{"title":"Boundary Mittag-Leffler stabilization and disturbance rejection for time fractional ODE diffusion-wave equation cascaded systems","authors":"Jiake Sun, Junmin Wang","doi":"10.1016/j.cnsns.2024.108568","DOIUrl":null,"url":null,"abstract":"<div><div>This paper investigates the boundary stabilization of time fractional-order ODE cascaded with time fractional-order diffusion-wave equation systems subject to external disturbance. We stabilize the systems by using sliding mode control method and backstepping method. We prove the existence of the generalized solution of the closed-loop systems by Galerkin’s method and successive approximation method. The Mittag-Leffler stability of the systems is proven by Lyapunov method. The numerical simulations are presented to illustrate the validity of the theoretical results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"142 ","pages":"Article 108568"},"PeriodicalIF":3.4000,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1007570424007536","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This paper investigates the boundary stabilization of time fractional-order ODE cascaded with time fractional-order diffusion-wave equation systems subject to external disturbance. We stabilize the systems by using sliding mode control method and backstepping method. We prove the existence of the generalized solution of the closed-loop systems by Galerkin’s method and successive approximation method. The Mittag-Leffler stability of the systems is proven by Lyapunov method. The numerical simulations are presented to illustrate the validity of the theoretical results.
期刊介绍：
The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity.
The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged.
Topics of interest:
Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity.
No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.
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