This paper deals with the pairwise synchronization of second-order linear time invariant (LTI) systems with incommensurable outputs through a matrix-weighted graph. The pairwise synchronization here means that the relative outputs have pairwise synchronized solutions for the identical LTI systems. For the matrix-weighted network, some necessary and sufficient conditions on the pairwise synchronization are given by means of the Jordan form, matrix decomposition and effective conductance. Moreover, the relationship between the global synchronization and the connectivity of its interconnection graph is also discussed. Examples and simulations are shown to verify the theoretical results.
{"title":"Pairwise synchronization of second-order matrix-weighted networks","authors":"Pengchao Lv, Bo Liu, Junjie Huang","doi":"10.1093/imamci/dnae026","DOIUrl":"https://doi.org/10.1093/imamci/dnae026","url":null,"abstract":"This paper deals with the pairwise synchronization of second-order linear time invariant (LTI) systems with incommensurable outputs through a matrix-weighted graph. The pairwise synchronization here means that the relative outputs have pairwise synchronized solutions for the identical LTI systems. For the matrix-weighted network, some necessary and sufficient conditions on the pairwise synchronization are given by means of the Jordan form, matrix decomposition and effective conductance. Moreover, the relationship between the global synchronization and the connectivity of its interconnection graph is also discussed. Examples and simulations are shown to verify the theoretical results.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218312","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}
Shuzhan Zhang, Jia Li, Dongya Zhao, Sarah K Spurgeon
This paper proposes a distributed economic model predictive control algorithm for parallel systems which uses only output feedback. Such parallel systems are a fundamental system architecture frequently encountered in process networks where, in many cases, the state of the plant is not measurable. Economic performance is a key consideration in the operation of such industrial plants and it is of interest to develop theoretically rigorous approaches to tackle what is a practically very relevant scenario. The competitive couplings and competitive constraints inherent in parallel systems are explicitly addressed in the proposed controller design framework. Three measures are considered for optimization of such parallel systems including an economic stage cost function, energy efficiency and tracking accuracy. An economic cost function is optimized by the resulting distributed controller which can realize global control performance while also reducing the computational time for large-scale parallel systems. Stability of the system is formally proved using the principles of dissipativity. Finally, the effectiveness of the proposed theoretical approach is verified by both numerical simulation and experimentation to demonstrate practical relevance.
{"title":"Output feedback distributed economic model predictive control for parallel system in process networks","authors":"Shuzhan Zhang, Jia Li, Dongya Zhao, Sarah K Spurgeon","doi":"10.1093/imamci/dnae025","DOIUrl":"https://doi.org/10.1093/imamci/dnae025","url":null,"abstract":"This paper proposes a distributed economic model predictive control algorithm for parallel systems which uses only output feedback. Such parallel systems are a fundamental system architecture frequently encountered in process networks where, in many cases, the state of the plant is not measurable. Economic performance is a key consideration in the operation of such industrial plants and it is of interest to develop theoretically rigorous approaches to tackle what is a practically very relevant scenario. The competitive couplings and competitive constraints inherent in parallel systems are explicitly addressed in the proposed controller design framework. Three measures are considered for optimization of such parallel systems including an economic stage cost function, energy efficiency and tracking accuracy. An economic cost function is optimized by the resulting distributed controller which can realize global control performance while also reducing the computational time for large-scale parallel systems. Stability of the system is formally proved using the principles of dissipativity. Finally, the effectiveness of the proposed theoretical approach is verified by both numerical simulation and experimentation to demonstrate practical relevance.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947450","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}
Linear differential systems, as it is known, are parameterized by means of polynomial matrices. Introducing appropriate topologies, it is shown that this parametrization becomes a quotient map.
