{"title":"Structural controllability analysis based on dilations under leader-follower framework","authors":"Shuhui Sun, Zhijian Ji, Chong Lin, Yungang Liu","doi":"10.1093/imamci/dnab032","DOIUrl":"https://doi.org/10.1093/imamci/dnab032","url":null,"abstract":"","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"20 1","pages":"1-21"},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76668873","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":"Positive observers for semilinear positive systems","authors":"Abdellaziz Binid, M. E. Achhab, M. Laabissi","doi":"10.1093/imamci/dnac018","DOIUrl":"https://doi.org/10.1093/imamci/dnac018","url":null,"abstract":"","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"16 1","pages":"968-984"},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81345551","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":"GE-evolution operator method for controllability of time-varying stochastic descriptor systems in Hilbert spaces","authors":"Zhao-qiang Ge","doi":"10.1093/imamci/dnab038","DOIUrl":"https://doi.org/10.1093/imamci/dnab038","url":null,"abstract":"","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"39 1","pages":"80-92"},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61175417","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}
M. B. Estrada, N. Aguillon, Marco Antonio Ortiz Castillo, J. Loiseau, M. Malabre, V. Azhmyakov, S. Salazar
Our paper deals with the stabilization of a class of time-dependent linear autonomous complex systems with a switched structure. The initially given switched dynamic system is assumed to be controlled by a specific state feedback strategy associated with the linear quadratic regulator (LQR) type control. The proposed control design guarantees stabilization of the closed-loop system for all of the possible location transitions. In the solution procedure of the Algebraic Riccati Equation related to the LQR control strategy, only the knowledge of the algebraic structure related to the switched system are needed. We prove that the proposed optimal LQR type state feedback control design stabilizes the closed-loop switched system for every possible active location. The theoretical approach proposed in this paper is finally applied to a model of the Single Wing Quadrotor Aircraft, when changing from its Quadrotor Flight Envelope to its Airplane Flight Envelope.
{"title":"Stabilization of a class of switched dynamic systems: the Riccati-equation-based Approach","authors":"M. B. Estrada, N. Aguillon, Marco Antonio Ortiz Castillo, J. Loiseau, M. Malabre, V. Azhmyakov, S. Salazar","doi":"10.1093/imamci/dnab022","DOIUrl":"https://doi.org/10.1093/imamci/dnab022","url":null,"abstract":"\u0000 Our paper deals with the stabilization of a class of time-dependent linear autonomous complex systems with a switched structure. The initially given switched dynamic system is assumed to be controlled by a specific state feedback strategy associated with the linear quadratic regulator (LQR) type control. The proposed control design guarantees stabilization of the closed-loop system for all of the possible location transitions. In the solution procedure of the Algebraic Riccati Equation related to the LQR control strategy, only the knowledge of the algebraic structure related to the switched system are needed. We prove that the proposed optimal LQR type state feedback control design stabilizes the closed-loop switched system for every possible active location. The theoretical approach proposed in this paper is finally applied to a model of the Single Wing Quadrotor Aircraft, when changing from its Quadrotor Flight Envelope to its Airplane Flight Envelope.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"101 1","pages":"518-532"},"PeriodicalIF":1.5,"publicationDate":"2021-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72858870","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 considers the problem of model orientation, i.e. the classification of the external signals into inputs and outputs. The problem is considered in the behavioural context where the external model is an autoregressive system. Orientation of a system automatically induces equivalent first order models in state–space or descriptor form via a realization procedure. A new realization procedure is proposed where the realization is implemented in two steps, first an intermediate ARMA realization is obtained. Then, this realization is transformed into the final descriptor system via an appropriate reduction procedure corresponding to the input/output partition of the external variables. Studying the dependency of the resulting system properties and invariants on the different selections of input and output variables and the structure of the initial external behaviour is considered in the paper.
