This paper investigates the bipartite tracking control problem for a family of networked multi-agent systems with periodic disturbances as well as input saturation. A low-computation two-bit-triggered adaptive control strategy is proposed to achieve precise trajectory tracking and maintain the boundedness of the closed-loop signals. Compared with the existing results, first, this paper considers the problems for the coexistence of cooperation and competition in multi-agent systems, which represents a more common situation; secondly, the explosion of complexity issue is avoided without introducing any auxiliary filters, making our result more applicable and less complex; thirdly, a function approximator incorporating Fourier series expansion and a radial basis function neural network is utilized to model time-varying periodic disturbance functions and lastly, unlike traditional event-triggered control, the issue of controlling signal transmission bits is further explored to conserve system transmission resources. The result from a comparative simulation illustrates the advantages of the proposed method.
{"title":"Adaptive saturated two-bit-triggered bipartite consensus control for networked MASs with periodic disturbances: a low-computation method","authors":"Wenjing Wu, Liang Zhang, Yuhang Wu, Heng Zhao","doi":"10.1093/imamci/dnae002","DOIUrl":"https://doi.org/10.1093/imamci/dnae002","url":null,"abstract":"This paper investigates the bipartite tracking control problem for a family of networked multi-agent systems with periodic disturbances as well as input saturation. A low-computation two-bit-triggered adaptive control strategy is proposed to achieve precise trajectory tracking and maintain the boundedness of the closed-loop signals. Compared with the existing results, first, this paper considers the problems for the coexistence of cooperation and competition in multi-agent systems, which represents a more common situation; secondly, the explosion of complexity issue is avoided without introducing any auxiliary filters, making our result more applicable and less complex; thirdly, a function approximator incorporating Fourier series expansion and a radial basis function neural network is utilized to model time-varying periodic disturbance functions and lastly, unlike traditional event-triggered control, the issue of controlling signal transmission bits is further explored to conserve system transmission resources. The result from a comparative simulation illustrates the advantages of the proposed method.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"18 2 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139980571","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 stability problem of Multiple n Inputs and Multiple n Outputs (MIMOn) cascade non-linear systems with random parameters is considered in this paper using the probability of stability estimation method. MIMOn cascade non-linear systems, particularly when the number of inputs and outputs exceeds three (n > 3), exhibit a unique property: the appearance of spatial hyperchaos that can lead to system instability. To achieve desired spatial dynamics and prevent the occurrence of spatial hyperchaos, it is necessary to select the appropriate parameter values for these systems. Moreover, the optimal parameter values enable the attainment of the highest probability of stability for stochastic MIMOn systems. The research presents the results of stability analysis using tools such as bifurcation diagram, Lyapunov diagram and spatial phase portraits, generated through MATLAB M-files, with a specific focus on a stochastic MIMO5 system (five inputs and five outputs).
