{"title":"Correction to: Optimal controls for nonlocal Cauchy problems of multi-term fractional evolution equations","authors":"","doi":"10.1093/imamci/dnac032","DOIUrl":"https://doi.org/10.1093/imamci/dnac032","url":null,"abstract":"","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67841021","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}
This work addresses existence and stabilization problem for a hybrid neutral stochastic delay differential equations with Lévy noise (HNSDDELN). The coefficients of such systems do not satisfy the conventional linear growth conditions, but are subject to high nonlinearity. We first prove the existence and uniqueness of the solution. We then design a delay feedback controller to make an unstable HNSDDELN $H_{infty }$ and asymptotically stable in ${mathbb{L}}^{p}$ . We end up with a numerical example that corroborates our theoretical findings.
{"title":"H∞ and Asymptotic Stability via delay feedback for hybrid neutral stochastic delay differential equations with Lévy noise","authors":"Mohamed Rhaima;Lassaad Mchiri;A Ben Makhlouf","doi":"10.1093/imamci/dnad002","DOIUrl":"https://doi.org/10.1093/imamci/dnad002","url":null,"abstract":"This work addresses existence and stabilization problem for a hybrid neutral stochastic delay differential equations with Lévy noise (HNSDDELN). The coefficients of such systems do not satisfy the conventional linear growth conditions, but are subject to high nonlinearity. We first prove the existence and uniqueness of the solution. We then design a delay feedback controller to make an unstable HNSDDELN \u0000<tex>$H_{infty }$</tex>\u0000 and asymptotically stable in \u0000<tex>${mathbb{L}}^{p}$</tex>\u0000. We end up with a numerical example that corroborates our theoretical findings.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67841023","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}
This article addresses the stochastically exponential stability and mean stability of positive time-varying systems with stochastic impulses. The term ‘stochastic impulse’ means the randomness of impulsive densities or intensities. More specifically, the impulsive maps are not unique and the impulsive intensities are independent random variables with different distributions. The occurrence instants of impulses are restricted by several different processes, e.g. a mode-dependent average impulsive interval, a Markov chain, a Poisson process and a renewal process. Using a time-varying copositive Lyapunov function and stochastic analysis theory, several stochastic stability conditions are given. Finally, an example with four cases is presented to show the effectiveness of the proposed results.
{"title":"Stability analysis for time-varying positive systems with stochastic impulses","authors":"Mingzheng Yu;Jian Liu;Ticao Jiao;Lei Wang;Qian Ma","doi":"10.1093/imamci/dnac030","DOIUrl":"https://doi.org/10.1093/imamci/dnac030","url":null,"abstract":"This article addresses the stochastically exponential stability and mean stability of positive time-varying systems with stochastic impulses. The term ‘stochastic impulse’ means the randomness of impulsive densities or intensities. More specifically, the impulsive maps are not unique and the impulsive intensities are independent random variables with different distributions. The occurrence instants of impulses are restricted by several different processes, e.g. a mode-dependent average impulsive interval, a Markov chain, a Poisson process and a renewal process. Using a time-varying copositive Lyapunov function and stochastic analysis theory, several stochastic stability conditions are given. Finally, an example with four cases is presented to show the effectiveness of the proposed results.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67841026","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}
{"title":"Flocking of the hybrid Cucker-Smale model with normalized communication weight","authors":"Jinhua Yan, Xiuxia Yin, Songlin Hu","doi":"10.1093/imamci/dnad005","DOIUrl":"https://doi.org/10.1093/imamci/dnad005","url":null,"abstract":"","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73388790","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}
This paper concerns some spectral properties of the scalar dynamical system defined by a linear delay-differential equation with two positive delays. More precisely, the existing links between the delays and the maximal multiplicity of the characteristic roots are explored, as well as the dominance of such roots compared with the spectrum localization. As a by-product of the analysis, the pole placement issue is revisited with more emphasis on the role of the delays as control parameters in defining a partial pole placement guaranteeing the closed-loop stability with an appropriate decay rate of the corresponding dynamical system.
{"title":"On the pole placement of scalar linear delay systems with two delays","authors":"Sébastien Fueyo;Guilherme Mazanti;Islam Boussaada;Yacine Chitour;Silviu-Iulian Niculescu","doi":"10.1093/imamci/dnad001","DOIUrl":"https://doi.org/10.1093/imamci/dnad001","url":null,"abstract":"This paper concerns some spectral properties of the scalar dynamical system defined by a linear delay-differential equation with two positive delays. More precisely, the existing links between the delays and the maximal multiplicity of the characteristic roots are explored, as well as the dominance of such roots compared with the spectrum localization. As a by-product of the analysis, the pole placement issue is revisited with more emphasis on the role of the delays as control parameters in defining a partial pole placement guaranteeing the closed-loop stability with an appropriate decay rate of the corresponding dynamical system.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67841022","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}
This study presents a spectral method for solving the two-dimensional variable-order fractional optimal control problems (2D-VOFOCPs). In this work, a dynamic system with variable-order fractional derivatives appears. The Caputo derivative, which is one of the most widely used and essential types of fractional derivatives, has been used to construct operational matrices. The shifted Gegenbauer polynomials are used as orthogonal bases. For this purpose, at first, the control and state functions are approximated by the shifted Gegenbauer polynomials with unknown coefficients. Then, by substituting the approximated functions into initial and boundary conditions, the dynamical system and the objective function, an algebraic equation system is achieved. The solution of the obtained system of the algebraic equation is equivalent to the solution of 2D-VOFOCP. Furthermore, the convergence of the method is studied. Eventually, two numerical examples are presented to illustrate the applicability and accuracy of the proposed method.
