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Impulse controllability for degenerate singular parabolic equations via logarithmic convexity method 用对数凸性方法求解退化奇异抛物方程的脉冲可控性
4区 计算机科学
IMA Journal of Mathematical Control and Information Pub Date : 2023-09-08 DOI: 10.1093/imamci/dnad025
Hamid Maarouf, Lahcen Maniar, Ilham Ouelddris, Jawad Salhi
{"title":"Impulse controllability for degenerate singular parabolic equations via logarithmic convexity method","authors":"Hamid Maarouf, Lahcen Maniar, Ilham Ouelddris, Jawad Salhi","doi":"10.1093/imamci/dnad025","DOIUrl":"https://doi.org/10.1093/imamci/dnad025","url":null,"abstract":"Abstract In this paper, we study null approximate controllability of degenerate singular parabolic equations under the action of an impulsive control. To this aim, we prove an observation estimate at one point in time for the problems associated to the operators: $$ begin{align*}& u_{t} -(x^{alpha} u_{x})_{x} - dfrac{mu}{x^{beta}} u = 0, qquad x in left(0, 1right), end{align*} $$ where the parameters $alpha geq 0$, $beta , mu in mathbb{R}$ satisfy suitable assumptions. The method of proof combines both the logarithmic convexity and the Carleman commutator.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136362020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uniform stabilization of a Schrödinger equation with partial Dirichlet delayed control 具有部分Dirichlet延迟控制的Schrödinger方程的一致镇定
IF 1.5 4区 计算机科学
IMA Journal of Mathematical Control and Information Pub Date : 2023-09-05 DOI: 10.1093/imamci/dnad022
Xiaorui Wang, Yanfang Li
{"title":"Uniform stabilization of a Schrödinger equation with partial Dirichlet delayed control","authors":"Xiaorui Wang, Yanfang Li","doi":"10.1093/imamci/dnad022","DOIUrl":"https://doi.org/10.1093/imamci/dnad022","url":null,"abstract":"\u0000 In this paper, the uniform stabilization of a multi-dimensional Schrödinger equation with partial Dirichlet delayed control is concerned. The control input is suffered from time delay. Herein a new feedback controller is adopted in the investigation. Firstly, we rewrite the delayed system under consideration into a cascaded system of a transport equation and a Schrödinger equation, and construct an exponentially stable target system. Then by defining a bounded invertible linear transformation and choosing some appropriate kernel functions, we establish the equivalence between the closed-loop system and the target system. Finally, the exponential stability of the closed-loop system is obtained.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47265747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Caputo’s fractional discrete-time stability connection for stabilizing controllers 用于稳定控制器的卡普托分数离散时间稳定连接
IF 1.5 4区 计算机科学
IMA Journal of Mathematical Control and Information Pub Date : 2023-08-09 DOI: 10.1093/imamci/dnad021
B. Hernández-Galván, Jesus R. Pulido-Luna, N. Cázarez-Castro, G. Fernández-Anaya, J. López-Rentería
{"title":"Caputo’s fractional discrete-time stability connection for stabilizing controllers","authors":"B. Hernández-Galván, Jesus R. Pulido-Luna, N. Cázarez-Castro, G. Fernández-Anaya, J. López-Rentería","doi":"10.1093/imamci/dnad021","DOIUrl":"https://doi.org/10.1093/imamci/dnad021","url":null,"abstract":"\u0000 This work aims to give a method to connect a set of polynomials having all of their zeros inside the stability zone for fractional difference systems with Caputo’s fractional discrete operator. Due to the complexity of the stability zone, it is necessary to use a set that describes explicitly the stability zone for fractional-order difference systems, in order to build a polynomial family with zeros belonging to the described zone. Such a construction of the polynomial family will be based on the connection of their zeros. Moreover, the applicability is shown with the design of a robust stabilizing controller, which is illustrated by stabilizing the fractional discrete Duffing oscillator.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47761814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A complete characterization of minima of the spectral abscissa and rightmost roots of second-order systems with input delay 具有输入延迟的二阶系统的谱横坐标极小值和最右根的完整表征
IF 1.5 4区 计算机科学
IMA Journal of Mathematical Control and Information Pub Date : 2023-06-21 DOI: 10.1093/imamci/dnad020
W. Michiels, S. Niculescu, I. Boussaada
