G Sangeetha, K Mathiyalagan, Yong-Ki Ma, Huiyan Zhang
Abstract This work addresses the problem of sliding mode control (SMC) design for a continuous-time non-linear stochastic system with Levy-type noise. A state observer model is constructed to estimate the unavailable state information. Furthermore, Levy-type noise is considered to analyse small perturbations and to characterize the appearance of large samples that will occur in the system. Lyapunov stability and SMC theory are used to provide some sufficient conditions that ensure the stochastic stability of the error system and reachability of the predefined sliding surface. Finally, an example is given to demonstrate the feasibility of the proposed approach.
{"title":"Observer-based SMC design for stochastic systems with Levy noise","authors":"G Sangeetha, K Mathiyalagan, Yong-Ki Ma, Huiyan Zhang","doi":"10.1093/imamci/dnad028","DOIUrl":"https://doi.org/10.1093/imamci/dnad028","url":null,"abstract":"Abstract This work addresses the problem of sliding mode control (SMC) design for a continuous-time non-linear stochastic system with Levy-type noise. A state observer model is constructed to estimate the unavailable state information. Furthermore, Levy-type noise is considered to analyse small perturbations and to characterize the appearance of large samples that will occur in the system. Lyapunov stability and SMC theory are used to provide some sufficient conditions that ensure the stochastic stability of the error system and reachability of the predefined sliding surface. Finally, an example is given to demonstrate the feasibility of the proposed approach.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135823410","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}
Abstract We consider tracking control of linear minimum phase systems with known arbitrary relative degree which are subject to possible output measurement losses. We provide a control law which guarantees the evolution of the tracking error within a (shifted) prescribed performance funnel whenever the output signal is available. The result requires a maximal duration of measurement losses and a minimal time of measurement availability, which both strongly depend on the internal dynamics of the system, and are derived explicitly. The controller is illustrated by a simulation of a mass-on-car system.
{"title":"Funnel control of linear systems with arbitrary relative degree under output measurement losses","authors":"Thomas Berger, Lukas Lanza","doi":"10.1093/imamci/dnad029","DOIUrl":"https://doi.org/10.1093/imamci/dnad029","url":null,"abstract":"Abstract We consider tracking control of linear minimum phase systems with known arbitrary relative degree which are subject to possible output measurement losses. We provide a control law which guarantees the evolution of the tracking error within a (shifted) prescribed performance funnel whenever the output signal is available. The result requires a maximal duration of measurement losses and a minimal time of measurement availability, which both strongly depend on the internal dynamics of the system, and are derived explicitly. The controller is illustrated by a simulation of a mass-on-car system.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135823402","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}
Abstract This paper studies the problems of both state estimation and observer-based control for a class of switched linear systems with stable and unstable subsystems. By combining slow switching and fast switching mechanism, the observer design and observer-based controller are presented. Firstly, a state observer is developed to estimate the states of switched system by designing admissible edge-dependent switching signal, and a multiple discontinuous Lyapunov function is also constructed to obtain the existence condition of observer. Secondly, based on the stability characteristics of subsystem and the estimated state information, an observer-based feedback controller is proposed. The stability of the closed-loop system is also guaranteed by Lyapunov stability theory. Finally, the feasibility of the proposed method is verified by simulation.
{"title":"Observer-based controller design for switched systems with stable and unstable subsystems","authors":"Donglei Xie, Yantao Chen, Ying Qiao","doi":"10.1093/imamci/dnad026","DOIUrl":"https://doi.org/10.1093/imamci/dnad026","url":null,"abstract":"Abstract This paper studies the problems of both state estimation and observer-based control for a class of switched linear systems with stable and unstable subsystems. By combining slow switching and fast switching mechanism, the observer design and observer-based controller are presented. Firstly, a state observer is developed to estimate the states of switched system by designing admissible edge-dependent switching signal, and a multiple discontinuous Lyapunov function is also constructed to obtain the existence condition of observer. Secondly, based on the stability characteristics of subsystem and the estimated state information, an observer-based feedback controller is proposed. The stability of the closed-loop system is also guaranteed by Lyapunov stability theory. Finally, the feasibility of the proposed method is verified by simulation.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136213029","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}
Abstract This paper studies the control problem for vehicle platoons under switching communication topologies, where the Predecessor-Following (PF)-failure topology is allowed. Firstly, we design a local optimization problem for each vehicle by using the state information of itself and its neighbouring vehicles, and then present Algorithm 1 based on Distributed Model Predictive Control (DMPC). By constructing a common Lyapunov function defined by the joint neighbourhood set, we derive sufficient conditions with respect to the weight matrices in the open-loop optimization problem and the switching topologies for ensuring the stability of the closed-loop system under Algorithm 1. Furthermore, we propose Algorithm 2 by introducing novel constraints into the local optimization problem for each vehicle, which utilize shrinking historical position errors to cope with PF-link failures, such that the string stability of the vehicle platoon is ensured. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed DMPC algorithms for the vehicel platoon under switching communication topologies.