{"title":"Continuous dependence of linear differential systems on polynomial matrices","authors":"Vakhtang Lomadze","doi":"10.1093/imamci/dnae019","DOIUrl":"https://doi.org/10.1093/imamci/dnae019","url":null,"abstract":"Linear differential systems, as it is known, are parameterized by means of polynomial matrices. Introducing appropriate topologies, it is shown that this parametrization becomes a quotient map.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501072","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}
In this paper, based on the partition technique, we use Meixner and Krawtchouk polynomials to present an input-independent model order reduction method. Our main contributions are twofold. First, the explicit difference relations of Meixner polynomials and Krawtchouk polynomials are expressed in an unified form. The parallel computation is carried out on the partitioned subsystems using the Krylov subspaces by which one can generate reduced systems independent of the expansion coefficients of input and can save the computation time. Second, a parallel adaptive enrichment strategy is used to choose the reduced order of reduced systems. Theoretical analysis shows that the proposed method characterizes the property of invariable coefficients. Finally, two numerical examples demonstrate that the proposed method achieves good reduction results in terms of accuracy and reduced CPU time.
{"title":"Model order reduction in parallel of discrete-time linear systems based on Meixner and Krawtchouk polynomials","authors":"Kang-Li Xu, Zhen Li, Yao-Lin Jiang, Li Li","doi":"10.1093/imamci/dnae018","DOIUrl":"https://doi.org/10.1093/imamci/dnae018","url":null,"abstract":"In this paper, based on the partition technique, we use Meixner and Krawtchouk polynomials to present an input-independent model order reduction method. Our main contributions are twofold. First, the explicit difference relations of Meixner polynomials and Krawtchouk polynomials are expressed in an unified form. The parallel computation is carried out on the partitioned subsystems using the Krylov subspaces by which one can generate reduced systems independent of the expansion coefficients of input and can save the computation time. Second, a parallel adaptive enrichment strategy is used to choose the reduced order of reduced systems. Theoretical analysis shows that the proposed method characterizes the property of invariable coefficients. Finally, two numerical examples demonstrate that the proposed method achieves good reduction results in terms of accuracy and reduced CPU time.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501073","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":"Correction to: Funnel control of linear systems with arbitrary relative degree under output measurement losses","authors":"","doi":"10.1093/imamci/dnae017","DOIUrl":"https://doi.org/10.1093/imamci/dnae017","url":null,"abstract":"","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141112916","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}
Shanggen Wu, Yuanzhen Feng, Ziyang Wang, Zhengxin Wang
The leader-following consensus problem of second-order heterogeneous nonlinear multi-agent systems (MASs) is studied in this paper. Based on the free-will arbitrary time (FWAT) theory, a piecewise distributed controller is developed to solve this problem within an arbitrary pre-specified convergence time. It should be noted that the pre-specified convergence time is independent of any system parameters and initial conditions. Furthermore, compared with the existing FWAT methods, consensus can still be maintained after the convergence time under the protocol designed in this work. Finally, numerical examples are given to illustrate the validity of the proposed method.
{"title":"Leader-following consensus of heterogeneous nonlinear multi-agent systems within arbitrary pre-specified time","authors":"Shanggen Wu, Yuanzhen Feng, Ziyang Wang, Zhengxin Wang","doi":"10.1093/imamci/dnae016","DOIUrl":"https://doi.org/10.1093/imamci/dnae016","url":null,"abstract":"The leader-following consensus problem of second-order heterogeneous nonlinear multi-agent systems (MASs) is studied in this paper. Based on the free-will arbitrary time (FWAT) theory, a piecewise distributed controller is developed to solve this problem within an arbitrary pre-specified convergence time. It should be noted that the pre-specified convergence time is independent of any system parameters and initial conditions. Furthermore, compared with the existing FWAT methods, consensus can still be maintained after the convergence time under the protocol designed in this work. Finally, numerical examples are given to illustrate the validity of the proposed method.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141063583","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}
El Mustapha Ait Ben Hassi, Mariem Jakhoukh, Lahcen Maniar, Walid Zouhair
The primary focus of this paper is to establish the internal null controllability for the one-dimensional heat equation featuring dynamic boundary conditions. This achievement is realized by introducing a new Carleman estimate and an observability inequality for the corresponding backward system. In conclusion, the paper includes a set of numerical experiments that serve to confirm the validity of the theoretical findings and underscore the effectiveness of the designed control with a minimal $L^{2}$-norm.
