Systems & Control Letters最新文献

{"title":"Delayed output feedback stabilization of ODE-heat cascades","authors":"Hugo Lhachemi","doi":"10.1016/j.sysconle.2025.106222","DOIUrl":"10.1016/j.sysconle.2025.106222","url":null,"abstract":"<div><div>This paper addresses the problem of output feedback stabilization of ODE-heat cascades. The ODE enters into the heat equation through a either Dirichlet or Neumann boundary condition. The system output applies solely to the heat equation and takes the form of either a distributed measurement or boundary/in-domain pointwise Dirichlet/Neumann measurement. The adopted approach relies on spectral reduction methods through a detailed study of the eigenelements of the ODE-heat cascade. A full characterization of the controllability and observability properties of each individual mode of the cascade is reported. Provided the satisfaction of these controllability and observability properties for the unstable modes, we show that a finite-dimensional output feedback control strategy can always be successfully designed for achieving the exponential stabilization of the ODE-heat cascade. We discuss in particular how such a strategy extends to the case of an input delay by designing a predictor feedback.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"205 ","pages":"Article 106222"},"PeriodicalIF":2.5,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106528","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}

{"title":"Adaptive control with magnitude and rate limited observer-based disturbance rejection","authors":"Ying-Chun Chen,&nbsp;Craig Woolsey","doi":"10.1016/j.sysconle.2025.106242","DOIUrl":"10.1016/j.sysconle.2025.106242","url":null,"abstract":"<div><div>This paper considers the problem of controlling a piecewise continuously differentiable system subject to time-varying matched uncertainties. The uncertainties are decomposed into two parts: a time-invariant linearly-parameterized portion and a time-varying unstructured portion. The former is addressed using conventional model reference adaptive control, while the latter is handled by disturbance observer-based control. The objective is to ensure good performance through observer-based disturbance rejection when possible, while preserving the robustness guarantees of adaptive control. A key feature of the observer-based disturbance compensation is a magnitude and rate limited integral action that prevents fast fluctuations in the control command due to the observer dynamics.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"205 ","pages":"Article 106242"},"PeriodicalIF":2.5,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106526","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}

{"title":"L∞/L2 Hankel norm analysis of linear periodically time-varying systems and detection of critical instants","authors":"Tomomichi Hagiwara ,&nbsp;Taichi Yuyama ,&nbsp;Jung Hoon Kim","doi":"10.1016/j.sysconle.2025.106235","DOIUrl":"10.1016/j.sysconle.2025.106235","url":null,"abstract":"&lt;div&gt;&lt;div&gt;This paper deals with the Hankel norm analysis of linear periodically time-varying (LPTV) systems, where &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is taken as the (past) input space and the (future) output is regarded as an element in &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. This norm is known to be important because of its coincidence with the well-known &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; norm for the special case of single-output linear time-invariant systems. For the period &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; of LPTV systems, an arbitrary instant &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Θ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is first taken to separate past and future, and then the quasi &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; Hankel norm at &lt;span&gt;&lt;math&gt;&lt;mi&gt;Θ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is defined. A computation method for the quasi &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; Hankel norm for each &lt;span&gt;&lt;math&gt;&lt;mi&gt;Θ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is further derived, and for &lt;em&gt;the&lt;/em&gt; &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; Hankel norm defined as the supremum of the quasi &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; Hankel norms over &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Θ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, its alternative and direct computation method is also provided, which is actually completely free from dealing with any quasi &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; Hankel norms. A relevant question of whether the supremum is attained as the maximum is also studied, in which case each maximum-attaining &lt;span&gt;&lt;math&gt;&lt;mi&gt;Θ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is called a critical instant. In particular, it is discussed when and how the existence/absence of a critical instant can be determined and some or all critical instants can be detected without directly computing all (or any of) the quasi &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; Hankel norms over &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Θ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. Finally, numerical example","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"205 ","pages":"Article 106235"},"PeriodicalIF":2.5,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106525","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}

