Systems & Control LettersPub Date : 2026-02-01Epub Date: 2026-01-06DOI: 10.1016/j.sysconle.2025.106289
Tomonori Sadamoto , Takashi Tanaka
{"title":"Policy gradient method for LQG control via input–output-history representation: Convergence to O(ϵ)-stationary points","authors":"Tomonori Sadamoto , Takashi Tanaka","doi":"10.1016/j.sysconle.2025.106289","DOIUrl":"10.1016/j.sysconle.2025.106289","url":null,"abstract":"<div><div>We study the policy gradient method (PGM) for the linear quadratic Gaussian (LQG) dynamic output-feedback control problem using an <em>input–output-history</em> (IOH) representation of the closed-loop system. First, we show that any dynamic output-feedback controller is equivalent to a static partial-state feedback gain for a new system representation characterized by a finite-length IOH. Leveraging this equivalence, we reformulate the search for an optimal dynamic output feedback controller as an optimization problem over the corresponding partial-state feedback gain. Next, we introduce a relaxed version of the IOH-based LQG problem by incorporating a small process noise with covariance <span><math><mrow><mi>ϵ</mi><mi>I</mi></mrow></math></span> into the new system to ensure coerciveness, a key condition for establishing gradient-based convergence guarantees. Consequently, we show that a vanilla PGM for the relaxed problem converges to an <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>ϵ</mi><mo>)</mo></mrow></mrow></math></span>-<em>stationary</em> point, i.e., <span><math><mover><mrow><mi>K</mi></mrow><mo>¯</mo></mover></math></span> satisfying <span><math><mrow><msub><mrow><mo>‖</mo><mo>∇</mo><mi>J</mi><mrow><mo>(</mo><mover><mrow><mi>K</mi></mrow><mo>¯</mo></mover><mo>)</mo></mrow><mo>‖</mo></mrow><mrow><mi>F</mi></mrow></msub><mo>≤</mo><mi>O</mi><mrow><mo>(</mo><mi>ϵ</mi><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>J</mi></math></span> denotes the original LQG cost. Numerical experiments empirically indicate convergence to the vicinity of the globally optimal LQG controller.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106289"},"PeriodicalIF":2.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145898077","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}
Systems & Control LettersPub Date : 2026-02-01Epub Date: 2026-01-19DOI: 10.1016/j.sysconle.2026.106359
Xiaopeng Shi , Chuanhou Gao , Denis Dochain , Yuzhen Fan
{"title":"Biochemical relaxation oscillator designed to control molecular computation","authors":"Xiaopeng Shi , Chuanhou Gao , Denis Dochain , Yuzhen Fan","doi":"10.1016/j.sysconle.2026.106359","DOIUrl":"10.1016/j.sysconle.2026.106359","url":null,"abstract":"<div><div>Embedding efficient calculation instructions into biochemical systems has always been a research focus in synthetic biology. Amongst this, the main challenge is how to overcome the contradiction between the parallel occurrence of biochemical reactions and the ordinal implementation of calculation instructions. In response to this challenge, the current work presents a new 4-dimensional biochemical oscillator model based on the relaxation oscillation to generate a pair of symmetric clock signals for dual-module regulation tasks through chemical reaction networks. The pair of symmetric clock signals separately act as a catalyst to participate the corresponding reaction modular of performing calculation, and control their on/off switch if the concentration of the clock signal is nonzero. The detailed discussions are subsequently made on the important effect of the oscillator parameters on controlling the period and the occurrence order of clock signals. Further, the oscillator is applied to control the iteration calculation, along with which a termination strategy is proposed to jump out of the loop.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106359"},"PeriodicalIF":2.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038503","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}
Systems & Control LettersPub Date : 2026-02-01Epub Date: 2026-01-14DOI: 10.1016/j.sysconle.2026.106356
Liangquan Zhang , Xun Li
{"title":"A Hilbert space method to LQ optimal control of conditional McKean–Vlasov dynamics","authors":"Liangquan Zhang , Xun Li","doi":"10.1016/j.sysconle.2026.106356","DOIUrl":"10.1016/j.sysconle.2026.106356","url":null,"abstract":"<div><div>In this paper, we employ a Hilbert space approach based on orthogonal decomposition to investigate an optimal control problem associated with a linear conditional McKean–Vlasov dynamic, where the control process is allowed to be adapted to the filtration generated by both common and idiosyncratic noises under random coefficients. By applying the stochastic maximum principle, we derive the optimal feedback control and characterize the corresponding value function in terms of backward stochastic Riccati differential equations. Furthermore, an application to conditional mean–variance portfolio selection in an incomplete market setting is provided.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106356"},"PeriodicalIF":2.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979539","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}
Systems & Control LettersPub Date : 2026-02-01Epub Date: 2026-01-22DOI: 10.1016/j.sysconle.2026.106357
