) over a long-haul fiber-optic link that is nonlinear and with non-Gaussian channel noise. Digital techniques such as digit...
This paper investigates the observer-based non-fragile output feedback tracking control problem for nonlinear networked systems with randomly occurring gain variations. The considered nonlinear networked systems are represented by a Takagi–Suge...
The problem of synthesis of stochastic sensitivity for equilibrium modes in nonlinear randomly forced dynamical systems with incomplete information is considered. We construct a feedback regulator that uses noisy data on some system state coordinates...
This paper investigates the event-triggered dissipative fuzzy tracking control problem of nonlinear networked systems with dynamic quantization and stochastic deception attacks, where the Takagi–Sugeno (T-S) fuzzy system theory is utilized to r...
State observers for systems having Lipschitz nonlinearities are considered for what concerns the stability of the estimation error by means of a decomposition of the dynamics of the error into the cascade of two systems. First, conditions are establi...
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