Real-world plants have various nonlinear characteristics such as friction and hysteresis, so nonlinear control is essential for precise control. In addition, actuators of plants have input constraints, which cause the integrator of the controller to...
In this paper, we investigate a class of nonlinear Schrödinger systems containing a nonlinear operator under Osgood-type conditions. By employing the iterative technique, the existence conditions for entire positive radial solutions of the above...
In this paper, a second-order operator splitting method combined with the barycentric Lagrange interpolation collocation method is proposed for the nonlinear Schrödinger equation. The equation is split into linear and nonlinear parts: the linear...
In this paper, we study the Liouville-type behaviors of the generalized Greiner operators with nonlinear boundary value conditions. We use the technique based upon the method of moving planes.
This paper studies operator and fractional order nonlinear robust control for a spiral counter-flow heat exchanger with uncertainties and disturbances. First, preliminary concepts are presented concerning fractional order derivative and calculus, fra...
Accurate flight training trajectory prediction is a key task in automatic flight maneuver evaluation and flight operations quality assurance (FOQA), which is crucial for pilot training and aviation safety management. The task is extremely challenging...
This paper introduces the optimal auxiliary function method (OAFM) for solving a nonlinear system of Belousov–Zhabotinsky equations. The system is characterized by its complex dynamics and is treated using the Caputo operator and concepts from...
Recently, the development of SiC and GaN high-performance semiconductor devices has led to higher efficiency in power conversion equipment. In order to perform thermal design of power conversion equipment and evaluation of the equipment, it is necess...
A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (...
This paper presents an action potential detector (APD) based on a high-order non-linear energy operator (HONEO). The APD consists of a HONEO, a positive threshold generator, a negative threshold generator, and an XOR. The APD is capable of detecting...
In this paper, we consider a boundary value problem for a nonlinear partial differential equation of mixed type with Hilfer operator of fractional integro-differentiation in a positive rectangular domain and with spectral parameter in a negative rect...
Recently, many kinds of soft actuators composed of flexible materials, such as silicon rubber, have been studied in the mechatronics field with increasing attention on the artificial muscle in welfare, medical care and biotechnology. Particularly, pn...
In this manuscript, a new family of Jacobian-free iterative methods for solving nonlinear systems is presented. The fourth-order convergence for all the elements of the class is established, proving, in addition, that one element of this family has o...
Recently, the studies of soft actuators have been getting increased attention among various fields. Soft actuators are very safe for fragile objects and have an affinity to humans because they are composed of flexible materials. A miniature flexible...
This paper investigates the problem of trajectory tracking control in the presence of bounded model uncertainty and external disturbance. To cope with this problem, we propose a novel intelligent operator-based sliding mode control scheme for stabili...
In this paper, an operator- and observer-based nonlinear tracking control scheme is proposed. Initially, the error-based extended state observer (eESO) is employed on the objective nonlinear plant, which addresses the compensation for perturbations l...
In nonlinear mechatronic systems with multiple coupled actuators, the allocation of control inputs affects both the feedback-system structure and the required actuator effort. This paper develops an operator-based nonlinear multi-input control framew...
Nonlinear model predictive control (NMPC) delivers high tracking accuracy for industrial processes but requires solving a nonlinear program at each sampling instant, limiting its applicability under tight real-time constraints. The Koopman operator p...
Triboelectric nanogenerators (TENGs) offer intrinsically high open-circuit voltages in the kilovolt range; however, conventional diode rectifier interfaces clamp the voltage prematurely, restricting access to the high-energy portion of the mechanical...
Currently, machine learning (ML) methods provide a practical approach to model complex systems. Unlike purely analytical models, ML methods can describe the uncertainties (e.g., hysteresis, temperature effects) that are difficult to deal with, potent...
This work presents the first-order comprehensive adjoint sensitivity analysis methodology (1st-CASAM) for computing efficiently the first-order sensitivities (i.e., functional derivatives) of operator-valued responses (i.e., model results) of general...
Reduction operators, i.e., the operators of nonclassical (or conditional) symmetry of a class of variable coefficient nonlinear wave equations with power nonlinearities, are investigated within the framework of a singular reduction operator. A classi...
The number of actuators of an underactuated robot is less than its degree of freedom. In other words, underactuated robots can be designed with fewer actuators than fully actuated ones. Although an underactuated robot is more complex than a fully act...
In recent years, with the growing interest in the Internet of Things (IoT) and decarbonization, energy harvesting has been attracting attention. Energy harvesting is a technology that converts ambient energy such as light, heat, and vibration into el...
The necessary and sufficient conditions of existence of the nonlinear operator equations’ branches of solutions in the neighbourhood of branching points are derived. The approach is based on the reduction of the nonlinear operator equations to...
