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On real and observable rational realizations of input–output equations 关于投入产出方程的实的和可观察的理性实现
IF 2.1 3区 计算机科学
Systems & Control Letters Pub Date : 2025-03-05 DOI: 10.1016/j.sysconle.2025.106059
Sebastian Falkensteiner , Dmitrii Pavlov , J. Rafael Sendra
{"title":"On real and observable rational realizations of input–output equations","authors":"Sebastian Falkensteiner ,&nbsp;Dmitrii Pavlov ,&nbsp;J. Rafael Sendra","doi":"10.1016/j.sysconle.2025.106059","DOIUrl":"10.1016/j.sysconle.2025.106059","url":null,"abstract":"<div><div>Given a single (differential–algebraic) input–output equation, we present a method for finding different representations of the associated system in the form of rational realizations; these are dynamical systems with rational right-hand sides. It has been shown that in the case where the input–output equation is of order one, rational realizations can be computed, if they exist. In this work, we focus first on the existence and actual computation of the so-called observable rational realizations, and secondly on rational realizations with real coefficients. The study of observable realizations allows to find every rational realization of a given first order input–output equation, and the necessary field extensions in this process. We show that for first order input–output equations the existence of a rational realization is equivalent to the existence of an observable rational realization. Moreover, we give a criterion to decide the existence of real rational realizations. The computation of observable and real realizations of first order input–output equations is fully algorithmic. We also present partial results for the case of higher order input–output equations.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"198 ","pages":"Article 106059"},"PeriodicalIF":2.1,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143549470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Left-coprimeness condition for the reachability in finite time of pseudo-rational systems of order zero with an application to difference delay systems 零阶伪有理系统有限时间可达性的左互素性条件及其在差分时滞系统上的应用
IF 2.1 3区 计算机科学
Systems & Control Letters Pub Date : 2025-02-25 DOI: 10.1016/j.sysconle.2025.106051
Sébastien Fueyo
{"title":"Left-coprimeness condition for the reachability in finite time of pseudo-rational systems of order zero with an application to difference delay systems","authors":"Sébastien Fueyo","doi":"10.1016/j.sysconle.2025.106051","DOIUrl":"10.1016/j.sysconle.2025.106051","url":null,"abstract":"<div><div>This paper investigates the finite-time reachability of pseudo-rational systems of order zero. A bound on the minimal time for reachability is derived, and the reachability property for integrable functions is characterized using a left-coprimeness condition. The results are further applied to difference delay systems with distributed delays.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"198 ","pages":"Article 106051"},"PeriodicalIF":2.1,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143487903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Partially observed linear quadratic stochastic optimal control problem in infinite horizon: A data-driven approach 无限视界部分观测线性二次型随机最优控制问题：数据驱动方法
IF 2.1 3区 计算机科学
Systems & Control Letters Pub Date : 2025-02-24 DOI: 10.1016/j.sysconle.2025.106050
Xun Li , Guangchen Wang , Jie Xiong , Heng Zhang
{"title":"Partially observed linear quadratic stochastic optimal control problem in infinite horizon: A data-driven approach","authors":"Xun Li ,&nbsp;Guangchen Wang ,&nbsp;Jie Xiong ,&nbsp;Heng Zhang","doi":"10.1016/j.sysconle.2025.106050","DOIUrl":"10.1016/j.sysconle.2025.106050","url":null,"abstract":"<div><div>This paper develops a data-driven algorithm to solve an infinite-horizon partially observed linear quadratic stochastic optimal control problem. The optimal control of this problem is related to an algebraic Riccati equation (ARE) and a filtering equation. First, we prove that the solution of a Riccati-type ordinary differential equation (ODE) converges to the unique positive semidefinite solution of the ARE. Next, we establish some data-based relationships among the system input, the system state and certain matrices that appear in the Riccati-type ODE and the filtering equation. Then, using these relationships, we design a data-driven algorithm to approximate the positive semidefinite solution of the ARE and the optimal control. The main feature of this algorithm is that it does not need the information of two system coefficients. Finally, we prove the convergence of the obtained algorithm and demonstrate its effectiveness by simulating a concrete example.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"198 ","pages":"Article 106050"},"PeriodicalIF":2.1,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Design of low-dimensional controllers for high-dimensional systems 高维系统的低维控制器设计
IF 2.1 3区 计算机科学
Systems & Control Letters Pub Date : 2025-02-21 DOI: 10.1016/j.sysconle.2025.106049
Mathieu Bajodek, Hugo Lhachemi, Giorgio Valmorbida
