Pub Date : 2025-03-19DOI: 10.1016/j.sysconle.2025.106069
Sebastián Zamorano
This paper examines the turnpike behavior of a controlled system with almost periodic inputs and a cost functional that includes an almost periodic tracking term and periodic observations. Roughly speaking, we establish that the optimal state–control pair for the controlled system remains exponentially close to the optimal pair of an almost periodic problem for a substantial portion of the time during which the control system evolves. Our approach heavily relies on a thorough investigation of differential Riccati equations, periodic differential Riccati equations, and almost periodic functions.
{"title":"Almost periodic turnpike phenomenon for time-dependent systems","authors":"Sebastián Zamorano","doi":"10.1016/j.sysconle.2025.106069","DOIUrl":"10.1016/j.sysconle.2025.106069","url":null,"abstract":"<div><div>This paper examines the turnpike behavior of a controlled system with almost periodic inputs and a cost functional that includes an almost periodic tracking term and periodic observations. Roughly speaking, we establish that the optimal state–control pair for the controlled system remains exponentially close to the optimal pair of an almost periodic problem for a substantial portion of the time during which the control system evolves. Our approach heavily relies on a thorough investigation of differential Riccati equations, periodic differential Riccati equations, and almost periodic functions.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"199 ","pages":"Article 106069"},"PeriodicalIF":2.1,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644905","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}
Pub Date : 2025-03-18DOI: 10.1016/j.sysconle.2025.106066
Ismaïla Balogoun , Jean Auriol , Islam Boussaada , Guilherme Mazanti
In this paper, we establish a necessary and sufficient stability condition for a class of two coupled first-order linear hyperbolic partial differential equations. Through a backstepping transform, the problem is reformulated as a stability problem for an integral difference equation, that is, a difference equation with distributed delay. Building upon a Stépán–Hassard argument variation theorem originally designed for time-delay systems of retarded type, we then introduce a theorem that counts the number of unstable roots of our integral difference equation. This leads to the expected necessary and sufficient stability criterion for the system of first-order linear hyperbolic partial differential equations. Finally, we validate our theoretical findings through simulations.
{"title":"A novel necessary and sufficient condition for the stability of 2×2 first-order linear hyperbolic systems","authors":"Ismaïla Balogoun , Jean Auriol , Islam Boussaada , Guilherme Mazanti","doi":"10.1016/j.sysconle.2025.106066","DOIUrl":"10.1016/j.sysconle.2025.106066","url":null,"abstract":"<div><div>In this paper, we establish a necessary and sufficient stability condition for a class of two coupled first-order linear hyperbolic partial differential equations. Through a backstepping transform, the problem is reformulated as a stability problem for an integral difference equation, that is, a difference equation with distributed delay. Building upon a Stépán–Hassard argument variation theorem originally designed for time-delay systems of retarded type, we then introduce a theorem that counts the number of unstable roots of our integral difference equation. This leads to the expected necessary and sufficient stability criterion for the system of first-order linear hyperbolic partial differential equations. Finally, we validate our theoretical findings through simulations.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"199 ","pages":"Article 106066"},"PeriodicalIF":2.1,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644904","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}
Pub Date : 2025-03-16DOI: 10.1016/j.sysconle.2025.106067
Wan-Ling Qi , Rui Wang , Ming-Sui Yang , Zhuo-Rui Pan , Kun-Zhi Liu
This paper investigates the problem of data-driven dynamic periodic event-triggered mechanism (DPETC) for unknown linear time-invariant (LTI) systems. First, we construct a set of all the systems that are compatible with the collected data. In order to stabilize the true system, we need to stabilize all the systems in the set. Next, we introduce the dynamic periodic event-triggered mechanism and the entire system is reformulated as a hybrid system. Sufficient conditions for -stability of the hybrid system are derived under some assumptions. Then we present a new approach to obtain data-dependent synthesis conditions in the form of linear matrix inequalitys (LMIs). Finally, a numerical example and a hardware-in-the-loop (HIL) example are given to verify the effectiveness of our approach.
