The main contribution of this paper is the development of $H_{infty }$ state and unknown input (UI) observers for noisy linear parameter-varying (LPV) systems. The observers are constructed in order to be unbiased (in particular the state estimation error is decoupled from the UI) and with a minimum $L_{2}$ transfer between the perturbations (that are assumed to be with finite energy) and the estimation errors. Contrary to equivalent observers developed in the literature, the present one relaxes a widely used rank condition on the system matrices for decoupling the UI. In order to do so, high-order derivation is needed, which is done using a high-order sliding modes differentiator. A method is given to design observer gains for LPV systems under polytopic form. Finally, three examples illustrate some aspects of the theoretical contributions, and compare this work to the existing ones.
{"title":"A new H∞ observer for continuous LPV systems with unknown inputs using an HOSM differentiator","authors":"Luc Meyer","doi":"10.1093/imamci/dnae008","DOIUrl":"https://doi.org/10.1093/imamci/dnae008","url":null,"abstract":"The main contribution of this paper is the development of $H_{infty }$ state and unknown input (UI) observers for noisy linear parameter-varying (LPV) systems. The observers are constructed in order to be unbiased (in particular the state estimation error is decoupled from the UI) and with a minimum $L_{2}$ transfer between the perturbations (that are assumed to be with finite energy) and the estimation errors. Contrary to equivalent observers developed in the literature, the present one relaxes a widely used rank condition on the system matrices for decoupling the UI. In order to do so, high-order derivation is needed, which is done using a high-order sliding modes differentiator. A method is given to design observer gains for LPV systems under polytopic form. Finally, three examples illustrate some aspects of the theoretical contributions, and compare this work to the existing ones.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140302631","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 deals with a hierarchical control problem for the heat equation with dynamic boundary conditions. The main goal consists of letting the state near from a prescribed target in a fixed observation region. The secondary objective is the null controllability. In other words, we reverse the roles of the leader and the follower addressed in the recent article. For this purpose, we combine some appropriate Carleman estimates and the Stackelberg strategy. We also extend our study for hierarchical-biobjective problems by applying the Stackelberg–Pareto strategy.
{"title":"Hierarchical control problem for the heat equation with dynamic boundary conditions","authors":"Omar Oukdach, Idriss Boutaayamou, Lahcen Maniar","doi":"10.1093/imamci/dnae009","DOIUrl":"https://doi.org/10.1093/imamci/dnae009","url":null,"abstract":"This paper deals with a hierarchical control problem for the heat equation with dynamic boundary conditions. The main goal consists of letting the state near from a prescribed target in a fixed observation region. The secondary objective is the null controllability. In other words, we reverse the roles of the leader and the follower addressed in the recent article. For this purpose, we combine some appropriate Carleman estimates and the Stackelberg strategy. We also extend our study for hierarchical-biobjective problems by applying the Stackelberg–Pareto strategy.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140302797","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}
Based on dissipativity theory, the consensus via iterative learning control (ILC) is investigated for P-one-sided Lipschitz (P-OSL) nonlinear multi-agent systems (MASs). This paper only considers the P-OSL condition without using the quadratically inner-bounded constraint. Firstly, the ILC protocol is designed for such nonlinear MASs. Then, the convergence conditions of the consensus algorithm under a connected communication graph are presented from the viewpoint of dissipativity. It is shown that, on a fixed finite-time interval, the proposed algorithm can achieve perfect consensus tracking. Finally, two examples are constructed to show the effectiveness of the proposed method.
{"title":"Dissipativity-based consensus for P-one-sided Lipschitz multi-agent systems via ILC","authors":"Panpan Gu, Shiji Zhao, Liping Chen, Yong Lin, Jiajia Wang, Senping Tian","doi":"10.1093/imamci/dnae007","DOIUrl":"https://doi.org/10.1093/imamci/dnae007","url":null,"abstract":"Based on dissipativity theory, the consensus via iterative learning control (ILC) is investigated for P-one-sided Lipschitz (P-OSL) nonlinear multi-agent systems (MASs). This paper only considers the P-OSL condition without using the quadratically inner-bounded constraint. Firstly, the ILC protocol is designed for such nonlinear MASs. Then, the convergence conditions of the consensus algorithm under a connected communication graph are presented from the viewpoint of dissipativity. It is shown that, on a fixed finite-time interval, the proposed algorithm can achieve perfect consensus tracking. Finally, two examples are constructed to show the effectiveness of the proposed method.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140098563","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 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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
{"title":"Correction to: On exponential stability in mean square of nonlinear delay differential equations with Markovian switching","authors":"","doi":"10.1093/imamci/dnae004","DOIUrl":"https://doi.org/10.1093/imamci/dnae004","url":null,"abstract":"","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139805037","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":null,"pages":null},"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}
{"title":"Correction to: On exponential stability in mean square of nonlinear delay differential equations with Markovian switching","authors":"","doi":"10.1093/imamci/dnae004","DOIUrl":"https://doi.org/10.1093/imamci/dnae004","url":null,"abstract":"","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139864757","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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