{"title":"Incremental stability analysis of random nonlinear systems with an application to random Lagrange systems","authors":"Ticao Jiao ,&nbsp;Yuxia Li ,&nbsp;Haibin Sun","doi":"10.1016/j.sysconle.2025.106232","DOIUrl":"10.1016/j.sysconle.2025.106232","url":null,"abstract":"<div><div>This paper is intended to investigate the incremental stability analysis of random nonlinear systems with colored noise and its application to random Lagrange systems. Under an analysis of the dynamical features of the considered random nonlinear systems, the definitions of incremental noise-to-state stability and incrementally asymptotic stability with respect to preliminary conditions and/or random processes are proposed. By introducing two extended forms of the original system, relevant incremental stability conditions are established based on Lyapunov functions with time-varying derivatives. We further provide an easily verifiable incremental noise-to-state stability result by using quadratic Lyapunov functions. To explain the application value of our devised results, an incremental stability control problem of random Lagrange systems is solved with the aid of a vector backstepping approach. We at last demonstrate the efficacy of our work through numerical simulations.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"205 ","pages":"Article 106232"},"PeriodicalIF":2.5,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106524","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}

{"title":"Power-constrained networked process control system design","authors":"Alejandro J. Rojas ,&nbsp;Hugo O. Garcés","doi":"10.1016/j.sysconle.2025.106231","DOIUrl":"10.1016/j.sysconle.2025.106231","url":null,"abstract":"<div><div>Networked control systems (NCSs) operate at the interface between the physical world and cyberspace enabling the realization of emergent cyber–physical systems that can be controlled over long distance, potentially even from the cloud, thereby reducing the complexity associated with wired solutions. Networked process control systems (NPCSs), as proposed herein, incorporate the challenges inherent in NCS design within the context of process control (the application of automatic control theory). For this purpose, the essential components of an NPCS are considered to be: on the process side, the presence of dominant unstable dynamics, modeled by a first-order (or at most a second-order) transfer function; and on the network side, the presence of additive white noise (AWN) channels on both over the control and feedback paths. The contribution of this work lies in the development of new optimal designs for the stabilization of a first-order unstable NPCS that minimize the associated channel power constraints, thereby mitigating signal distortion, and preserving battery life in cases where the transmitters are not connected to an external power supply. The NPCS optimal controller configures the closed loop dynamics to exhibit a repeated stable pole, while simultaneously minimizing one of the following objectives: the input power of the AWN channel over the control path; the input power of the AWN channel over the feedback path; or the sum of the input powers of both AWN channels, all under a constant reference signal. To illustrate the theoretical developments, a first-principles-based linearized ball and beam model is derived, demonstrating the effectiveness of the proposed NPCS optimal controller designs, and their properties, in comparison to those of a classical proportional-integral (PI) design. The contributions presented in this work are readily extendable to any arbitrary linear plant model possessing a single unstable pole.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"205 ","pages":"Article 106231"},"PeriodicalIF":2.5,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046684","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}

{"title":"Good Lie Brackets for classical and quantum harmonic oscillators","authors":"Andrei Agrachev ,&nbsp;Bettina Kazandjian ,&nbsp;Eugenio Pozzoli","doi":"10.1016/j.sysconle.2025.106233","DOIUrl":"10.1016/j.sysconle.2025.106233","url":null,"abstract":"<div><div>We study the small-time controllability problem on the Lie groups <span><math><mrow><mi>S</mi><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>S</mi><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo>⋉</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>d</mi></mrow></msub><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> with Lie bracket methods (here <span><math><mrow><msub><mrow><mi>H</mi></mrow><mrow><mi>d</mi></mrow></msub><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> denotes the <span><math><mrow><mo>(</mo><mn>2</mn><mi>d</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional real Heisenberg group). Then, using unitary representations of <span><math><mrow><mi>S</mi><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo>⋉</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>d</mi></mrow></msub><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> on <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo><mi>ℂ</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>r</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>T</mi></mrow><mrow><mo>∗</mo></mrow></msup><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo><mi>R</mi><mo>)</mo></mrow><mo>,</mo><mi>r</mi><mo>∈</mo><mrow><mo>[</mo><mn>1</mn><mo>,</mo><mi>∞</mi><mo>]</mo></mrow></mrow></math></span>, we recover small-time reachability properties of the Schrödinger PDE for the quantum harmonic oscillator, and find new small-time reachability properties of the Liouville PDE for the classical harmonic oscillator.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"205 ","pages":"Article 106233"},"PeriodicalIF":2.5,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046683","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}

{"title":"Global controllability properties of linear control systems","authors":"Fritz Colonius ,&nbsp;Alexandre J. Santana","doi":"10.1016/j.sysconle.2025.106229","DOIUrl":"10.1016/j.sysconle.2025.106229","url":null,"abstract":"<div><div>For linear control systems with bounded control range, the state space is compactified using the Poincaré sphere. The linearization of the induced control flow allows the construction of invariant manifolds on the sphere and of corresponding manifolds in the state space of the linear control system.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"205 ","pages":"Article 106229"},"PeriodicalIF":2.5,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020292","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}