{"title":"Data-driven dynamic periodic event-triggered control for unknown linear systems: A hybrid system approach","authors":"Wan-Ling Qi , Rui Wang , Ming-Sui Yang , Zhuo-Rui Pan , Kun-Zhi Liu","doi":"10.1016/j.sysconle.2025.106067","DOIUrl":"10.1016/j.sysconle.2025.106067","url":null,"abstract":"<div><div>This paper investigates the problem of data-driven dynamic periodic event-triggered mechanism (DPETC) for unknown linear time-invariant (LTI) systems. First, we construct a set of all the systems that are compatible with the collected data. In order to stabilize the true system, we need to stabilize all the systems in the set. Next, we introduce the dynamic periodic event-triggered mechanism and the entire system is reformulated as a hybrid system. Sufficient conditions for <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-stability of the hybrid system are derived under some assumptions. Then we present a new approach to obtain data-dependent synthesis conditions in the form of linear matrix inequalitys (LMIs). Finally, a numerical example and a hardware-in-the-loop (HIL) example are given to verify the effectiveness of our approach.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"199 ","pages":"Article 106067"},"PeriodicalIF":2.1,"publicationDate":"2025-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143629308","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}
Pub Date : 2025-03-14DOI: 10.1016/j.sysconle.2025.106068
Lijun Long , Chunxiao Huang , Yiguang Hong
This paper studies input-to-state robust safety (ISRSf) for switched nonlinear systems, and provides a way to describe and analyze the robustness of systems’ safety with respect to external inputs in the switched systems framework. Without requiring the ISRSf of each subsystem, ISRSf via state-dependent switching law is obtained by exploiting a multiple barrier functions method, and a sufficient condition for ruling out Zeno phenomenon is provided. Moreover, ISRSf of switched cascade-connected systems is achieved by using multiple barrier functions and a designed dual switching law. Finally, two illustrative examples, which include a simple mobile robot navigation with controller switching, are presented to demonstrate the feasibility of the theoretical results.
{"title":"Input-to-state robust safety of switched nonlinear systems using multiple barrier functions","authors":"Lijun Long , Chunxiao Huang , Yiguang Hong","doi":"10.1016/j.sysconle.2025.106068","DOIUrl":"10.1016/j.sysconle.2025.106068","url":null,"abstract":"<div><div>This paper studies input-to-state robust safety (ISRSf) for switched nonlinear systems, and provides a way to describe and analyze the robustness of systems’ safety with respect to external inputs in the switched systems framework. Without requiring the ISRSf of each subsystem, ISRSf via state-dependent switching law is obtained by exploiting a multiple barrier functions method, and a sufficient condition for ruling out Zeno phenomenon is provided. Moreover, ISRSf of switched cascade-connected systems is achieved by using multiple barrier functions and a designed dual switching law. Finally, two illustrative examples, which include a simple mobile robot navigation with controller switching, are presented to demonstrate the feasibility of the theoretical results.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"199 ","pages":"Article 106068"},"PeriodicalIF":2.1,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143620783","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}
Pub Date : 2025-03-11DOI: 10.1016/j.sysconle.2025.106062
Mohammadreza Doostmohammadian , Zulfiya R. Gabidullina , Hamid R. Rabiee
This paper proposes an accelerated consensus-based distributed iterative algorithm for resource allocation and scheduling. The proposed gradient-tracking algorithm introduces an auxiliary variable to add momentum towards the optimal state. We prove that this solution is all-time feasible, implying that the coupling constraint always holds along the algorithm iterative procedure; therefore, the algorithm can be terminated at any time. This is in contrast to the ADMM-based solutions that meet constraint feasibility asymptotically. Further, we show that the proposed algorithm can handle possible link nonlinearity due to logarithmically-quantized data transmission (or any sign-preserving odd sector-bound nonlinear mapping). We prove convergence over uniformly-connected dynamic networks (i.e., a hybrid setup) that may occur in mobile and time-varying multi-agent networks. Further, the latency issue over the network is addressed by proposing delay-tolerant solutions. To our best knowledge, accelerated momentum-based convergence, nonlinear linking, all-time feasibility, uniform network connectivity, and handling (possible) time delays are not altogether addressed in the literature. These contributions make our solution practical in many real-world applications.