本文采用稳定性概率估计方法，研究了具有随机参数的多 n 输入和多 n 输出（MIMOn）级联非线性系统的稳定性问题。MIMOn 级联非线性系统，尤其是当输入和输出的数量超过三个（n > 3）时，会表现出一种独特的特性：出现空间超混沌，从而导致系统不稳定。为了实现理想的空间动力学并防止出现空间超混沌，有必要为这些系统选择合适的参数值。此外，最佳参数值能使随机 MIMOn 系统达到最高的稳定性概率。本研究介绍了使用分岔图、Lyapunov 图和空间相位肖像等工具进行稳定性分析的结果，这些工具是通过 MATLAB M 文件生成的，重点是随机 MIMO5 系统（五个输入和五个输出）。
{"title":"Probability of stability calculation of MIMOn cascade non-linear systems with random parameters","authors":"Bojana M Zlatkovic, Biljana Samardzic","doi":"10.1093/imamci/dnae005","DOIUrl":"https://doi.org/10.1093/imamci/dnae005","url":null,"abstract":"The stability problem of Multiple n Inputs and Multiple n Outputs (MIMOn) cascade non-linear systems with random parameters is considered in this paper using the probability of stability estimation method. MIMOn cascade non-linear systems, particularly when the number of inputs and outputs exceeds three (n > 3), exhibit a unique property: the appearance of spatial hyperchaos that can lead to system instability. To achieve desired spatial dynamics and prevent the occurrence of spatial hyperchaos, it is necessary to select the appropriate parameter values for these systems. Moreover, the optimal parameter values enable the attainment of the highest probability of stability for stochastic MIMOn systems. The research presents the results of stability analysis using tools such as bifurcation diagram, Lyapunov diagram and spatial phase portraits, generated through MATLAB M-files, with a specific focus on a stochastic MIMO5 system (five inputs and five outputs).","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"14 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139980591","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 observed that the reduced-order models (ROMs) by some existing limited Gramians-based techniques deviate significantly from the high-order model, resulting in a large approximation inaccuracy. Therefore, this paper introduces a novel solution for finite-frequency model reduction using new frequency-weighted Gramians by employing balanced truncation. This work provides a novel structure of fictitious input and output matrices, resulting in the proposed continuous-time system Gramians. The suggested strategy provides stable ROMs even when input and output weightings are incorporated into the system. Furthermore, the proposed approach is extended with the frequency-interval Gramians, ensuring stable ROMs. The proposed simulation outcomes are compared with other well-known frequency-weighted and frequency-interval Gramians-based techniques using numerical examples to demonstrate the efficacy of the suggested strategies.
{"title":"Frequency-weighted and frequency interval Gramian framework-based model reduction using singular value decomposition","authors":"Vineet Sharma, Deepak Kumar","doi":"10.1093/imamci/dnad036","DOIUrl":"https://doi.org/10.1093/imamci/dnad036","url":null,"abstract":"It is observed that the reduced-order models (ROMs) by some existing limited Gramians-based techniques deviate significantly from the high-order model, resulting in a large approximation inaccuracy. Therefore, this paper introduces a novel solution for finite-frequency model reduction using new frequency-weighted Gramians by employing balanced truncation. This work provides a novel structure of fictitious input and output matrices, resulting in the proposed continuous-time system Gramians. The suggested strategy provides stable ROMs even when input and output weightings are incorporated into the system. Furthermore, the proposed approach is extended with the frequency-interval Gramians, ensuring stable ROMs. The proposed simulation outcomes are compared with other well-known frequency-weighted and frequency-interval Gramians-based techniques using numerical examples to demonstrate the efficacy of the suggested strategies.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"35 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139904173","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 article, we study the output regulation of two coupled heat equations with recycle, where the disturbances are distributed in all channels, the control is implemented at the left boundary $x=0$ and the point temperature at $x=2$ is the only noncollocated measurement. The output control is divided into two parts: one is to stabilize the unstable heat system by the noncollocated static feedback, and the other is to achieve output regulation by solving the regulator equation and estimating the disturbances, where an observer is constructed to estimate the state of heat system and exosystem synchronously. The closed-loop system is proved to be well-posed and uniformly bounded using the Riesz basis approach, and the integral output tracks successfully the reference signal exponentially. The numerical simulations are carried out to demonstrate the proposed controller is effective and the tracking error converges to zero.
{"title":"Performance output regulation of coupled heat equations with recycle","authors":"Xiu-Fang Yu, Jun-Min Wang, Xiao-Hui Wu","doi":"10.1093/imamci/dnae001","DOIUrl":"https://doi.org/10.1093/imamci/dnae001","url":null,"abstract":"In this article, we study the output regulation of two coupled heat equations with recycle, where the disturbances are distributed in all channels, the control is implemented at the left boundary $x=0$ and the point temperature at $x=2$ is the only noncollocated measurement. The output control is divided into two parts: one is to stabilize the unstable heat system by the noncollocated static feedback, and the other is to achieve output regulation by solving the regulator equation and estimating the disturbances, where an observer is constructed to estimate the state of heat system and exosystem synchronously. The closed-loop system is proved to be well-posed and uniformly bounded using the Riesz basis approach, and the integral output tracks successfully the reference signal exponentially. The numerical simulations are carried out to demonstrate the proposed controller is effective and the tracking error converges to zero.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"19 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139754668","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}
Absolute stability criteria that are sufficient for global exponential stability are shown, under a Lipschitz assumption, to be sufficient for the a priori stronger exponential input-to-state stability property. Important corollaries of this result are as follows: (i) absolute stability results obtained using Zames–Falb multipliers for systems containing slope-restricted nonlinearities provide exponential input-to-state-stability under a mild detectability assumption; and (ii) more generally, many absolute stability results obtained via Integral Quadratic Constraint methods provide, with the additional Lipschitz assumption, this stronger property.
