Pub Date : 2025-06-25DOI: 10.1016/j.nahs.2025.101617
Shen Cong
We attempt to offer an informative insight into the stability mechanism of Markovian switching systems from the perspective of Lyapunov method. With this aim, our efforts are devoted to refining a stability criterion that was posed in Cong (2018) and moreover, showing that all kinds of existing results derived from Lyapunov method in principle can be recovered as special cases of the refined one, due to overlooking certain things that may influence stability. To do so, it requires us to fully understand the construction and the computation of the Lyapunov function used in proving our result, which in turn requires us to work with renewal theory other than confining ourselves within the context of Markov chain theory for describing switching signals.
{"title":"A refined stability result for linear Markovian switching systems and its implications","authors":"Shen Cong","doi":"10.1016/j.nahs.2025.101617","DOIUrl":"10.1016/j.nahs.2025.101617","url":null,"abstract":"<div><div>We attempt to offer an informative insight into the stability mechanism of Markovian switching systems from the perspective of Lyapunov method. With this aim, our efforts are devoted to refining a stability criterion that was posed in Cong (2018) and moreover, showing that all kinds of existing results derived from Lyapunov method in principle can be recovered as special cases of the refined one, due to overlooking certain things that may influence stability. To do so, it requires us to fully understand the construction and the computation of the Lyapunov function used in proving our result, which in turn requires us to work with renewal theory other than confining ourselves within the context of Markov chain theory for describing switching signals.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"58 ","pages":"Article 101617"},"PeriodicalIF":3.7,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144469914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-05-30DOI: 10.1016/j.nahs.2025.101607
B.C. van Huijgevoort , M.H.W. Engelaar , S. Soudjani , S. Haesaert
We present SySCoRe 2.0, a MATLAB toolset that synthesizes controllers for stochastic systems to satisfy temporal logic specifications. Starting from a system description and a co-safe temporal logic specification, SySCoRe provides all necessary functions for synthesizing a robust controller and quantifying the associated formal robustness guarantees. It distinguishes itself from other available tools by supporting both stochastic model order reduction techniques and space discretizations, and by being applicable to nonlinear dynamics and complex co-safe temporal logic specifications over infinite horizons. To achieve this, SySCoRe generates a finite abstraction from a possibly reduced-order version of the provided model and performs probabilistic model checking. Then, it establishes a probabilistic coupling between the original model and its finite abstraction encoded in an approximate simulation relation, based on which a lower bound on the satisfaction probability is computed. The error computed by SySCoRe does not grow linearly in the horizon of the specification, thus it provides non-trivial lower bounds for infinite-horizon specifications and unbounded disturbances. SySCoRe exploits a tensor representation to facilitate an efficient computation of transition probabilities in the finite abstraction. We showcase these features on several benchmarks and compare the performance of the toolset with existing tools and with the previous version of SySCoRe.
{"title":"SySCoRe 2.0: Toolset for formal control synthesis of continuous-state stochastic systems and temporal logic specifications","authors":"B.C. van Huijgevoort , M.H.W. Engelaar , S. Soudjani , S. Haesaert","doi":"10.1016/j.nahs.2025.101607","DOIUrl":"10.1016/j.nahs.2025.101607","url":null,"abstract":"<div><div>We present <span>SySCoRe</span> 2.0, a <span>MATLAB</span> toolset that synthesizes controllers for stochastic systems to satisfy temporal logic specifications. Starting from a system description and a co-safe temporal logic specification, <span>SySCoRe</span> provides all necessary functions for synthesizing a robust controller and quantifying the associated formal robustness guarantees. It distinguishes itself from other available tools by supporting both stochastic model order reduction techniques and space discretizations, and by being applicable to nonlinear dynamics and complex co-safe temporal logic specifications over infinite horizons. To achieve this, <span>SySCoRe</span> generates a finite abstraction from a possibly reduced-order version of the provided model and performs probabilistic model checking. Then, it establishes a probabilistic coupling between the original model and its finite abstraction encoded in an approximate simulation relation, based on which a lower bound on the satisfaction probability is computed. The error computed by <span>SySCoRe</span> does not grow linearly in the horizon of the specification, thus it provides non-trivial lower bounds for infinite-horizon specifications and unbounded disturbances. <span>SySCoRe</span> exploits a tensor representation to facilitate an efficient computation of transition probabilities in the finite abstraction. We showcase these features on several benchmarks and compare the performance of the toolset with existing tools and with the previous version of <span>SySCoRe</span>.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"58 ","pages":"Article 101607"},"PeriodicalIF":3.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144178526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-05-28DOI: 10.1016/j.nahs.2025.101609
Yafei Zhai , Fubao Xi
As a continuation of the study by Hou and Shao [Sci. China Math., 63 (2020), pp. 1169-1180], this work makes three key advances in studying state-dependent switching Cox–Ingersoll–Ross processes. First, we establish tail behavior results for stationary distributions across both finite and infinite regimes-a significant extension beyond their framework. Second, through novel auxiliary Markov chains, we explicitly construct a comparison theorem specifically adapted for state-dependent switching diffusions. Third, we derive sufficient recurrence conditions for infinite-regime cases. Our approach provides rigorous control of state-dependent switching component processes with Markov chains and remains applicable to broader classes of state-dependent switching diffusion processes.