{"title":"A numerical approach for solving a class of two-dimensional variable-order fractional optimal control problems using Gegenbauer operational matrix","authors":"Farzaneh Soufivand;Fahimeh Soltanian;Kamal Mamehrashi","doi":"10.1093/imamci/dnac031","DOIUrl":"https://doi.org/10.1093/imamci/dnac031","url":null,"abstract":"This study presents a spectral method for solving the two-dimensional variable-order fractional optimal control problems (2D-VOFOCPs). In this work, a dynamic system with variable-order fractional derivatives appears. The Caputo derivative, which is one of the most widely used and essential types of fractional derivatives, has been used to construct operational matrices. The shifted Gegenbauer polynomials are used as orthogonal bases. For this purpose, at first, the control and state functions are approximated by the shifted Gegenbauer polynomials with unknown coefficients. Then, by substituting the approximated functions into initial and boundary conditions, the dynamical system and the objective function, an algebraic equation system is achieved. The solution of the obtained system of the algebraic equation is equivalent to the solution of 2D-VOFOCP. Furthermore, the convergence of the method is studied. Eventually, two numerical examples are presented to illustrate the applicability and accuracy of the proposed method.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67841025","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}
Yanliang Cui, Guangtian Shi, Lanlan Xu, Juanjuan Ji
{"title":"Average dwell time based networked predictive control for switched linear systems with data transmission time-varying delays","authors":"Yanliang Cui, Guangtian Shi, Lanlan Xu, Juanjuan Ji","doi":"10.1093/imamci/dnad007","DOIUrl":"https://doi.org/10.1093/imamci/dnad007","url":null,"abstract":"","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88971562","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}
This paper deals with the leader-following consensus control for a class of parametric output feedback non-linear multi-agent systems. To design distributed control laws without using agent’s own out information, non-linear functions of agent’s own output are transformed into non-linear functions of relative output information using mean value theorem and variable separation technique. By introducing an input-driven filter and employing adaptive backstepping method, distributed adaptive non-linear control laws are designed using only relative output measurements. The proposed control law is also independent of the Laplacian matrix. Therefore, it can solve the leader-following consensus problem for any directed communication graph that contains a spanning tree with the root node being the leader agent. A numerical example is given to illustrate the effectiveness of the proposed scheme.
{"title":"Distributed adaptive leader-following consensus control for a class of non-linear output feedback systems","authors":"Chuanrui Wang, Hui Sun, Shuai Zhang","doi":"10.1093/imamci/dnac026","DOIUrl":"https://doi.org/10.1093/imamci/dnac026","url":null,"abstract":"\u0000 This paper deals with the leader-following consensus control for a class of parametric output feedback non-linear multi-agent systems. To design distributed control laws without using agent’s own out information, non-linear functions of agent’s own output are transformed into non-linear functions of relative output information using mean value theorem and variable separation technique. By introducing an input-driven filter and employing adaptive backstepping method, distributed adaptive non-linear control laws are designed using only relative output measurements. The proposed control law is also independent of the Laplacian matrix. Therefore, it can solve the leader-following consensus problem for any directed communication graph that contains a spanning tree with the root node being the leader agent. A numerical example is given to illustrate the effectiveness of the proposed scheme.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88779290","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}
Le Trung Hieu, P. H. A. Ngoc, Tran Thai Bao, H. Dinh
By a novel approach, we present some new criteria for the exponential stability in mean square of solutions of non-linear stochastic difference systems with time-varying delays. A discussion of the obtained results is given. Illustrative examples and simulations are provided.
{"title":"Explicit criteria for exponential stability in mean square of stochastic difference systems with delays","authors":"Le Trung Hieu, P. H. A. Ngoc, Tran Thai Bao, H. Dinh","doi":"10.1093/imamci/dnac025","DOIUrl":"https://doi.org/10.1093/imamci/dnac025","url":null,"abstract":"\u0000 By a novel approach, we present some new criteria for the exponential stability in mean square of solutions of non-linear stochastic difference systems with time-varying delays. A discussion of the obtained results is given. Illustrative examples and simulations are provided.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73163075","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}
The problem of bipartite synchronization is addressed for discrete-time networks with antagonistic interactions via hybrid control with impulsive effects. Firstly, a hybrid state-feedback controller, which combines a pinning state-feedback controller and an impulsive state-feedback controller, is presented, and the criterion of the bipartite synchronization is derived by applying the average impulsive interval method. Secondly, for the case of the network states not all being measured, a hybrid measurement-feedback controller, which combines a pinning measurement-feedback controller and a pinning impulsive measurement-feedback controller, is proposed. The time-varying Lyapunov function method is utilized to design the hybrid measurement-feedback controller such that the bipartite synchronization is realized. Finally, some numerical simulations are performed to illustrate the efficiency of the proposed controller design methods.
{"title":"Bipartite synchronization of discrete-time networks with antagonistic interactions via hybrid control","authors":"Xiaomei Zhang, Lin He, Lei Zhou, Suying Sheng","doi":"10.1093/imamci/dnac022","DOIUrl":"https://doi.org/10.1093/imamci/dnac022","url":null,"abstract":"\u0000 The problem of bipartite synchronization is addressed for discrete-time networks with antagonistic interactions via hybrid control with impulsive effects. Firstly, a hybrid state-feedback controller, which combines a pinning state-feedback controller and an impulsive state-feedback controller, is presented, and the criterion of the bipartite synchronization is derived by applying the average impulsive interval method. Secondly, for the case of the network states not all being measured, a hybrid measurement-feedback controller, which combines a pinning measurement-feedback controller and a pinning impulsive measurement-feedback controller, is proposed. The time-varying Lyapunov function method is utilized to design the hybrid measurement-feedback controller such that the bipartite synchronization is realized. Finally, some numerical simulations are performed to illustrate the efficiency of the proposed controller design methods.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80533377","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}
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