在 Lipschitz 假设下，对全局指数稳定性来说足够的绝对稳定性标准被证明对更强的先验指数输入到状态稳定性特性来说也足够了。这一结果的重要推论如下：(i) 对于包含斜率受限非线性的系统，使用 Zames-Falb 乘法器得到的绝对稳定性结果在温和的可探测性假设下提供了指数输入到状态稳定性；以及 (ii) 更一般地说，通过积分二次约束方法得到的许多绝对稳定性结果在额外的 Lipschitz 假设下提供了这种更强的性质。
{"title":"Exponential input-to-state stability for Lur’e systems via Integral Quadratic Constraints and Zames–Falb multipliers","authors":"Ross Drummond, Chris Guiver, Matthew C Turner","doi":"10.1093/imamci/dnae003","DOIUrl":"https://doi.org/10.1093/imamci/dnae003","url":null,"abstract":"Absolute stability criteria that are sufficient for global exponential stability are shown, under a Lipschitz assumption, to be sufficient for the a priori stronger exponential input-to-state stability property. Important corollaries of this result are as follows: (i) absolute stability results obtained using Zames–Falb multipliers for systems containing slope-restricted nonlinearities provide exponential input-to-state-stability under a mild detectability assumption; and (ii) more generally, many absolute stability results obtained via Integral Quadratic Constraint methods provide, with the additional Lipschitz assumption, this stronger property.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"4 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139754564","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 event-triggered formation control of first-order continuous multi-agent systems is studied based on complex Laplacian in this paper. Periodic event-triggered control is designed in which continuous communication between agents is not required. For each agent, two different triggering conditions are discussed. The first one relies on the inter-neighboring communication at each verification time, while the second one only need the broadcast states of neighbors at their triggering instants. According to the Lyapunov stability theory and algebraic graph theory, consensus conditions on the verification period and parameters in the triggering conditions are also provided. It is demonstrated that the maximum verification period under two triggering conditions are two times larger than the existing results. And a certain amount of communication between neighbors can be further reduced in the second one. Finally, the simulation examples prove the validity of the results proposed.
{"title":"Periodic event-triggered formation control of multi-agent systems via complex Laplacian","authors":"Xiaoya Guo, Xia Chen, Lu Fu","doi":"10.1093/imamci/dnad035","DOIUrl":"https://doi.org/10.1093/imamci/dnad035","url":null,"abstract":"The event-triggered formation control of first-order continuous multi-agent systems is studied based on complex Laplacian in this paper. Periodic event-triggered control is designed in which continuous communication between agents is not required. For each agent, two different triggering conditions are discussed. The first one relies on the inter-neighboring communication at each verification time, while the second one only need the broadcast states of neighbors at their triggering instants. According to the Lyapunov stability theory and algebraic graph theory, consensus conditions on the verification period and parameters in the triggering conditions are also provided. It is demonstrated that the maximum verification period under two triggering conditions are two times larger than the existing results. And a certain amount of communication between neighbors can be further reduced in the second one. Finally, the simulation examples prove the validity of the results proposed.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"137 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139588821","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 focus on the topic of model order reduction (MOR) for coupled systems. At first, an approximation via Laguerre polynomials expansions to controllability and observability gramians for such systems are presented, which provides a low-rank decomposition form whose factors are constructed from a recurrence formula instead of Lyapunov equations. Then, in combination of balanced truncation and dominant subspace projection method, a series of MOR algorithms are proposed that preserve the coupled structures. What’s more, some main properties of reduced-order models, such as stability preservation, are well discussed. Finally, three numerical simulations are provided to illustrate the effectiveness of our algorithms.