{"title":"A distributed influence measurement algorithm in leader–follower networks","authors":"Hyung-Gon Lee ,&nbsp;Jeong-Min Ma ,&nbsp;Nam-Jin Park ,&nbsp;Hyo-Sung Ahn","doi":"10.1016/j.sysconle.2025.106230","DOIUrl":"10.1016/j.sysconle.2025.106230","url":null,"abstract":"<div><div>This study proposes a <em>vector-wise step-sized consensus dynamics (VSCD)</em> for distributed networks represented by positively weighted leader–follower graphs. Unlike traditional discrete consensus dynamics, VSCD employs node-specific vector step sizes, enabling faster convergence. We define an influence matrix in continuous consensus dynamics and extend it to a discrete influence matrix in VSCD, demonstrating equivalent convergence properties under specific vector step size conditions. To facilitate the application of VSCD in distributed networks, we analyze the maximum boundary vector step size conditions using graph-theoretic methods. Building on this formulation, we propose a fully <em>distributed influence measurement algorithm (DIMA)</em>, which enables each node in a distributed network to determine its valid influence nodes and their corresponding influence using only local information, without requiring global parameters. The effectiveness and scalability of the proposed methods are validated through simulations.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"205 ","pages":"Article 106230"},"PeriodicalIF":2.5,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010955","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}

{"title":"Data-driven adversarial online control for unknown linear systems","authors":"Zishun Liu,&nbsp;Yongxin Chen","doi":"10.1016/j.sysconle.2025.106224","DOIUrl":"10.1016/j.sysconle.2025.106224","url":null,"abstract":"<div><div>We consider the online control problem with an unknown linear dynamical system in the presence of adversarial perturbations and adversarial convex loss functions. Although the problem is widely studied in model-based control, it remains unclear whether data-driven approaches, which bypass the system identification step, can solve the problem. In this work, we present a novel data-driven online adaptive control algorithm to address this online control problem. Our algorithm leverages the behavioral systems theory to learn a non-parametric system representation and then adopts a perturbation-based controller updated by online gradient descent. We prove that our algorithm guarantees an <span><math><mrow><mover><mrow><mi>O</mi></mrow><mrow><mo>̃</mo></mrow></mover><mrow><mo>(</mo><msup><mrow><mi>T</mi></mrow><mrow><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> regret bound with high probability, which matches the best-known regret bound for this problem. Furthermore, we extend our algorithm and performance guarantee to the cases with output feedback. A numerical experiment is conducted to validate our theoretical results.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"205 ","pages":"Article 106224"},"PeriodicalIF":2.5,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020291","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}

{"title":"Harnessing optimal robustness towards PI regulators of linear perturbed unstable systems","authors":"Qi Mao ,&nbsp;Jun Chen ,&nbsp;Fei Xie ,&nbsp;Liqian Dou ,&nbsp;Bailing Tian ,&nbsp;Qun Zong","doi":"10.1016/j.sysconle.2025.106225","DOIUrl":"10.1016/j.sysconle.2025.106225","url":null,"abstract":"<div><div>In this paper, we investigate how a regulator can be implemented for gaining the optimal robustness margin of second-order plants in the presence of uncertain perturbations. We are primarily interested in an intricate system, i.e., the second-order unstable plant with a zero relative degree that is accompanied by at least one unstable pole and non-minimum phase dynamics, both implemented by the proportional and proportional–integral (PI) type regulators. More specifically, we shall examine three scenarios of the system ranging from the worst case of two unstable poles and two minimum phase zeros to the case of one unstable pole and one minimum phase zero. For each class of systems, we furnish the bi-dimensional feasible horizons for the controller parameters of PI regulators. Drawing upon the feasible domains, we derive the explicit expressions of the optimal robustness margin against unknown uncertainties. Beyond that, we determine the regulator parameters for accomplishing the maximum margins, i.e., the optimum proportional and integral gains. At last, we extend to explore the optimum robustness margin achievable with a PI regulator for third-order non-minimum phase systems. Our results illustrate that the optimal robustness margins obtainable are dependent on the locations of the system’s unstable poles and non-minimum phase dynamics while attaining the optimized margin is relevant to the control parameters of the PI regulator, thus casting insight upon the design and adaptation of the regulator parameters.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"205 ","pages":"Article 106225"},"PeriodicalIF":2.5,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144989546","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}