Systems & Control Letters最新文献

{"title":"Optimal covariance control for partially observed linear stochastic systems under chance constraints","authors":"Dipankar Maity ,&nbsp;Panagiotis Tsiotras","doi":"10.1016/j.sysconle.2025.106249","DOIUrl":"10.1016/j.sysconle.2025.106249","url":null,"abstract":"<div><div>We consider the optimal control problem of a partially observed discrete-time linear stochastic system with chance constraints on the state and control trajectories, while simultaneously controlling the first and second order moments of the state. Using a distribution-independent approximation of the chance constraints, we show that the class of affine controllers contains the optimal controller. Furthermore, this distribution-independent approximation is carried out while ensuring that any feasible solution for the approximated problem is also feasible for the original problem. Finally, we design a convex optimization problem to solve offline for the optimal controller for the approximated problem.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"205 ","pages":"Article 106249"},"PeriodicalIF":2.5,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220778","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":"Distributed generalized Nash equilibrium seeking approach via surrogate functions for noncooperative nonconvex games","authors":"Yuexin Liu ,&nbsp;Jie Zhong ,&nbsp;Yan Wang ,&nbsp;Wenyin Xu","doi":"10.1016/j.sysconle.2025.106251","DOIUrl":"10.1016/j.sysconle.2025.106251","url":null,"abstract":"<div><div>This paper addresses distributed generalized Nash equilibrium seeking in noncooperative nonconvex games, where the decisions of players are subject to coupled nonconvex constraints and bound constraints. To address the limitations of existing approaches that either cannot handle bound constraints or require external augmentation terms (which incur high computational costs), a multi-agent system based on surrogate functions for nonconvex games is proposed. The convergence of the multi-agent system to a local variational generalized Nash equilibrium is proven. To demonstrate the effectiveness of the proposed multi-agent system, three numerical examples are presented to validate the main theoretical results.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"205 ","pages":"Article 106251"},"PeriodicalIF":2.5,"publicationDate":"2025-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220777","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":"Dynamic event-triggered control for leader-following consensus of second-order multi-agent systems with disturbance","authors":"Wei Zheng ,&nbsp;Cong Liu ,&nbsp;Xiaopeng Yang ,&nbsp;Hak-Keung Lam ,&nbsp;Fuchun Sun","doi":"10.1016/j.sysconle.2025.106248","DOIUrl":"10.1016/j.sysconle.2025.106248","url":null,"abstract":"<div><div>In this paper, the leader-following consensus problem of second-order multi-agent systems (MASs) with bounded disturbance under the undirected graph is investigated. Firstly, the distributed fixed-time observers are proposed to estimate the tracking errors between leader and follower. Then, with the help of observer and dynamic event-triggered mechanism, the consensus controller is designed to guarantee MASs for achieving the asymptotically consensus, in which the controller is designed based on backstepping approach and only need local cooperative information. Meanwhile, the Zeno behavior can be excluded. Finally, a second-order MASs example is used to verify the event-triggered controller in this paper.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"205 ","pages":"Article 106248"},"PeriodicalIF":2.5,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158747","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":"An optimal sequence for sub-Markov decision processes with risk sensitivity","authors":"Tanhao Huang,&nbsp;Jinwen Chen","doi":"10.1016/j.sysconle.2025.106245","DOIUrl":"10.1016/j.sysconle.2025.106245","url":null,"abstract":"<div><div>This paper deals with sub-Markov decision processes with risk-sensitivity. The processes are not assumed to be communicating, thus the optimal average reward <span><math><mrow><msup><mrow><mi>J</mi></mrow><mrow><mo>∗</mo></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> may depend on the initial state <span><math><mi>x</mi></math></span>. The aim of this paper is to characterize this dependence. It is shown that the values of <span><math><msup><mrow><mi>J</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> are determined by a system of Poisson equations. By partitioning the state space in a proper way we derive such equations and obtain the associated optimal sequence. The partition of the state space is constructive which is closely related to the state communication, transience or absorption.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"205 ","pages":"Article 106245"},"PeriodicalIF":2.5,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145118857","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 Bayesian update method for exponential family projection filters with non-conjugate likelihoods","authors":"Muhammad Fuady Emzir","doi":"10.1016/j.sysconle.2025.106234","DOIUrl":"10.1016/j.sysconle.2025.106234","url":null,"abstract":"<div><div>The projection filter is one of the approximations to the solution of the optimal filtering problem. It approximates the filtering density by projecting the dynamics of the square-root filtering density onto the tangent space of the square-root parametric density manifold. While the projection filters for exponential and mixture families with continuous measurement processes have been well studied, the continuous-discrete projection filtering algorithm for non-conjugate priors has received less attention. In this paper, we introduce a simple Riemannian optimization method to be used for the Bayesian update step in the continuous-discrete projection filter for exponential families. Specifically, we show that the Bayesian update can be formulated as an optimization problem of <span><math><mi>α</mi></math></span>-Rényi divergence, where the corresponding Riemannian gradient can be easily computed. We demonstrate the effectiveness of the proposed method via two highly non-Gaussian Bayesian update problems.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"205 ","pages":"Article 106234"},"PeriodicalIF":2.5,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106475","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 boundary estimation for uncertain cascaded hyperbolic PDE-ODEs","authors":"Chen Yang,&nbsp;Yan Zhao,&nbsp;Shengyuan Xu,&nbsp;Baoyong Zhang","doi":"10.1016/j.sysconle.2025.106243","DOIUrl":"10.1016/j.sysconle.2025.106243","url":null,"abstract":"<div><div>The paper is concerned with the adaptive boundary estimation problem for a class of hyperbolic partial differential equations (PDEs) cascaded with a set of ordinary differential equations (ODEs). The cascade system consists of <span><math><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></math></span> coupled hyperbolic PDEs, subject to uncertain parameters in domain and the ODEs entering the PDEs through the left boundary of the PDEs. The adaptive boundary observer is designed to estimate the system state and the unknown parameters. In order to facilitate the design of the observer, the observer error system is transformed into a target system by a Volterra integral transformation and a state transformation, and then a swapping filter design method is proposed by combining the method of least-squares with a variable forgetting factor. The stability analysis shows the exponential convergence of both the state estimation error and the parameter estimation error under the persistent excitation condition of the filter. Finally, the obtained theoretical results are applied to the linearized Aw–Rascle–Zhang (ARZ) traffic flow model involving the in-domain relaxation time and the boundary flux fluctuation uncertainties, which verifies the effectiveness of the proposed method.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"205 ","pages":"Article 106243"},"PeriodicalIF":2.5,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106527","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":"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}