本文重点讨论耦合系统的模型阶次缩减（MOR）问题。首先，本文提出了一种通过拉盖尔多项式展开对此类系统的可控性和可观测性格兰进行近似的方法，它提供了一种低阶分解形式，其因子由递推公式而非 Lyapunov 方程构建。然后，结合平衡截断法和优势子空间投影法，提出了一系列保留耦合结构的 MOR 算法。此外，还充分讨论了减阶模型的一些主要特性，如稳定性保持等。最后，我们提供了三个数值模拟来说明我们算法的有效性。
{"title":"Dimension reduction based on approximate gramians via Laguerre polynomials for coupled systems","authors":"Zhen-Zhong Qi, Zhi-Hua Xiao, Jia-Wei Yuan","doi":"10.1093/imamci/dnad034","DOIUrl":"https://doi.org/10.1093/imamci/dnad034","url":null,"abstract":"In this paper, we focus on the topic of model order reduction (MOR) for coupled systems. At first, an approximation via Laguerre polynomials expansions to controllability and observability gramians for such systems are presented, which provides a low-rank decomposition form whose factors are constructed from a recurrence formula instead of Lyapunov equations. Then, in combination of balanced truncation and dominant subspace projection method, a series of MOR algorithms are proposed that preserve the coupled structures. What’s more, some main properties of reduced-order models, such as stability preservation, are well discussed. Finally, three numerical simulations are provided to illustrate the effectiveness of our algorithms.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"17 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139475197","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, by the transformation form of the discrete algebraic Riccati equation (DARE), we propose a new inverse-free iterative algorithm to obtain the positive definite solution of the DARE. Furthermore, the monotone convergence is proved and convergence rate analysis is presented for the derived algorithm. Compared with some existing algorithms, numerical examples demonstrate the feasibility and effectiveness of our algorithm.
{"title":"A new inversion-free iterative algorithm for the discrete algebraic Riccati equation","authors":"Li Wang, Yuli Zhu","doi":"10.1093/imamci/dnad033","DOIUrl":"https://doi.org/10.1093/imamci/dnad033","url":null,"abstract":"\u0000 In this paper, by the transformation form of the discrete algebraic Riccati equation (DARE), we propose a new inverse-free iterative algorithm to obtain the positive definite solution of the DARE. Furthermore, the monotone convergence is proved and convergence rate analysis is presented for the derived algorithm. Compared with some existing algorithms, numerical examples demonstrate the feasibility and effectiveness of our algorithm.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"25 16","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138955102","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}
Florentina Nicolau, Hugues Mounier, Ioannis P Androulakis
In this paper, we study several existing quantitative models of the hypothalamic–pituitary–adrenal (HPA) axis from a control systems theory viewpoint, that is, we suppose that we can act on the dynamics of the HPA axis throughout some parameters, which are the system inputs. In particular, we will focus on flatness and Liouvillian properties of the considered control systems of the HPA axis. We first study the minimal three-dimensional model of Bangsgaard and Ottesen (2017, Math. Biosci., 287:24–35) and the semi-mechanistic four-dimensional model of Gupta et al. (2007, Theor. Biol. Medical Model., 4(1):8) which are shown to be flat, and then, we consider the more involved and important model proposed in Rao & Androulakis (2019, Sci. Rep., 9(1):11212; 2020, IFAC-PapersOnLine, 53(2):15858–15863), with seven states, for which we prove that for the nominal values of the parameters involved in the model, flatness no longer holds. The more involved model satisfies however a similar but weaker property than flatness: it is a Liouvillian system.