In this article, we study the JF iterative algorithm to approximate the fixed points of a non-linear operator that satisfies condition (E) in uniformly convex Banach spaces. Further, some weak and strong convergence results are presented for the same...
In recent years, vibration control utilizing smart materials has garnered considerable attention. In this paper, we aim to achieve vibration suppression of a plate structure with a tail-fin shape by employing piezoelectric actuators—one of the...
In this paper, we study a new filtration class
Spectral methods form a cornerstone of linear dynamics, where evolution is resolved into harmonic modes governed by eigenvalues and spectral measures of normal operators. For nonlinear dynamical systems, however, the harmonic eigenfunction paradigm t...
This paper presents the application of an economic model predictive control (MPC) for the operational management of water distribution networks (WDNs) with periodic operation and nonlinear constraint relaxation. In addition to minimizing operational...
We investigate a novel nonlinear consensus from the extreme points of doubly stochastic quadratic operators (EDSQO), based on majorization theory and Markov chains for time-varying multi-agent distributed systems. We describe a dynamic system that ha...
In this paper, a novel approach that uses a deep learning technique is proposed to detect and identify a variety of image operations. First, we propose the spatial domain-based nonlinear residual (SDNR) feature extraction method by constructing resid...
An algorithm for the symbolic computation of recursion operators for systems of nonlinear differential-difference equations (DDEs) is presented. Recursion operators allow one to generate an infinite sequence of generalized symmetries. The existence o...
Recent decades have witnessed the emergence of interesting models of fractional partial differential equations. In the current work, a class of parabolic equations with regularized Hyper-Bessel derivative and the exponential source is investigated. M...
The purpose of the research is the study of a nonconstant gradient constrained problem for nonlinear monotone operators. In particular, we study a stationary variational inequality, defined by a strongly monotone operator, in a convex set of gradient...
This article explores nonlinear convergence to limit the effects of the consensus problem that usually occurs in multi-agent systems. Most of the existing research essentially considers the outline of linear protocols, using complex mathematical equa...
Sustainability is becoming the core theme of every organization to protect the planet from the drastic effects of climate change. Many organizations have drastically changed their practices to encourage green habits for sustainable operations. Practi...
Current risk assessment in railway track maintenance operations faces challenges (low spatiotemporal accuracy, limited adaptability to various scenarios, and tendency of linear fuzzy comprehensive evaluation (FCE) methods to underestimate high-risk f...
This study addresses the high-precision position control problem of pilot-operated proportional directional valves under dead-zone nonlinearity. A fuzzy PID-based position control strategy optimized by the dung beetle optimizer (DBO-FPID) is proposed...
This paper proposes a Chebyshev spectral collocation method for nonlinear Volterra–Hammerstein integral equations of the second kind with smooth kernels. We approximate the unknown solution using a finite Chebyshev expansion and place collocati...
In this paper, we study the existence/non-existence of ground states for the following type of elliptic equations with mixed local and nonlocal operators and general nonlinearity:
The main crux of this work is to study the existence of extremal solutions for a new class of nonlinear sequential fractional differential equations (NSFDEs) with nonlinear boundary conditions (NBCs) under the
Forced periodic operation (FPO) has emerged as a promising process intensification strategy for catalytic reactors. In this study, the nonlinear frequency response (NFR) methodology was applied to investigate square-wave FPO of an isothermal CSTR for...
At present, most urban rail transit systems adopt an operation mode with a single long routing. The departure frequency is determined by the maximum section passenger flow. However, when the passenger flow varies greatly within different sections, th...
This article proposed two novel techniques for solving the fractional-order Boussinesq equation. Several new approximate analytical solutions of the second- and fourth-order time-fractional Boussinesq equation are derived using the Laplace transform...
In this study, we aim to provide reliable methods for the initial value problem of the fractional modified Korteweg–de Vries (mKdV) equations. Fractional differential equations are essential for more precise simulation of numerous processes. Th...
The fractional Schrödinger–Korteweg-de Vries (S-KdV) equation is an important mathematical model that incorporates the nonlinear dynamics of the KdV equation with the quantum mechanical effects described by the Schrödinger equation. M...
This paper is devoted to introducing a nonlinear reconstruction operator, the piecewise polynomial harmonic (PPH), on nonuniform grids. We define this operator and we study its main properties, such as its reproduction of second-degree polynomials, a...
This paper develops an adaptive model predictive control (AMPC) scheme for uncertain nonaffine nonlinear systems by integrating deep Koopman operator theory into a fully data-driven modeling framework. Complex nonlinear systems typically feature prom...
This work illustrates the application of a comprehensive first-order adjoint sensitivity analysis methodology (1st-CASAM) to a heat conduction and convection analytical benchmark problem which simulates heat removal from a nuclear reactor fuel rod. T...
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