{"title":"Distributed model predictive control of vehicle platoons under switching communication topologies","authors":"Liang Chen, Jingyuan Zhan, Liguo Zhang","doi":"10.1093/imamci/dnad023","DOIUrl":"https://doi.org/10.1093/imamci/dnad023","url":null,"abstract":"Abstract This paper studies the control problem for vehicle platoons under switching communication topologies, where the Predecessor-Following (PF)-failure topology is allowed. Firstly, we design a local optimization problem for each vehicle by using the state information of itself and its neighbouring vehicles, and then present Algorithm 1 based on Distributed Model Predictive Control (DMPC). By constructing a common Lyapunov function defined by the joint neighbourhood set, we derive sufficient conditions with respect to the weight matrices in the open-loop optimization problem and the switching topologies for ensuring the stability of the closed-loop system under Algorithm 1. Furthermore, we propose Algorithm 2 by introducing novel constraints into the local optimization problem for each vehicle, which utilize shrinking historical position errors to cope with PF-link failures, such that the string stability of the vehicle platoon is ensured. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed DMPC algorithms for the vehicel platoon under switching communication topologies.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135738731","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}
Sheng Gao, Hailong Zhang, Weiguo Kong, Zhaoguang Wang
Abstract This study investigates the fault estimation problem for a class of Lipschitz non-linear systems with sensor faults and disturbances. An augmented system consisting of system states and sensor faults is constructed to estimate sensor faults by designing an augmented state. A novel L∞ performance index is presented to reduce the influence of disturbances on fault estimation results. An unknown input observer (UIO) is proposed based on the L∞ performance index to achieve an asymptotic estimation of sensor faults. The design conditions of the L∞ UIO are deduced and solved using linear matrix inequalities. The effectiveness of the proposed L∞ UIO and the fault estimation performance are demonstrated via numerical simulations of a single-link flexible joint robot.
{"title":"Sensor fault estimation based on <i>L</i>∞ unknown input observer","authors":"Sheng Gao, Hailong Zhang, Weiguo Kong, Zhaoguang Wang","doi":"10.1093/imamci/dnad024","DOIUrl":"https://doi.org/10.1093/imamci/dnad024","url":null,"abstract":"Abstract This study investigates the fault estimation problem for a class of Lipschitz non-linear systems with sensor faults and disturbances. An augmented system consisting of system states and sensor faults is constructed to estimate sensor faults by designing an augmented state. A novel L∞ performance index is presented to reduce the influence of disturbances on fault estimation results. An unknown input observer (UIO) is proposed based on the L∞ performance index to achieve an asymptotic estimation of sensor faults. The design conditions of the L∞ UIO are deduced and solved using linear matrix inequalities. The effectiveness of the proposed L∞ UIO and the fault estimation performance are demonstrated via numerical simulations of a single-link flexible joint robot.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136375872","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}
Hamid Maarouf, Lahcen Maniar, Ilham Ouelddris, Jawad Salhi
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.
摘要本文研究了在脉冲控制作用下退化奇异抛物型方程的零近似可控性。为此，我们证明了与算子:$$ begin{align*}& u_{t} -(x^{alpha} u_{x})_{x} - dfrac{mu}{x^{beta}} u = 0, qquad x in left(0, 1right), end{align*} $$相关的问题在一个时间点的观测估计，其中参数$alpha geq 0$, $beta , mu in mathbb{R}$满足适当的假设。证明方法结合了对数凸性和卡尔曼对易子。
{"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":"64 1","pages":"0"},"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}
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.
{"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":" ","pages":""},"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}
B. Hernández-Galván, Jesus R. Pulido-Luna, N. Cázarez-Castro, G. Fernández-Anaya, J. López-Rentería
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.
{"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":" ","pages":""},"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}
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.
{"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":" ","pages":""},"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}
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.
{"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":" ","pages":""},"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}
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