{"title":"Internal null controllability for the one-dimensional heat equation with dynamic boundary conditions","authors":"El Mustapha Ait Ben Hassi, Mariem Jakhoukh, Lahcen Maniar, Walid Zouhair","doi":"10.1093/imamci/dnae015","DOIUrl":"https://doi.org/10.1093/imamci/dnae015","url":null,"abstract":"The primary focus of this paper is to establish the internal null controllability for the one-dimensional heat equation featuring dynamic boundary conditions. This achievement is realized by introducing a new Carleman estimate and an observability inequality for the corresponding backward system. In conclusion, the paper includes a set of numerical experiments that serve to confirm the validity of the theoretical findings and underscore the effectiveness of the designed control with a minimal $L^{2}$-norm.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140832407","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}
In this paper, we mainly study a class of conformable impulsive delay differential equations (CIDDEs). We first define a conformable impulsive delayed matrix function, and construct an explicit solution for linear CIDDEs by virtue of variation of constants method. Subsequently, based on impulsive delayed Grammian matrix, we study the relative controllability for the addressed linear equations. Moreover, with the help of Krasnoselskii’s fixed point theorem, relative controllability for the considered semilinear equations is proposed. Finally, two examples with numerical simulations are given to illustrate the main results.
{"title":"Relative controllability for conformable impulsive delay differential equations","authors":"Danfeng Luo, Jizhao Huang","doi":"10.1093/imamci/dnae013","DOIUrl":"https://doi.org/10.1093/imamci/dnae013","url":null,"abstract":"\u0000 In this paper, we mainly study a class of conformable impulsive delay differential equations (CIDDEs). We first define a conformable impulsive delayed matrix function, and construct an explicit solution for linear CIDDEs by virtue of variation of constants method. Subsequently, based on impulsive delayed Grammian matrix, we study the relative controllability for the addressed linear equations. Moreover, with the help of Krasnoselskii’s fixed point theorem, relative controllability for the considered semilinear equations is proposed. Finally, two examples with numerical simulations are given to illustrate the main results.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140678196","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 paper explores an optimal control problem concerning transport processes in a porous medium. The transport phenomena is governed by diffusion-reaction equations, which is basically a semi-linear parabolic system. An $L^{2}$-cost (energy) functional is introduced, and control (distributed) is applied in the porous part of the medium. The primary objective is to characterize a given control to be an optimal control and analyse the relationship between optimal control and the adjoint state. The analysis commences with the microscopic description of the controlled system followed by upscaling the system via periodic homogenization.
{"title":"Existence of solution for an optimal control problem in a heterogeneous porous medium","authors":"A Kundu, H S Mahato","doi":"10.1093/imamci/dnae011","DOIUrl":"https://doi.org/10.1093/imamci/dnae011","url":null,"abstract":"The paper explores an optimal control problem concerning transport processes in a porous medium. The transport phenomena is governed by diffusion-reaction equations, which is basically a semi-linear parabolic system. An $L^{2}$-cost (energy) functional is introduced, and control (distributed) is applied in the porous part of the medium. The primary objective is to characterize a given control to be an optimal control and analyse the relationship between optimal control and the adjoint state. The analysis commences with the microscopic description of the controlled system followed by upscaling the system via periodic homogenization.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140583128","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}
A general $N$-dimensional non-monotone delayed diffusive Lotka–Volterra model is considered in our paper. First, we obtain the global stability of the model subject to Neumann boundary condition by using a small delay result for delayed systems. Second, the limits at $+infty $ of bounded travelling wave solutions are confirmed by virtue of such global stability. Therefore, the existence of co-existence state travelling wave solutions is established. Finally, an example is given to illustrate the biological significance of the assumptions in the current paper.
{"title":"Stability and co-existence state traveling wave solution for a general N-dimensional diffusive delayed Lotka-Volterra equation in a cylinder","authors":"Yanling Tian, Shuyuan Shen, Jinji Yang","doi":"10.1093/imamci/dnae012","DOIUrl":"https://doi.org/10.1093/imamci/dnae012","url":null,"abstract":"\u0000 A general $N$-dimensional non-monotone delayed diffusive Lotka–Volterra model is considered in our paper. First, we obtain the global stability of the model subject to Neumann boundary condition by using a small delay result for delayed systems. Second, the limits at $+infty $ of bounded travelling wave solutions are confirmed by virtue of such global stability. Therefore, the existence of co-existence state travelling wave solutions is established. Finally, an example is given to illustrate the biological significance of the assumptions in the current paper.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140367538","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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