作为侯、邵研究的延续[Sci。中国数学。， 63 (2020), pp. 1169-1180]，这项工作在研究状态依赖开关Cox-Ingersoll-Ross过程方面取得了三个关键进展。首先，我们建立了有限和无限状态下平稳分布的尾部行为结果-这是对其框架的重要扩展。其次，通过新的辅助马尔可夫链，我们明确地构造了一个特别适用于状态相关切换扩散的比较定理。第三，我们得到了无限区情形的充分递归条件。我们的方法提供了具有马尔可夫链的状态相关切换组件过程的严格控制，并且仍然适用于更广泛类别的状态相关切换扩散过程。
{"title":"The tail behavior of Cox–Ingersoll–Ross processes with state-dependent switching","authors":"Yafei Zhai , Fubao Xi","doi":"10.1016/j.nahs.2025.101609","DOIUrl":"10.1016/j.nahs.2025.101609","url":null,"abstract":"<div><div>As a continuation of the study by Hou and Shao [Sci. China Math., 63 (2020), pp. 1169-1180], this work makes three key advances in studying state-dependent switching Cox–Ingersoll–Ross processes. First, we establish tail behavior results for stationary distributions across both finite and infinite regimes-a significant extension beyond their framework. Second, through novel auxiliary Markov chains, we explicitly construct a comparison theorem specifically adapted for state-dependent switching diffusions. Third, we derive sufficient recurrence conditions for infinite-regime cases. Our approach provides rigorous control of state-dependent switching component processes with Markov chains and remains applicable to broader classes of state-dependent switching diffusion processes.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"57 ","pages":"Article 101609"},"PeriodicalIF":3.7,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144166907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-05-20DOI: 10.1016/j.nahs.2025.101604
D.A. Deenen , E. Maljaars , L.C. Sebeke , B. de Jager , E. Heijman , H. Grüll , W.P.M.H. Heemels
A switched-actuator system with setup times (SAcSS) is a system in which the actuator configuration has to be switched during operation, and where the switching induces non-negligible actuator downtime. Optimally controlling SAcSSs requires the online solving of both a discrete actuator allocation problem, in which the switch-induced actuator downtime is taken into account, as well as an optimization problem for the (typically continuous) control inputs. Mixed-integer model predictive control (MI-MPC) offers a powerful framework for tackling such problems. However, the efficient modeling of SAcSSs for MI-MPC is not straightforward, and real-time feasibility is often a major hurdle in practice. It is the objective of this paper to provide an intuitive and systematic modeling procedure tailored to SAcSSs, which is specifically designed to allow for user-friendly controller synthesis, and to yield efficient MI-MPCs. We apply these new results in a case study of large-volume magnetic-resonance-guided high-intensity focused ultrasound hyperthermia, which involves the heating of tumors (using real-valued local heating controls, as well as discrete range-extending actuator relocation during which no heating is allowed) to enhance the efficacy of radio- and chemotherapy.
{"title":"Model predictive control of switched-actuator systems with setup times, and application to hyperthermia cancer therapies","authors":"D.A. Deenen , E. Maljaars , L.C. Sebeke , B. de Jager , E. Heijman , H. Grüll , W.P.M.H. Heemels","doi":"10.1016/j.nahs.2025.101604","DOIUrl":"10.1016/j.nahs.2025.101604","url":null,"abstract":"<div><div>A switched-actuator system with setup times (SAcSS) is a system in which the actuator configuration has to be switched during operation, and where the switching induces non-negligible actuator downtime. Optimally controlling SAcSSs requires the online solving of both a discrete actuator allocation problem, in which the switch-induced actuator downtime is taken into account, as well as an optimization problem for the (typically continuous) control inputs. Mixed-integer model predictive control (MI-MPC) offers a powerful framework for tackling such problems. However, the efficient modeling of SAcSSs for MI-MPC is not straightforward, and real-time feasibility is often a major hurdle in practice. It is the objective of this paper to provide an intuitive and systematic modeling procedure tailored to SAcSSs, which is specifically designed to allow for user-friendly controller synthesis, and to yield efficient MI-MPCs. We apply these new results in a case study of large-volume magnetic-resonance-guided high-intensity focused ultrasound hyperthermia, which involves the heating of tumors (using real-valued local heating controls, as well as discrete range-extending actuator relocation during which no heating is allowed) to enhance the efficacy of radio- and chemotherapy.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"57 ","pages":"Article 101604"},"PeriodicalIF":3.7,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144089442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-05-15DOI: 10.1016/j.nahs.2025.101601
Aili Fan , Lin Du , Junmin Li , Yuhua Du , Zichen Deng , Jinde Cao
In this article, we mainly address the function matrix projective synchronization (FMPS) problem with prescribed performance (PP) between a drive network (DN) with time-varying uncertain coupling, and its corresponding response network (RN) with mismatched dimensions. A new hybrid adaptive learning law is proposed, which consists of a discrete adaptive law designed for unknown time-varying coupling coefficients, and a continuous adaptive law designed for time-invariant coefficients. The proposed work extends the adaptive synchronization control that is originally applicable only with the constant coupling coefficient to the case where the coefficients are time-varying. To ensure the state trajectories of the RN are projectively synchronized to those of the DN while complying with PP constraints, a PP controller is designed. Meanwhile, to reduce the communication load, the event-triggered communication (ETC) mechanism is implemented. Finally, the effectiveness of the designed control scheme, adaptive laws and ETC protocol is validated through simulation.