本文从控制系统理论的角度研究了几种现有的下丘脑-垂体-肾上腺(HPA)轴的定量模型，即假设我们可以通过作为系统输入的某些参数来作用于HPA轴的动力学。特别地，我们将关注所考虑的HPA轴控制系统的平面性和Liouvillian性质。我们首先研究了Bangsgaard和Ottesen(2017，数学)的最小三维模型。Biosci。Gupta et al. (2007, theory .)的半机械四维模型。医学杂志。医学模式。， 4(1):8)表明是平坦的，然后，我们考虑Rao &Androulakis (2019, Sci。代表,9 (1):11212;2020，中国机械工程学报，53(2):15858-15863)，我们证明了对于模型中涉及的参数的标称值，平坦性不再成立。然而，更复杂的模型满足一个与平面性相似但较弱的性质:它是一个刘维系统。
{"title":"HPA axis differential flatness and Liouvillian study for higher resiliency investigations","authors":"Florentina Nicolau, Hugues Mounier, Ioannis P Androulakis","doi":"10.1093/imamci/dnad030","DOIUrl":"https://doi.org/10.1093/imamci/dnad030","url":null,"abstract":"In this paper, we study several existing quantitative models of the hypothalamic–pituitary–adrenal (HPA) axis from a control systems theory viewpoint, that is, we suppose that we can act on the dynamics of the HPA axis throughout some parameters, which are the system inputs. In particular, we will focus on flatness and Liouvillian properties of the considered control systems of the HPA axis. We first study the minimal three-dimensional model of Bangsgaard and Ottesen (2017, Math. Biosci., 287:24–35) and the semi-mechanistic four-dimensional model of Gupta et al. (2007, Theor. Biol. Medical Model., 4(1):8) which are shown to be flat, and then, we consider the more involved and important model proposed in Rao & Androulakis (2019, Sci. Rep., 9(1):11212; 2020, IFAC-PapersOnLine, 53(2):15858–15863), with seven states, for which we prove that for the nominal values of the parameters involved in the model, flatness no longer holds. The more involved model satisfies however a similar but weaker property than flatness: it is a Liouvillian system.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"29 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138537973","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 study presents a novel approach for the state and output feedback exponential control of cascaded unstable ODE-wave equations with nonlinear boundary condition. The new approach can be also used to investigate the state and output feedback stabilization of other cascaded ODE-partial differential equation (PDE) systems with nonlinear boundary condition. The interconnection between the ODE and wave PDE with the nonlinear boundary is bi-directional at two points. First, an exponential controller is planned and the well-posed and exponential stability of the closed-loop system is derived. Next, an exponential observer is designed, whereby the exponential stability of the overall error system is shown. Then, an observer-based output feedback control that causes the overall real system to be exponentially stable is built. The existence and exponential stability of the solution to the overall closed-loop system are further deduced. Finally, simulation results are given to verify the effectiveness, feasibility and validity of the proposed technique.
{"title":"On a new method for the state and output feedback exponential stabilization of a cascaded wave PDE-ODE system with nonlinear boundary condition","authors":"Najmeh Ghaderi","doi":"10.1093/imamci/dnad027","DOIUrl":"https://doi.org/10.1093/imamci/dnad027","url":null,"abstract":"Abstract This study presents a novel approach for the state and output feedback exponential control of cascaded unstable ODE-wave equations with nonlinear boundary condition. The new approach can be also used to investigate the state and output feedback stabilization of other cascaded ODE-partial differential equation (PDE) systems with nonlinear boundary condition. The interconnection between the ODE and wave PDE with the nonlinear boundary is bi-directional at two points. First, an exponential controller is planned and the well-posed and exponential stability of the closed-loop system is derived. Next, an exponential observer is designed, whereby the exponential stability of the overall error system is shown. Then, an observer-based output feedback control that causes the overall real system to be exponentially stable is built. The existence and exponential stability of the solution to the overall closed-loop system are further deduced. Finally, simulation results are given to verify the effectiveness, feasibility and validity of the proposed technique.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134905561","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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