{"title":"Momentum-based distributed resource scheduling optimization subject to sector-bound nonlinearity and latency","authors":"Mohammadreza Doostmohammadian , Zulfiya R. Gabidullina , Hamid R. Rabiee","doi":"10.1016/j.sysconle.2025.106062","DOIUrl":"10.1016/j.sysconle.2025.106062","url":null,"abstract":"<div><div>This paper proposes an accelerated consensus-based distributed iterative algorithm for resource allocation and scheduling. The proposed gradient-tracking algorithm introduces an auxiliary variable to add momentum towards the optimal state. We prove that this solution is all-time feasible, implying that the coupling constraint always holds along the algorithm iterative procedure; therefore, the algorithm can be terminated at any time. This is in contrast to the ADMM-based solutions that meet constraint feasibility asymptotically. Further, we show that the proposed algorithm can handle possible link nonlinearity due to logarithmically-quantized data transmission (or any sign-preserving odd sector-bound nonlinear mapping). We prove convergence over uniformly-connected dynamic networks (i.e., a hybrid setup) that may occur in mobile and time-varying multi-agent networks. Further, the latency issue over the network is addressed by proposing delay-tolerant solutions. To our best knowledge, accelerated momentum-based convergence, nonlinear linking, all-time feasibility, uniform network connectivity, and handling (possible) time delays are not <em>altogether</em> addressed in the literature. These contributions make our solution practical in many real-world applications.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"199 ","pages":"Article 106062"},"PeriodicalIF":2.1,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592844","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}
Pub Date : 2025-03-11DOI: 10.1016/j.sysconle.2025.106064
Samira Mahmooee, Omid RabieiMotlagh, Haji M. Mohammadinejad
We consider a control problem containing a small Markov jump process and an on–off switch. A novel stochastic time-averaging (not a probability-averaging) technique is presented to calculate an approximate non-stochastic control that steers the system into a small neighborhood of the target point. We compute the control’s accuracy and the admissibility of the corresponding probabilities. This result will be utilized to manage a resonant power converter. The numerical plot confirms the accuracy of the estimated control outlined in this research.
{"title":"A non-stochastic control method for systems under small random jumps","authors":"Samira Mahmooee, Omid RabieiMotlagh, Haji M. Mohammadinejad","doi":"10.1016/j.sysconle.2025.106064","DOIUrl":"10.1016/j.sysconle.2025.106064","url":null,"abstract":"<div><div>We consider a control problem containing a small Markov jump process and an on–off switch. A novel stochastic time-averaging (not a probability-averaging) technique is presented to calculate an approximate non-stochastic control that steers the system into a small neighborhood of the target point. We compute the control’s accuracy and the admissibility of the corresponding probabilities. This result will be utilized to manage a resonant power converter. The numerical plot confirms the accuracy of the estimated control outlined in this research.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"199 ","pages":"Article 106064"},"PeriodicalIF":2.1,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592843","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}
Pub Date : 2025-03-10DOI: 10.1016/j.sysconle.2025.106065
Reza Lavaei, Frank Cao, Amy K. Strong, Leila J. Bridgeman
This paper provides a method to analyze the local, small-signal -gain of control-affine nonlinear systems on compact sets via iterative semi-definite programs. First, a continuous piecewise affine storage function and the corresponding upper bound on the local -gain are found on a bounded, compact set’s triangulation. Then, to ensure that the state does not escape this set, a continuous piecewise affine barrier function is found that is robust to small-signal inputs. Local, small-signal stability then holds inside each sublevel set of the barrier function inside the set where the storage function was found. The method’s effectiveness is shown in a numerical example.