{"title":"Design of low-dimensional controllers for high-dimensional systems","authors":"Mathieu Bajodek,&nbsp;Hugo Lhachemi,&nbsp;Giorgio Valmorbida","doi":"10.1016/j.sysconle.2025.106049","DOIUrl":"10.1016/j.sysconle.2025.106049","url":null,"abstract":"<div><div>This article presents proposals for the design of reduced-order controllers for high-dimensional dynamical systems. The objective is to develop efficient control strategies that ensure stability and robustness with reduced computational complexity. By leveraging the concept of partial pole placement, which involves placing a subset of the closed-loop system’s poles, this study aims to strike a balance between reduced-order modeling and control effectiveness. The proposed approach addresses the challenges posed by high-dimensional systems and provides a systematic framework for controller design. When an infinite-dimensional operator is Riesz spectral, our theoretical analysis highlights the potential of partial pole placement in advancing control design. Model uncertainties, introduced by an error in the spectral decomposition, can also be allowed. This is particularly illustrated in the case of systems modeled by coupled ordinary-partial differential equations (ODE-PDE).</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"198 ","pages":"Article 106049"},"PeriodicalIF":2.1,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The shortest experiment for linear system identification 线性系统辨识的最短实验
IF 2.1 3区 计算机科学
Systems & Control Letters Pub Date : 2025-02-20 DOI: 10.1016/j.sysconle.2025.106045
M.K. Camlibel , H.J. van Waarde , P. Rapisarda
{"title":"The shortest experiment for linear system identification","authors":"M.K. Camlibel ,&nbsp;H.J. van Waarde ,&nbsp;P. Rapisarda","doi":"10.1016/j.sysconle.2025.106045","DOIUrl":"10.1016/j.sysconle.2025.106045","url":null,"abstract":"<div><div>In this paper we study the following problem: given an upper bound of the state-space dimension and lag on a linear time-invariant system, design a sequence of inputs so that the system dynamics can be recovered from the resulting input–output data. As our main result we propose a new online experiment design method, meaning that the selection of the inputs is iterative and guided by past data samples. We show that this approach leads to the shortest possible experiments for linear system identification. In terms of sample complexity, the proposed method outperforms offline methods based on persistency of excitation as well as existing online experiment design methods.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"197 ","pages":"Article 106045"},"PeriodicalIF":2.1,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143445843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Improved residual mode separation for finite-dimensional control of PDEs: Application to the Euler–Bernoulli beam 改进的残余模态分离用于偏微分方程有限维控制：在欧拉-伯努利梁中的应用
IF 2.1 3区 计算机科学
Systems & Control Letters Pub Date : 2025-02-20 DOI: 10.1016/j.sysconle.2025.106048
Anton Selivanov , Emilia Fridman
{"title":"Improved residual mode separation for finite-dimensional control of PDEs: Application to the Euler–Bernoulli beam","authors":"Anton Selivanov ,&nbsp;Emilia Fridman","doi":"10.1016/j.sysconle.2025.106048","DOIUrl":"10.1016/j.sysconle.2025.106048","url":null,"abstract":"<div><div>We consider a simply-supported Euler–Bernoulli beam with viscous and Kelvin–Voigt damping. Our objective is to attenuate the effect of an unknown distributed disturbance using one piezoelectric actuator. We show how to design a state-feedback controller based on a finite number of dominating modes that guarantees that the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> gain is not greater than a given value. If the remaining (infinitely many) modes are simply ignored, the calculated <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> gain is wrong. This happens because of the spillover phenomenon that occurs when the effect of the control on truncated modes is not accounted for in the feedback design. We propose a simple modification of the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> cost that prevents spillover. The key idea is to treat the control as a disturbance in the truncated modes and find the corresponding <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> gains using the bounded real lemma. These <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> gains are added to the control weight in the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> cost for the dominating modes, which prevents spillover. A numerical simulation of an aluminum beam with realistic parameters demonstrates the effectiveness of the proposed method. The presented approach is applicable to other types of PDEs, such as the heat, wave, and Kuramoto–Sivashinsky equations, as well as their semilinear versions. The proposed method gives a Lyapunov functional that can also be used for guaranteed cost control, regional stability analysis, and input-to-state stability.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"197 ","pages":"Article 106048"},"PeriodicalIF":2.1,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143453968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Finite-dimensional observer-based boundary control for a one-dimensional stochastic heat equation 一维随机热方程的有限维观测器边界控制
IF 2.1 3区 计算机科学
Systems & Control Letters Pub Date : 2025-02-18 DOI: 10.1016/j.sysconle.2025.106046
Yu-Shuo Shang , Ze-Hao Wu , Hua-Cheng Zhou