{"title":"Realizations and orientation of implicit systems","authors":"Dimitris Vafiadis","doi":"10.1093/imamci/dnab025","DOIUrl":"https://doi.org/10.1093/imamci/dnab025","url":null,"abstract":"\u0000 The paper considers the problem of model orientation, i.e. the classification of the external signals into inputs and outputs. The problem is considered in the behavioural context where the external model is an autoregressive system. Orientation of a system automatically induces equivalent first order models in state–space or descriptor form via a realization procedure. A new realization procedure is proposed where the realization is implemented in two steps, first an intermediate ARMA realization is obtained. Then, this realization is transformed into the final descriptor system via an appropriate reduction procedure corresponding to the input/output partition of the external variables. Studying the dependency of the resulting system properties and invariants on the different selections of input and output variables and the structure of the initial external behaviour is considered in the paper.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"10 1","pages":"498-517"},"PeriodicalIF":1.5,"publicationDate":"2021-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78279345","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}
We introduce the concept of non-uniform input-to-state stability for networks. It combines the uniform global stability with the uniform attractivity of any subnetwork while it allows for non-uniform convergence of all components. For an infinite network consisting of input-to-state stable subsystems, which do not necessarily have a uniform $mathscr{K}mathscr{L}$ -bound on the transient behaviour, we show the following: if the gain operator satisfies the uniform small-gain condition, then the whole network is non-uniformly input-to-state stable and all its finite subnetworks are input-to-state stable.
{"title":"Non-uniform ISS small-gain theorem for infinite networks","authors":"Andrii Mironchenko","doi":"10.1093/imamci/dnab026","DOIUrl":"https://doi.org/10.1093/imamci/dnab026","url":null,"abstract":"We introduce the concept of non-uniform input-to-state stability for networks. It combines the uniform global stability with the uniform attractivity of any subnetwork while it allows for non-uniform convergence of all components. For an infinite network consisting of input-to-state stable subsystems, which do not necessarily have a uniform \u0000<tex>$mathscr{K}mathscr{L}$</tex>\u0000-bound on the transient behaviour, we show the following: if the gain operator satisfies the uniform small-gain condition, then the whole network is non-uniformly input-to-state stable and all its finite subnetworks are input-to-state stable.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"38 4","pages":"1029-1045"},"PeriodicalIF":1.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67895357","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 is devoted to the robust consensus tracking problem of second-order nonlinear multi-agent systems (MASs) with the interval uncertain topologies. For the second-order MASs including one leader agent and multiple follower agents, a control protocol is proposed by combining the iterative learning control scheme with the sliding mode control method. By analyzing the convergence of sliding mode variables, the consensus conditions including the unknown eigenvalues and the undetermined weight coefficient are obtained. In order to deal with the difficulties of weight coefficient design caused by the unknown eigenvalues of graphs, a min-max optimization problem is formulated based on the fastest convergence of the λ-norm of sliding mode variables, then the optimal weight coefficient is obtained by solving the min-max optimization problem. Moreover, for the undirected and directed interval uncertain graphs, two algorithms about the optimal weight coefficients are proposed, respectively. Finally, three numerical simulation examples are presented to demonstrate the effectiveness of the proposed methods.
{"title":"Iterative learning control for consensus of second-order multi-agent systems with interval uncertain topologies","authors":"Liming Wang;Guoshan Zhang","doi":"10.1093/imamci/dnab024","DOIUrl":"https://doi.org/10.1093/imamci/dnab024","url":null,"abstract":"This paper is devoted to the robust consensus tracking problem of second-order nonlinear multi-agent systems (MASs) with the interval uncertain topologies. For the second-order MASs including one leader agent and multiple follower agents, a control protocol is proposed by combining the iterative learning control scheme with the sliding mode control method. By analyzing the convergence of sliding mode variables, the consensus conditions including the unknown eigenvalues and the undetermined weight coefficient are obtained. In order to deal with the difficulties of weight coefficient design caused by the unknown eigenvalues of graphs, a min-max optimization problem is formulated based on the fastest convergence of the λ-norm of sliding mode variables, then the optimal weight coefficient is obtained by solving the min-max optimization problem. Moreover, for the undirected and directed interval uncertain graphs, two algorithms about the optimal weight coefficients are proposed, respectively. Finally, three numerical simulation examples are presented to demonstrate the effectiveness of the proposed methods.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"38 4","pages":"1084-1108"},"PeriodicalIF":1.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68072256","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 focuses on leader-following and leaderless consensus problems of discrete-time multiagent systems. A distributed observer-based consensus protocol is proposed to investigate the consensus problem for multiagent systems of general discrete-time linear dynamics. By means of the observer, the distributed control law of each agent is designed using local information to guarantee consensus, and the corresponding sufficient conditions are obtained by exploiting graph and control theory approach. A modified distributed event-triggered consensus protocol is designed to reduce communication congestion. Detailed analysis of the leaderless and the leader-following consensus is presented for both observer-based and full-information protocols. Finally, two simulation examples are provided to demonstrate the effectiveness and capabilities of the established theories.
