A fuzzy integral controller with an event-triggered strategy for a class of nonlinear continuous singularly perturbed systems is proposed in this manuscript. Since the singularly perturbed systems are characterized by the parasitic parameter ɛ, which leads the systems to have multi-time-scale dynamics, a state feedback controller is proposed and designed for manipulating the effects of the parasitic parameter with the ɛ free functions by utilizing the Takagi-Sugeno fuzzy model, integral feedback, and event-triggered mechanism. As a result, we demonstrate that the proposed method maintain almost the same performance as the conventional controllers with less steady-state error while producing fewer events, which makes the communication channels between the plant system and the controller more available, through the examples of electrical engineering problems.
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http://dx.doi.org/10.1016/j.isatra.2023.04.011 | DOI Listing |
Heliyon
January 2025
Department of Mathematics, Dilla University, Dilla, Ethiopia.
This paper deals with the numerical investigation of a singularly perturbed parabolic differential-difference equation with a time lag. The proposed method comprises the method ( ) and the non-standard finite difference methods for temporal and spatial variable discretization, respectively. Besides, the Richardson extrapolation technique is employed to boost the accuracy and order of convergence of the scheme.
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December 2024
School of Mathematics and Statistics, Guangxi Normal University, Guilin 541006, China. Electronic address:
This paper addresses the event-based sliding mode control problem for singularly perturbed systems with switching parameters. Unlike traditional Markovian switching systems, singularly perturbed S-MSSs allow more flexible state transitions, which can be described by a general distribution rather than the exponential distribution assumed in Markovian switching systems. To enhance the performance of such systems, a novel memory-based dynamic event-triggered protocol (DETP) is proposed, incorporating a memory term for the auxiliary offset variable.
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December 2024
Department of Mathematics, Jimma University, Jimma, Ethiopia.
Objective: The main purpose of this work is to present an exponentially fitted non-polynomial cubic spline method for solving time-fractional singularly perturbed convection-diffusion problem involving large temporal lag.
Result: The time-fractional derivative is considered in the Caputo sense and discretized using backward Euler technique. Then, on uniform mesh discretization, a non-polynomial cubic spline scheme is constructed along the spatial direction.
J Math Biol
November 2024
Department of Mathematics, Imperial College London, London, SW7 2AZ, UK.
There are many processes in cell biology that can be modeled in terms of particles diffusing in a two-dimensional (2D) or three-dimensional (3D) bounded domain containing a set of small subdomains or interior compartments , (singularly-perturbed diffusion problems). The domain could represent the cell membrane, the cell cytoplasm, the cell nucleus or the extracellular volume, while an individual compartment could represent a synapse, a membrane protein cluster, a biological condensate, or a quorum sensing bacterial cell. In this review we use a combination of matched asymptotic analysis and Green's function methods to solve a general type of singular boundary value problems (BVP) in 2D and 3D, in which an inhomogeneous Robin condition is imposed on each interior boundary .
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November 2024
College of Mathematics and Statistics, Fujian Normal University, Fuzhou 350007, Fujian, People's Republic of China.
This article is concerned with the existence and spectral stability of pulses in singularly perturbed two-component reaction-diffusion systems with slowly mixed nonlinearity. In this paper, the slow nonlinearity is referred to be "mixed" in the sense that it is generated by a trigonometric function multiplied by a power function. We demonstrate via geometric singular perturbation theory that this model can support both the single-pulse and the double-hump solutions.
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