Abstract We focus in this paper on determining whether or not a periodic stochastic feedback control based on Lévy noise can stabilize or destabilize a given non-linear hybrid system. Using the Lyapunov functions and the periodic functions, we establish some sufficient conditions on the stability and instability for non-linear hybrid systems with Lévy noise. Moreover, we use some numerical examples and simulations to illustrate that an unstable (or stable) non-linear hybrid system can be stabilized (or destabilized) via periodic stochastic feedback control based on Lévy noise.
{"title":"Stabilization and destabilization of hybrid systems by periodic stochastic controls based on Lévy noise","authors":"Wenrui Li, Weiyin Fei, Yong Liang, Xuerong Mao","doi":"10.1093/imamci/dnad008","DOIUrl":"https://doi.org/10.1093/imamci/dnad008","url":null,"abstract":"Abstract We focus in this paper on determining whether or not a periodic stochastic feedback control based on Lévy noise can stabilize or destabilize a given non-linear hybrid system. Using the Lyapunov functions and the periodic functions, we establish some sufficient conditions on the stability and instability for non-linear hybrid systems with Lévy noise. Moreover, we use some numerical examples and simulations to illustrate that an unstable (or stable) non-linear hybrid system can be stabilized (or destabilized) via periodic stochastic feedback control based on Lévy noise.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135183166","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 feedback stabilization of a class of delayed evolution equations in real Hilbert space is considered. By virtue of an observability-type inequality and a delayed control, sufficient conditions ensuring the strong and weak stabilization are provided. For the strong stabilization, the speed of convergence is successfully established. Various applications with numerical simulations are considered.
{"title":"Polynomial stability and weak stabilization for some partial functional differential equations with delay","authors":"Soufiane Boumasmoud, K. Ezzinbi","doi":"10.1093/imamci/dnad004","DOIUrl":"https://doi.org/10.1093/imamci/dnad004","url":null,"abstract":"\u0000 The feedback stabilization of a class of delayed evolution equations in real Hilbert space is considered. By virtue of an observability-type inequality and a delayed control, sufficient conditions ensuring the strong and weak stabilization are provided. For the strong stabilization, the speed of convergence is successfully established. Various applications with numerical simulations are considered.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"8 1","pages":"152-178"},"PeriodicalIF":1.5,"publicationDate":"2023-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84183257","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 study Nash equilibria for the deterministic ergodic N-players game. We introduce pure strategies, mixed strategies and Nash equilibria associated with those. We show that a Nash equilibrium in mixed strategies exists and it is a Mather measure for the Lagrangian system defined by the cost functional. In conclusion, we show that the mean field limit of the N-players game is described by the ergodic partial differential equation’s system for a continuum of players.
{"title":"Differential N-players game: Nash equilibria and Mather measures","authors":"Cristian Mendico","doi":"10.1093/imamci/dnad006","DOIUrl":"https://doi.org/10.1093/imamci/dnad006","url":null,"abstract":"\u0000 We study Nash equilibria for the deterministic ergodic N-players game. We introduce pure strategies, mixed strategies and Nash equilibria associated with those. We show that a Nash equilibrium in mixed strategies exists and it is a Mather measure for the Lagrangian system defined by the cost functional. In conclusion, we show that the mean field limit of the N-players game is described by the ergodic partial differential equation’s system for a continuum of players.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"18 1","pages":"192-209"},"PeriodicalIF":1.5,"publicationDate":"2023-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89827715","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":"Exponential state estimate of positive systems with time-varying delays: a Lyapunov-Razumikhin approach","authors":"Tran Ngoc Nguyen","doi":"10.1093/imamci/dnad003","DOIUrl":"https://doi.org/10.1093/imamci/dnad003","url":null,"abstract":"","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"40 1","pages":"135-151"},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61176149","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}
It is shown that an oblique projection-based feedback control is able to stabilize the state of the Kuramoto–Sivashinsky equation, evolving in rectangular domains, to a given time-dependent trajectory. The actuators consist of a finite number of indicator functions supported in small subdomains. Simulations are presented, in the one-dimensional case under periodic boundary conditions and in the two-dimensional case under Neumann boundary conditions, showing the stabilizing performance of the feedback control.
{"title":"Feedback semiglobal stabilization to trajectories for the Kuramoto–Sivashinsky equation","authors":"Sérgio S Rodrigues;Dagmawi A Seifu","doi":"10.1093/imamci/dnac033","DOIUrl":"https://doi.org/10.1093/imamci/dnac033","url":null,"abstract":"It is shown that an oblique projection-based feedback control is able to stabilize the state of the Kuramoto–Sivashinsky equation, evolving in rectangular domains, to a given time-dependent trajectory. The actuators consist of a finite number of indicator functions supported in small subdomains. Simulations are presented, in the one-dimensional case under periodic boundary conditions and in the two-dimensional case under Neumann boundary conditions, showing the stabilizing performance of the feedback control.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"40 1","pages":"38-80"},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67841024","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: 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":"40 1","pages":"133-133"},"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":"40 1","pages":"106-132"},"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}
{"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":"88 1","pages":"179-191"},"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 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":"40 1","pages":"20-37"},"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}
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":"40 1","pages":"81-105"},"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}
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