{"title":"A complete characterization of minima of the spectral abscissa and rightmost roots of second-order systems with input delay","authors":"W. Michiels, S. Niculescu, I. Boussaada","doi":"10.1093/imamci/dnad020","DOIUrl":"https://doi.org/10.1093/imamci/dnad020","url":null,"abstract":"\u0000 The numerical minimization of the spectral abscissa function of linear time-invariant time-delay systems, an established approach to compute stabilizing controllers with a fixed structure, often gives rise to minima characterized by active characteristic roots with multiplicity higher than one. At the same time, recent theoretical results reveal situations where the so-called multiplicity induced dominancy property holds, i.e., a sufficiently high multiplicity implies that the root is dominant. Using an integrative approach, combining analytical characterizations, computation of characteristic roots and numerical optimization, a complete characterization of the stabilizability of second-order systems with input delays is provided, for both state feedback and delayed output feedback. The level sets of the minimal achievable spectral abscissa are also characterized. These results shed light on the complex relations between (configurations involving) multiple roots, the property of being dominant roots and the property of corresponding to (local/global) minimizers of the spectral abscissa function.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45408094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Separation principle of delay perturbed singular systems 时滞扰动奇异系统的分离原理
IF 1.5 4区 计算机科学
IMA Journal of Mathematical Control and Information Pub Date : 2023-06-13 DOI: 10.1093/imamci/dnad019
Khawla Ben Mrad, I. Ellouze
{"title":"Separation principle of delay perturbed singular systems","authors":"Khawla Ben Mrad, I. Ellouze","doi":"10.1093/imamci/dnad019","DOIUrl":"https://doi.org/10.1093/imamci/dnad019","url":null,"abstract":"\u0000 In this paper, we establish a separation principle for a class of time-varying delay perturbed singular systems. Furthermore, we propose a singular observer to estimate the system states. Based on the Lyapunov–Krasovskii functionals, the practical stability of the proposed singular observer is achieved. These results are applied to show that a separation principle for perturbed singular systems can be obtained. Eventually, we provide a numerical example to verify the validity of the proposed results.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46664932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Robust error feedback output regulation of a 2 × 2 hyperbolic system 2 × 2双曲系统的鲁棒误差反馈输出调节
4区 计算机科学
IMA Journal of Mathematical Control and Information Pub Date : 2023-05-30 DOI: 10.1093/imamci/dnad015
Wei-Wei Liu, Jun-Min Wang, Xiang-Dong Liu
{"title":"Robust error feedback output regulation of a 2 × 2 hyperbolic system","authors":"Wei-Wei Liu, Jun-Min Wang, Xiang-Dong Liu","doi":"10.1093/imamci/dnad015","DOIUrl":"https://doi.org/10.1093/imamci/dnad015","url":null,"abstract":"Abstract In this paper, we consider the robust error feedback output regulation problem for a linear $ 2 times 2 $ hyperbolic system with system uncertainties and disturbance signals. Using the backstepping method, the state feedback controller for the system without the system uncertainties and the external disturbance signals (nominal system) is designed. In terms of the measurable regulation error, an observer system is designed to recover the state of the nominal system, and an observer-based error feedback controller is obtained to solve the robust output regulation problem. Moreover, we prove that the controller is robust to the system uncertainties and the disturbance signals, and show that the state of the closed-loop system is bounded. The numerical simulations are presented to illustrate the effectiveness of the theoretical results.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135642750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global exponential stabilization of the linearized Korteweg-de Vries equation with a state delay 具有状态延迟的线性化Korteweg-de Vries方程的全局指数镇定
4区 计算机科学
IMA Journal of Mathematical Control and Information Pub Date : 2023-05-30 DOI: 10.1093/imamci/dnad016
Habib Ayadi, Mariem Jlassi
{"title":"Global exponential stabilization of the linearized Korteweg-de Vries equation with a state delay","authors":"Habib Ayadi, Mariem Jlassi","doi":"10.1093/imamci/dnad016","DOIUrl":"https://doi.org/10.1093/imamci/dnad016","url":null,"abstract":"Abstract In this paper, well-posedness and global boundary exponential stabilization problems are studied for the one-dimensional linearized Korteweg-de Vries equation (KdV) with state delay, which is posed in bounded interval $[0,2pi ]$ and actuated at the left boundary by Dirichlet condition. Based on the infinite-dimensional backstepping method for the delay-free case, a linear Volterra-type integral transformation maps the system into another homogeneous target system, and an explicit feedback control law is obtained. Under this feedback, we prove the well-posedness of the considered system in an appropriate Banach space and its exponential stabilization in the topology of $L^{2}(0,2pi )$-norm by the use of an appropriate Lyapunov–Razumikhin functional. Moreover, under the same feedback law, we get the local exponential stability for the non-linear KdV equation. A numerical example is provided to illustrate the result.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135643522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Prescribed-time stabilization of uncertain heat equation with Dirichlet boundary control Dirichlet边界控制下不确定热方程的规定时间镇定