{"title":"Distributed event-triggered consensus protocols for discrete-time multiagent systems","authors":"Bilal J Karaki;Magdi S Mahmoud","doi":"10.1093/imamci/dnab023","DOIUrl":"https://doi.org/10.1093/imamci/dnab023","url":null,"abstract":"This paper focuses on leader-following and leaderless consensus problems of discrete-time multiagent systems. A distributed observer-based consensus protocol is proposed to investigate the consensus problem for multiagent systems of general discrete-time linear dynamics. By means of the observer, the distributed control law of each agent is designed using local information to guarantee consensus, and the corresponding sufficient conditions are obtained by exploiting graph and control theory approach. A modified distributed event-triggered consensus protocol is designed to reduce communication congestion. Detailed analysis of the leaderless and the leader-following consensus is presented for both observer-based and full-information protocols. Finally, two simulation examples are provided to demonstrate the effectiveness and capabilities of the established theories.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"38 4","pages":"1046-1071"},"PeriodicalIF":1.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67895356","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}
For the two-dimensional canonical system, an extended set of bounded finite-time stabilizing positional controls is proposed. For the construction of such controls, which depend on a certain parameter, the Korobov's controllability function method is used. Such an extension is based on the enlarging of the interval of the mentioned parameter, as well as the use of the non-uniqueness of the controllability function for some regions of the phase space ${mathbb R}^2.$ Additionally, we characterize a region of initial conditions $x^0$ on ${mathbb R}^2$ of the given system for which the time of motion from $x^0$ to the origin is less than the value of the controllability function.
{"title":"Extended set of solutions of a bounded finite-time stabilization problem via the controllability function","authors":"A E Choque-Rivero","doi":"10.1093/imamci/dnab028","DOIUrl":"10.1093/imamci/dnab028","url":null,"abstract":"For the two-dimensional canonical system, an extended set of bounded finite-time stabilizing positional controls is proposed. For the construction of such controls, which depend on a certain parameter, the Korobov's controllability function method is used. Such an extension is based on the enlarging of the interval of the mentioned parameter, as well as the use of the non-uniqueness of the controllability function for some regions of the phase space \u0000<tex>${mathbb R}^2.$</tex>\u0000 Additionally, we characterize a region of initial conditions \u0000<tex>$x^0$</tex>\u0000 on \u0000<tex>${mathbb R}^2$</tex>\u0000 of the given system for which the time of motion from \u0000<tex>$x^0$</tex>\u0000 to the origin is less than the value of the controllability function.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"38 4","pages":"1174-1188"},"PeriodicalIF":1.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61174724","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 work, a time-implicit discretization for stochastic linear quadratic problems subject to stochastic differential equations with control-dependence noises is proposed, and the convergence rate of this discretization is proved. Compared to the existing results, the control variables are stochastic processes and can be contained in systems’ diffusion term. Based on this discretization, a gradient descent algorithm and its convergence rate are presented. Finally, a numerical example is provided to support the theoretical finding.
{"title":"Error analysis of a discretization for stochastic linear quadratic control problems governed by SDEs","authors":"Yanqing Wang","doi":"10.1093/imamci/dnab031","DOIUrl":"10.1093/imamci/dnab031","url":null,"abstract":"In this work, a time-implicit discretization for stochastic linear quadratic problems subject to stochastic differential equations with control-dependence noises is proposed, and the convergence rate of this discretization is proved. Compared to the existing results, the control variables are stochastic processes and can be contained in systems’ diffusion term. Based on this discretization, a gradient descent algorithm and its convergence rate are presented. Finally, a numerical example is provided to support the theoretical finding.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"38 4","pages":"1148-1173"},"PeriodicalIF":1.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61174866","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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