Yonghan Li , Chenyu Wu , Taoran Wu , Shijie Wang , Bai Xue
{"title":"Converse barrier certificates for finite-time safety verification of continuous-time perturbed deterministic systems","authors":"Yonghan Li , Chenyu Wu , Taoran Wu , Shijie Wang , Bai Xue","doi":"10.1016/j.sysconle.2026.106357","DOIUrl":"10.1016/j.sysconle.2026.106357","url":null,"abstract":"<div><div>In this paper, we investigate the problem of verifying the finite-time safety of continuous-time perturbed deterministic systems represented by ordinary differential equations in the presence of measurable disturbances. Given a finite-time horizon, if the system is safe, it, starting from a compact initial set, will remain within an open and bounded safe region throughout the specified time horizon, regardless of the disturbances. The main contribution of this work is a converse theorem: we prove that a continuously differentiable, time-dependent barrier certificate exists if and only if the system is safe over the finite-time horizon. The existence problem is explored by finding a continuously differentiable approximation of a unique Lipschitz viscosity solution to a Hamilton–Jacobi equation.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106357"},"PeriodicalIF":2.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038505","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}
Systems & Control LettersPub Date : 2026-02-01Epub Date: 2026-01-15DOI: 10.1016/j.sysconle.2025.106340
Xuqian Ju , Qing Sun , Dario Dennstädt , Karl Worthmann , Dajun Du , Minrui Fei
{"title":"Model predictive control for nonlinear switched systems based on Koopman theory","authors":"Xuqian Ju , Qing Sun , Dario Dennstädt , Karl Worthmann , Dajun Du , Minrui Fei","doi":"10.1016/j.sysconle.2025.106340","DOIUrl":"10.1016/j.sysconle.2025.106340","url":null,"abstract":"<div><div>This paper presents a novel data-driven predictive control strategy for discrete-time switched nonlinear systems. By leveraging the Koopman operator framework, we construct a linear surrogate model that effectively captures the systems’ nonlinear dynamics, significantly enhancing prediction accuracy over standard Koopman methods that ignore switching behavior. We then formulate a Model Predictive Control (MPC) scheme based on this linear predictor. The proposed controller is designed for systems with known switching times, incorporating the sequence into the optimization horizon. Critically, we also formulate the controller to handle cases where the switching sequence is a decision variable, thereby enabling joint optimization of both the control input and the discrete mode switching. Numerical simulations demonstrate the method’s feasibility and its significant advantages in both state prediction and control performance compared to traditional nonlinear and switched-system control strategies.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106340"},"PeriodicalIF":2.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979606","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}
Systems & Control LettersPub Date : 2026-02-01Epub Date: 2026-01-15DOI: 10.1016/j.sysconle.2026.106355
Nguyen Trong Hieu , Dang Hai Nguyen
{"title":"Complete classification of the long-term behavior of a tumor–immune model with impulsive therapeutic interventions","authors":"Nguyen Trong Hieu , Dang Hai Nguyen","doi":"10.1016/j.sysconle.2026.106355","DOIUrl":"10.1016/j.sysconle.2026.106355","url":null,"abstract":"<div><div>We propose and analyze a stochastic tumor–immune interaction model subject to periodic impulsive treatment, capturing the combined effects of chemotherapy and immunotherapy. The model extends previous deterministic frameworks by incorporating environmental noise and treatment-induced state-dependent impulses, leading to a hybrid stochastic differential system. We rigorously classify the long-term behavior of the system, providing sharp conditions for the extinction and persistence of tumor cells. Unlike earlier studies that treat impulses deterministically and yield limited insight, our framework accounts for random fluctuations in treatment efficacy and immune response. We derive explicit threshold conditions that determine the effectiveness of the combined therapies, offering practical guidelines for improving treatment outcomes. Our analysis framework can be extended to study a broad class of stochastic hybrid models recently introduced in tumor–immune dynamics.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106355"},"PeriodicalIF":2.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979540","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}
Systems & Control LettersPub Date : 2026-02-01Epub Date: 2026-01-16DOI: 10.1016/j.sysconle.2025.106339
Javier F. Rosenblueth, Niels H. Wacher
{"title":"The Legendre–Clebsch condition for a control problem of Bolza","authors":"Javier F. Rosenblueth, Niels H. Wacher","doi":"10.1016/j.sysconle.2025.106339","DOIUrl":"10.1016/j.sysconle.2025.106339","url":null,"abstract":"<div><div>This paper gives a direct and elementary proof of the Legendre–Clebsch necessary condition of optimality for a control problem of Bolza involving equality and inequality mixed constraints. The novelty of the approach consists in showing that the condition holds even if the standard rank hypothesis (or nondegeneracy condition) made on the nature of the mixed constraints is replaced with a weaker hypothesis based on the multipliers associated with the extremal under consideration, thus broadening its range of applicability.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106339"},"PeriodicalIF":2.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979607","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}