IF 1.5 4区 计算机科学
IMA Journal of Mathematical Control and Information Pub Date : 2023-05-29 DOI: 10.1093/imamci/dnad017
Chengzhou Wei, Junmi Li
{"title":"Prescribed-time stabilization of uncertain heat equation with Dirichlet boundary control","authors":"Chengzhou Wei, Junmi Li","doi":"10.1093/imamci/dnad017","DOIUrl":"https://doi.org/10.1093/imamci/dnad017","url":null,"abstract":"\u0000 This paper designs a Dirichlet boundary controller to stabilize a heat equation with boundary disturbance within a prescribed finite time independent of initial conditions. We first use boundary measurements and time-varying gain to construct a disturbance estimator that estimates the disturbance itself and the system state within a prescribed time. We then design the estimation-based prescribed time boundary controller by the backstepping transformation with a time-varying kernel. The control gain proposed here diverges as the time approaches the prescribed time. Nevertheless, we can demonstrate the controller’s boundedness and the system’s prescribed time stability. A simulation example illustrates the theoretical result.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44008555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Parameter estimation and velocity signal extraction for one-dimensional wave equation with harmonic corrupted boundary observation 含谐波破坏边界观测的一维波动方程参数估计与速度信号提取
IF 1.5 4区 计算机科学
IMA Journal of Mathematical Control and Information Pub Date : 2023-05-29 DOI: 10.1093/imamci/dnad018
Shuang-yun Huang, Feng-Fei Jin
{"title":"Parameter estimation and velocity signal extraction for one-dimensional wave equation with harmonic corrupted boundary observation","authors":"Shuang-yun Huang, Feng-Fei Jin","doi":"10.1093/imamci/dnad018","DOIUrl":"https://doi.org/10.1093/imamci/dnad018","url":null,"abstract":"\u0000 In this paper, we consider parameter estimation and velocity signal extraction from a disturbed boundary velocity signal for an unstable wave equation. Firstly, an adaptive observer is designed based on the boundary displacement and the corrupted boundary velocity. Then the design of the feedback law adopts the backstepping method of infinite dimensional system. Finally, as time approaches infinity, the estimated parameters converge to the unknown parameters, the initial value disturbance can be obtained, and the velocity signal can be asymptotically recovered. Meanwhile, the asymptotic stability of the closed-loop system can be proved by $C_{0}$-semigroup theory and Lyapunov method. Numerical simulation shows that the proposed scheme is reasonable.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76289622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Adaptive stabilization for a wave equation subject to boundary control matched harmonic disturbance 边界控制下匹配谐波扰动波动方程的自适应镇定
IF 1.5 4区 计算机科学
IMA Journal of Mathematical Control and Information Pub Date : 2023-05-14 DOI: 10.1093/imamci/dnad010
Jun-Jun Liu, Yanxiao Zhao
{"title":"Adaptive stabilization for a wave equation subject to boundary control matched harmonic disturbance","authors":"Jun-Jun Liu, Yanxiao Zhao","doi":"10.1093/imamci/dnad010","DOIUrl":"https://doi.org/10.1093/imamci/dnad010","url":null,"abstract":"\u0000 In this paper, we are concerned with adaptive stabilization for a wave equation subject to boundary control matched harmonic disturbance. We use the adaptive and Lyapunov approach to estimate unknown disturbance and construct an adaptive boundary feedback controller. By the semigroup theory and Lasalle‘s invariance theorem, the well-posedness and asymptotic stability of the closed-loop system is proved, respectively. At the same time, it is shown that the parameter estimates involved in the constructed controller converge to their own real values as time goes to infinity. Some numerical simulations are offered at the end of the paper to illustrate the effectiveness of theoretical results.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42528303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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