{"title":"Iterative, local, small-signal L2 stability analysis of nonlinear constrained systems","authors":"Reza Lavaei, Frank Cao, Amy K. Strong, Leila J. Bridgeman","doi":"10.1016/j.sysconle.2025.106065","DOIUrl":"10.1016/j.sysconle.2025.106065","url":null,"abstract":"<div><div>This paper provides a method to analyze the local, small-signal <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-gain of control-affine nonlinear systems on compact sets via iterative semi-definite programs. First, a continuous piecewise affine storage function and the corresponding upper bound on the local <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-gain are found on a bounded, compact set’s triangulation. Then, to ensure that the state does not escape this set, a continuous piecewise affine barrier function is found that is robust to small-signal inputs. Local, small-signal <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> stability then holds inside each sublevel set of the barrier function inside the set where the storage function was found. The method’s effectiveness is shown in a numerical example.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"199 ","pages":"Article 106065"},"PeriodicalIF":2.1,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143577500","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}
Pub Date : 2025-03-10DOI: 10.1016/j.sysconle.2025.106063
Jianchun Zhang , Wenshuo Li , Xiang Yu , Lei Guo
In order to quantitatively manage the failure probability/reliability of control systems, we propose a reliability-guaranteed anti-disturbance control (RADC) method via the closed-loop uncertainty quantification (CL-UQ). Specifically, multiple probabilistic intervals are proposed to model the parameter and disturbance uncertainties. Through the CL-UQ analysis, the uncertainty characteristic of the system states can also be depicted by multiple probabilistic intervals. Combining with the designed prescribed performance threshold, a time-varying reliability model for the control process is established. On this basis, the control optimization problem with a reliability constraint for the RADC is formulated to obtain the optimal feedback gain and observer gain. A simulation example of spacecraft attitude stabilization shows that the CL-UQ results meet with the high accuracy and the RADC effectively reduces the conservatism of the traditional anti-disturbance control.
{"title":"Reliability-guaranteed anti-disturbance control via closed-loop uncertainty quantification","authors":"Jianchun Zhang , Wenshuo Li , Xiang Yu , Lei Guo","doi":"10.1016/j.sysconle.2025.106063","DOIUrl":"10.1016/j.sysconle.2025.106063","url":null,"abstract":"<div><div>In order to quantitatively manage the failure probability/reliability of control systems, we propose a reliability-guaranteed anti-disturbance control (RADC) method via the closed-loop uncertainty quantification (CL-UQ). Specifically, multiple probabilistic intervals are proposed to model the parameter and disturbance uncertainties. Through the CL-UQ analysis, the uncertainty characteristic of the system states can also be depicted by multiple probabilistic intervals. Combining with the designed prescribed performance threshold, a time-varying reliability model for the control process is established. On this basis, the control optimization problem with a reliability constraint for the RADC is formulated to obtain the optimal feedback gain and observer gain. A simulation example of spacecraft attitude stabilization shows that the CL-UQ results meet with the high accuracy and the RADC effectively reduces the conservatism of the traditional anti-disturbance control.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"199 ","pages":"Article 106063"},"PeriodicalIF":2.1,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143576714","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}
Pub Date : 2025-03-05DOI: 10.1016/j.sysconle.2025.106059
Sebastian Falkensteiner , Dmitrii Pavlov , J. Rafael Sendra
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.
{"title":"On real and observable rational realizations of input–output equations","authors":"Sebastian Falkensteiner , Dmitrii Pavlov , 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}
Pub Date : 2025-02-25DOI: 10.1016/j.sysconle.2025.106051
Sébastien Fueyo
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.
{"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}
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