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Partially observed linear quadratic stochastic optimal control problem in infinite horizon: A data-driven approach
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
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
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
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
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
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
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
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
Uniform exponential stability of semi-discrete scheme for Euler–Bernoulli beam equation with non-collocated feedback
IF 2.1 3区 计算机科学
Systems & Control Letters Pub Date : 2025-02-11 DOI: 10.1016/j.sysconle.2024.106017
Han-Jing Ren , Bao-Zhu Guo
{"title":"Uniform exponential stability of semi-discrete scheme for Euler–Bernoulli beam equation with non-collocated feedback","authors":"Han-Jing Ren ,&nbsp;Bao-Zhu Guo","doi":"10.1016/j.sysconle.2024.106017","DOIUrl":"10.1016/j.sysconle.2024.106017","url":null,"abstract":"<div><div>In this paper, we study the uniform exponential stability of a semi-discrete scheme for an Euler–Bernoulli beam equation under an observer-based output stabilizing feedback control studied in Guo et al. (2008), where the Riesz basis approach was employed. However, it is crucial to note that the Riesz basis approach falls short when applied to the uniform exponential stability of discrete schemes. Since the original system and observer together constitutes a coupled system described by partial differential equations (PDEs), this paper innovatively constructs a Lyapunov function specifically tailored for this coupled PDEs, which gives a much direct, simple alternative approach to exponential stability. In addition, this methodology can be seamlessly applied to assess the uniform exponential stability of a semi-discretized finite difference scheme corresponding to this coupled PDE. Although the semi-discretization process is still an order reduction approach studied in our previous works, it is novel in the sense that the order of the derivatives with respect to the spatial variable has been reduced to the first order, which not only eliminates the effect of the low order derivative on the boundary in previous study but also simplifies significantly the proof of the uniform exponential stability of the semi-discrete scheme.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"197 ","pages":"Article 106017"},"PeriodicalIF":2.1,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143379177","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
Attack detection and security control for quadrotor under stealthy attacks
IF 2.1 3区 计算机科学
Systems & Control Letters Pub Date : 2025-02-08 DOI: 10.1016/j.sysconle.2025.106031
Chengwei Wu , Yupeng Zhu , Lezhong Xu , Hongming Zhu , Quanqi Zhang , Jiajing Zhu , Weiran Yao
{"title":"Attack detection and security control for quadrotor under stealthy attacks","authors":"Chengwei Wu ,&nbsp;Yupeng Zhu ,&nbsp;Lezhong Xu ,&nbsp;Hongming Zhu ,&nbsp;Quanqi Zhang ,&nbsp;Jiajing Zhu ,&nbsp;Weiran Yao","doi":"10.1016/j.sysconle.2025.106031","DOIUrl":"10.1016/j.sysconle.2025.106031","url":null,"abstract":"<div><div>When malicious attacks occur, the security issues of unmanned aerial vehicles are full of challenges. This paper investigates the attack detection and security control problems for quadrotors with stealthy false data injection attacks. Decoupled linear models are provided to describe the dynamics. A novel cyber-attack detection scheme integrating watermarking signals and auxiliary functions is devised to detect stealthy false data injection attacks. To determine which sensor data is attacked, an attack location algorithm is developed based on the observability of the derived linear model. Furthermore, a security control scheme is provided to mitigate stealthy false data injection attacks. Finally, simulation results are presented to validate the proposed theories in this paper.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"197 ","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143349682","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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