This paper presents a two-phase non-singular terminal sliding mode control scheme for a class of nonlinear systems in the presence of external disturbances. A two-phase terminal sliding mode surface is constructed and utilized, such that our control...
This paper investigates the observer-based fuzzy controller design method for nonlinear discrete-time singular systems that are represented by Takagi-Sugeno (T-S) fuzzy models. At first, the nonlinearity can be well-approximated with several local li...
In this paper, the Singular-Polynomial-Fuzzy-Model (SPFM) approach problem and impulse elimination are investigated based on sliding mode control for a class of nonlinear singular system (NSS) with impulses. Considering two numerical examples, the SP...
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...
This article focuses on designing an adaptive sliding mode controller via state and output feedback for nonlinear singular fractional-order systems (SFOSs) with mismatched uncertainties. Firstly, on the basis of extending the dimension of the SFOS, a...
This paper discusses an observer-based fuzzy control problem for uncertain nonlinear singular systems under Multi-Performance Requirements (MPRs). The approach used in the paper is to model the system using a Takagi–Sugeno (T-S) fuzzy model tha...
In this paper, sufficient conditions ensuring existence and multiplicity of positive solutions for a class of nonlinear singular fractional differential systems are derived with Riemann–Stieltjes coupled integral boundary value conditions in Ba...
Iterative differential equations provide a new idea to study functional differential equations. The study of iterative equations can provide new methods for the study of differential equations with state-dependent delays. In this paper, we are concer...
This paper focuses on the sliding mode control (SMC) problem for a class of uncertain singular fractional order systems (SFOSs). The uncertainties occur in both state and derivative matrices. A radial basis function (RBF) neural network strategy was...
The nonlinear Volterra–Fredholm integral Equation (NVFIE) with a singular kernel is discussed such that the kernel of position can take the Hilbert kernel form, Carleman function, logarithmic form, or Cauchy kernel. Using the quadrature method,...
In this paper, a mathematical model based on the T-S fuzzy model is proposed to solve the fault estimation (FE) and fault-tolerant control (FTC) problem for singular nonlinear time-varying delay (TVD) systems with sensor fault. TVD is is extremely di...
In unmanned systems, especially in large-scale and complex ones, sensor and communication failures occur from time to time and are hard to avoid. Therefore, this paper studies the fault detection problem of a class of unknown nonlinear singular uncer...
This study examines the concept of impulse controllability within singular hybrid coupled systems through the utilisation of decentralised proportional plus derivative (P-D) output feedback. By employing the Differential Mean Value Theorem, the nonli...
The singularity of Jacobian happens when we are looking for a root, with multiplicity greater than one, of a system of nonlinear equations. The purpose of this article is two-fold. Firstly, we will present a modification of an existing method that co...
The mathematical theories and methods of fractional calculus are relatively mature, which have been widely used in signal processing, control systems, nonlinear dynamics, financial models, etc. The studies of some basic theories of fractional differe...
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 form...
In this study, we present a general form of nonlinear two-time-scale systems, where singular perturbation analysis is used to separate the dynamics of the slow and fast subsystems. Machine learning techniques are utilized to approximate the dynamics...
Within a given time interval we consider a nonlinear system of differential equations describing psoriasis treatment. Its phase variables define the concentrations of T-lymphocytes, keratinocytes and dendritic cells. Two scalar bounded controls are i...
Applied in many fields, nonlinear systems involving delay and algebraic equations are referred to as singular systems. These systems remain challenging due to saturation constraints that affect actuators and cause harm to their operation. Furthermore...
For a class of fractional-order singular multi-agent systems (FOSMASs) with local Lipschitz nonlinearity, this paper proposes a closed-loop
A modification to an existing iterative method for computing zeros with unknown multiplicities of nonlinear equations or a system of nonlinear equations is presented. We introduce preconditioners to nonlinear equations or a system of nonlinear equati...
This paper mathematically explains how state derivative space (SDS) system form with state derivative related feedback can supplement standard state space system with state related feedback in control designs. Practically, inverse optimal control is...
Controlled dynamic systems with an entropy operator (DSEO) are considered. Mathematical models of such systems were used to study the dynamic properties in demo-economic systems, the spatiotemporal evolution of traffic flows, recurrent procedures for...
A model of production funds acquisition, which includes two differential links of the zero order and two series-connected inertial links, is considered in a one-sector economy. Zero-order differential links correspond to the equations of the Ramsey m...
Pursuing sustainable energy solutions has prompted researchers to focus on optimizing energy extraction from renewable sources. Control laws that optimize energy extraction require accurate modeling, often resulting in time-varying, nonlinear differe...