Systems & Control LettersPub Date : 2026-02-01Epub Date: 2026-01-24DOI: 10.1016/j.sysconle.2026.106364
Jiayao Zhang, Zhi Li
{"title":"Containment control for high-order systems with convex state and nonconvex input constraints under switching topologies","authors":"Jiayao Zhang, Zhi Li","doi":"10.1016/j.sysconle.2026.106364","DOIUrl":"10.1016/j.sysconle.2026.106364","url":null,"abstract":"<div><div>In this paper, we investigate the containment control for high-order systems subject to both convex state constraints and nonconvex input constraints under switching topologies. The primary challenge lies in addressing the complex nonlinearities arising from these diverse constraints and the intricate couplings in high-order system states. To address the constrained containment, we propose a nonlinear distributed control protocol that ensures all followers converge to the convex hull formed by stationary leaders, while guaranteeing that both state and input trajectories remain within their respective constrained sets. By introducing scaling factors and projection errors, the original constrained high-order system is transformed into an equivalent unconstrained system. Subsequently, a Lyapunov function is constructed based on the maximum distance between each follower and the convex hull. Using convex analysis together with properties of the projection operator, we demonstrate that this Lyapunov function is monotonically nonincreasing, which effectively eliminates the errors introduced by the convex constraints. Furthermore, by incorporating the lower bound of the scaling factor and Lyapunov stability, it can be proven that all followers converge to a convex hull, provided that there exists at least one directed path to one of the leaders for all followers in the union of topologies. A numerical simulation confirms the effectiveness of the proposed theorem.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106364"},"PeriodicalIF":2.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038499","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 state estimation of linear descriptor systems","authors":"Juhi Jaiswal , Vikas Kumar Mishra , Raghunathan Rengaswamy , Naim Bajcinca","doi":"10.1016/j.sysconle.2026.106360","DOIUrl":"10.1016/j.sysconle.2026.106360","url":null,"abstract":"<div><div>In this paper, we study the problem of state estimation using a network of distributed observers for continuous-time linear descriptor systems. Remarkably, the network of state observers is obtained as state-space systems even though the underlying distributed system is a linear descriptor system. We derive sufficient conditions in terms of the underlying system matrices for the existence of this network of state observers. The derived sufficient conditions consist of solving a linear matrix inequality, making the design easily implementable. Moreover, we introduce the notion of joint detectability of the original system and show that it is necessary for the design of the distributed observers. Finally, the developed theory is illustrated with a numerical example.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106360"},"PeriodicalIF":2.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038502","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}
Systems & Control LettersPub Date : 2026-02-01Epub Date: 2026-01-06DOI: 10.1016/j.sysconle.2026.106344
Yury Orlov , Miguel Arambula , Denis Efimov
{"title":"Prescribed-time output feedback for linear systems in normal form: Robustness analysis and digital implementation under measurement noise","authors":"Yury Orlov , Miguel Arambula , Denis Efimov","doi":"10.1016/j.sysconle.2026.106344","DOIUrl":"10.1016/j.sysconle.2026.106344","url":null,"abstract":"<div><div>The well-known prescribed-time stabilizing design faces the need of using time-varying high gains which escape to infinity as time approaches the desired instant. In the presence of external disturbances and measurement noise, the corresponding state response is significantly amplified as well that leads to the lack of robustness in the closed-loop implementation. For eliminating this drawback, the implicit Euler discretization was recently developed for state feedback and observer design. The resulting implementation conserved desired robustness properties beyond the prescribed-time interval and also ensured bounded state dynamics in the presence of measurement noise. In the present work, the proposed robust prescribed-time design is further developed towards its output feedback extension the separation principle is not valid in this setting). The effectiveness of the design is additionally supported by numerical experiments.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106344"},"PeriodicalIF":2.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145898076","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}