{"title":"Finite-dimensional observer-based boundary control for a one-dimensional stochastic heat equation","authors":"Yu-Shuo Shang ,&nbsp;Ze-Hao Wu ,&nbsp;Hua-Cheng Zhou","doi":"10.1016/j.sysconle.2025.106046","DOIUrl":"10.1016/j.sysconle.2025.106046","url":null,"abstract":"<div><div>In this article, we investigate the finite-dimensional observer-based boundary control for a one-dimensional stochastic heat equation with nonlinear multiplicative noise and non-local sensing measurement. We adopt the modal decomposition to divide the system into two subsystems: one unstable with finite positive eigenvalues and the other essentially stable. We design the controller for the unstable subsystem by dynamic extension and demonstrate that the proposed controller actually leads to the resulting closed-loop system to be well-posed and exponentially stable, both in the mean square and almost sure senses. Finally, some numerical simulations are performed to illustrate the effectiveness of the proposed method.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"197 ","pages":"Article 106046"},"PeriodicalIF":2.1,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143428905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Infinite-horizon BSDE approach for exponential stabilization of discrete-time stochastic system 离散时间随机系统指数镇定的无限视界BSDE方法
IF 2.1 3区 计算机科学
Systems & Control Letters Pub Date : 2025-02-17 DOI: 10.1016/j.sysconle.2025.106047
Yue Sun , Juanjuan Xu , Wei Wang , Huanshui Zhang
{"title":"Infinite-horizon BSDE approach for exponential stabilization of discrete-time stochastic system","authors":"Yue Sun ,&nbsp;Juanjuan Xu ,&nbsp;Wei Wang ,&nbsp;Huanshui Zhang","doi":"10.1016/j.sysconle.2025.106047","DOIUrl":"10.1016/j.sysconle.2025.106047","url":null,"abstract":"<div><div>In this paper, the exponential stabilizability via closed loop for a kind of discrete-time stochastic systems with multiplicative noise is taken into consideration. The main contribution is to provide the necessary and sufficient condition for the exponential stabilizability via closed loop of the stochastic system in accordance with the exact controllability. The key technique is to use the open-loop solvability of a type of backward stochastic difference equations in infinite horizon.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"197 ","pages":"Article 106047"},"PeriodicalIF":2.1,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143422217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Balanced truncation with conformal maps 保角映射的平衡截断
IF 2.1 3区 计算机科学
Systems & Control Letters Pub Date : 2025-02-12 DOI: 10.1016/j.sysconle.2025.106044
Alessandro Borghi , Tobias Breiten , Serkan Gugercin
{"title":"Balanced truncation with conformal maps","authors":"Alessandro Borghi ,&nbsp;Tobias Breiten ,&nbsp;Serkan Gugercin","doi":"10.1016/j.sysconle.2025.106044","DOIUrl":"10.1016/j.sysconle.2025.106044","url":null,"abstract":"<div><div>We consider the problem of constructing reduced models for large scale systems with poles in general domains in the complex plane (as opposed to, e.g., the open left-half plane or the open unit disk). Our goal is to design a model reduction scheme, building upon theoretically established methodologies, yet encompassing this new class of models. To this aim, we develop a balanced truncation framework through conformal maps to handle poles in general domains. The major difference from classical balanced truncation resides in the formulation of the Gramians. We show that these new Gramians can still be computed by solving modified Lyapunov equations for specific conformal maps. A numerical algorithm to perform balanced truncation with conformal maps is developed and is tested on three numerical examples, namely a heat model, the Schrödinger equation, and the undamped linear wave equation, the latter two having spectra on the imaginary axis.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"197 ","pages":"Article 106044"},"PeriodicalIF":2.1,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143388076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Projected incrementally scattering passive systems on closed convex sets 闭凸集上的投影增量散射被动系统
IF 2.1 3区 计算机科学
Systems & Control Letters Pub Date : 2025-02-11 DOI: 10.1016/j.sysconle.2025.106033
Shantanu Singh , Sébastien Fueyo , George Weiss
{"title":"Projected incrementally scattering passive systems on closed convex sets","authors":"Shantanu Singh ,&nbsp;Sébastien Fueyo ,&nbsp;George Weiss","doi":"10.1016/j.sysconle.2025.106033","DOIUrl":"10.1016/j.sysconle.2025.106033","url":null,"abstract":"<div><div>In this article we show that the projected dynamical system obtained by restricting the state of an incrementally scattering passive system to a closed and convex subset <span><math><mi>K</mi></math></span> of the state space (a real Hilbert space), is also an incrementally scattering passive system. First we show that the projection of a maximal dissipative operator to the tangent cones of <span><math><mi>K</mi></math></span> is again maximal dissipative, hence, it determines a contraction semigroup. Using this result, we prove our earlier claim. Our results are based on the Crandall–Pazy theorem, Rockafellar’s theorem on sums of operators and Moreau’s decomposition theorem. We give an application of our results to Maxwell’s equations on a cylindrical domain, approximately describing a fault current limiter, restricting the average current through the cylinder (in the direction of its axis) so that its absolute value cannot exceed a given threshold.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"197 ","pages":"Article 106033"},"PeriodicalIF":2.1,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143379063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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