We address the problems in the trajectory tracking control of a multi-joint robotic arm, including uncertainty in the internal modeling of its significant external unknown time-varying disturbances. With the control objective of tracking the desired...
Nonlinear distortion in loudspeaker systems degrades sound quality and must be properly compensated for by linearization techniques. One technique to reduce nonlinear distortion is to use a Volterra Filter, which approximates the nonlinearity of the...
Several types of linear and nonlinear singularly perturbed time-delay differential systems are considered. Asymptotic stability of the linear systems and asymptotic stability of the trivial solution of the nonlinear systems, valid for any sufficientl...
We study the dynamics of a partially incoherent optical pulse that propagates in a slowly responding nonlinear Kerr medium. We show that irrespective of the sign of the dispersion (either normal or anomalous), the incoherent pulse as a whole exhibits...
The performance of various nonlinear frequency division multiplexed (NFDM) fiber-optic transmission systems has been observed to decrease with increasing signal duration. For a class of NFDM systems known as b-modulators, we show that the nonlinear b...
In this paper, we study the stationary boundary value problem derived from the magnetic (non) insulated regime on a plane diode. Our main goal is to prove the existence of non-negative solutions for that nonlinear singular system of second-order ordi...
Optical soliton solutions in a magneto-optical waveguide and other exact solutions are investigated for the coupled system of the nonlinear Biswas–Milovic equation with Kudryashov’s law using the extended F-expansion method. Various types...
In order to effectively identify the signs of instability in the aerodynamic system of an axial compressor, a wavelet singular spectral entropy algorithm incorporated within the wavelet transform, singular value decomposition and information entropy...
In this study, an adaptive nonsingular terminal sliding mode control technique according to the barrier function is designed for the performance improvement and robust stability of nonlinear systems with outdoor disturbances. For this reason, a novel...
Aiming at the problems of model uncertainties and other external interference in trajectory tracking control of n-degree of freedom manipulators, a non-singular terminal sliding mode controller with nonlinear disturbance observer (NDO–NTSMC) tr...
This work numerically investigates the fully nonlinear evolution of the free surface of a deep non-conducting liquid in a strong tangential electric field based on the method of dynamic conformal transformations. Direct numerical simulation revealed...
Uncertain singular non-causal systems represent a class of singular systems distinguished by the presence of regularity constraints and the involvement of uncertain variables. This paper considers optimal control problems for such systems under the H...
Nonlinear signal models are widely used in power amplifier predistortion, full-duplex self-interference cancellation, and other scenarios. The parallel Hammerstein (PH) model is a typical nonlinear signal model, but its serial and parallel hybrid arc...
This paper formulates the properties of point reachability and approximate point reachability of either a targeted state or output values in a general dynamic system which possess a linear time-varying dynamics with respect to a given reference nomin...
In the present study, the Homotopy Levenberg−Marquardt Algorithm (HLMA) and the Parameter Variation Levenberg–Marquardt Algorithm (PV–LMA), both developed in the context of high-temperature composition, are proposed to address the e...
This work proposes a non-singular fast terminal sliding mode control (NFTSMC) strategy based on the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm and a nonlinear disturbance observer (NDO) to address the issues of modeling errors, m...
In this paper, the new generalized Radhakrishnan–Kundu–Lakshmanan equations with powers of nonlinearity are studied, which is one of the important mathematical models in nonlinear optics. Using the complex envelope traveling wave solution, the new ge...
The convective Cahn–Hilliard–Oono equation is analyzed under the conditions
The current study examines optical soliton solutions in a complicated system of metamaterial-based optical solutions coupled with extremely dispersive couplers. The conformable fractional derivative (CFD) influences the nonlinear refractive index, wh...
We present recent advances in the analysis of nonlinear problems involving singular (degenerate) operators. The results are obtained within the framework of p-regularity theory, which has been successfully developed over the past four decades. We ill...
The frequency of a nonlinear vibration system is nonlinearly related to its amplitude, and this relationship is critical in the design of a packaging system and a microelectromechanical system (MEMS). This paper proposes a straightforward frequency p...
In this study, we present a spectral method for solving nonlinear Volterra integral equations with weakly singular kernels based on the Genocchi polynomials. Many other interesting results concerning nonlinear equations with discontinuous symmetric k...
This study examines the generalized nonlinear Hunter–Saxton (HS) model:
Based on the hydrodynamic description, the dynamics of nonlinear cylindrical waves in an isentropic plasma are investigated. The problem is considered in an electrostatic formulation for a two-dimensional plasma medium where ions form a stationary ba...
Addressing trajectory and attitude control challenges in quadrotor UAVs amid compound faults and unknown external disturbances, this paper introduces a fault-tolerant control method predicated on nonlinear extended state observers. Initially, the UAV...
of 6