{"title":"Prescribed performance projective synchronization for unknown complex networks with mismatched dimensions via event-triggered mechanism","authors":"Aili Fan , Lin Du , Junmin Li , Yuhua Du , Zichen Deng , Jinde Cao","doi":"10.1016/j.nahs.2025.101601","DOIUrl":"10.1016/j.nahs.2025.101601","url":null,"abstract":"<div><div>In this article, we mainly address the function matrix projective synchronization (FMPS) problem with prescribed performance (PP) between a drive network (DN) with time-varying uncertain coupling, and its corresponding response network (RN) with mismatched dimensions. A new hybrid adaptive learning law is proposed, which consists of a discrete adaptive law designed for unknown time-varying coupling coefficients, and a continuous adaptive law designed for time-invariant coefficients. The proposed work extends the adaptive synchronization control that is originally applicable only with the constant coupling coefficient to the case where the coefficients are time-varying. To ensure the state trajectories of the RN are projectively synchronized to those of the DN while complying with PP constraints, a PP controller is designed. Meanwhile, to reduce the communication load, the event-triggered communication (ETC) mechanism is implemented. Finally, the effectiveness of the designed control scheme, adaptive laws and ETC protocol is validated through simulation.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"57 ","pages":"Article 101601"},"PeriodicalIF":3.7,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143948256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the problem of predictive monitoring (PM), i.e., predicting at runtime the satisfaction of a desired property from the current system’s state. Due to its relevance for runtime safety assurance and online control, PM methods need to be efficient to enable timely interventions against predicted violations, while providing correctness guarantees. We introduce quantitative predictive monitoring (QPM), a PM method to support stochastic processes and rich specifications given in Signal Temporal Logic (STL). QPM provides a quantitative measure of satisfaction of some property by predicting its quantitative (a.k.a. robust) STL semantics, either spatial or temporal. QPM derives prediction intervals that are highly efficient to compute and with probabilistic guarantees, in that the intervals cover with arbitrary probability the STL robustness values relative to the stochastic evolution of the system. To do so, we take a machine-learning approach and leverage recent advances in conformal inference for quantile regression, thereby avoiding expensive Monte Carlo simulations at runtime to estimate the intervals. We also show how our monitors can be combined in a compositional manner to handle composite formulas, without retraining the predictors or sacrificing the guarantees. We further equip QPM with techniques to ensure conditional validity of the prediction intervals, i.e., such that the probabilistic guarantees hold relative to any state of the system (or any satisfaction value), thereby significantly enhancing the consistency and reliability of the resulting monitor. We demonstrate the effectiveness and scalability of QPM over a benchmark of five discrete-time stochastic processes with varying degrees of complexity, including a stochastic multi-agent system.
{"title":"Conformal quantitative predictive monitoring of stochastic systems with conditional validity","authors":"Francesca Cairoli , Tom Kuipers , Luca Bortolussi , Nicola Paoletti","doi":"10.1016/j.nahs.2025.101606","DOIUrl":"10.1016/j.nahs.2025.101606","url":null,"abstract":"<div><div>We consider the problem of predictive monitoring (PM), i.e., predicting at runtime the satisfaction of a desired property from the current system’s state. Due to its relevance for runtime safety assurance and online control, PM methods need to be efficient to enable timely interventions against predicted violations, while providing correctness guarantees. We introduce <em>quantitative predictive monitoring (QPM)</em>, a PM method to support stochastic processes and rich specifications given in Signal Temporal Logic (STL). QPM provides a quantitative measure of satisfaction of some property <span><math><mi>ϕ</mi></math></span> by predicting its quantitative (a.k.a. robust) STL semantics, either spatial or temporal. QPM derives prediction intervals that are highly efficient to compute and with probabilistic guarantees, in that the intervals cover with arbitrary probability the STL robustness values relative to the stochastic evolution of the system. To do so, we take a machine-learning approach and leverage recent advances in conformal inference for quantile regression, thereby avoiding expensive Monte Carlo simulations at runtime to estimate the intervals. We also show how our monitors can be combined in a compositional manner to handle composite formulas, without retraining the predictors or sacrificing the guarantees. We further equip QPM with techniques to ensure conditional validity of the prediction intervals, i.e., such that the probabilistic guarantees hold relative to any state of the system (or any satisfaction value), thereby significantly enhancing the consistency and reliability of the resulting monitor. We demonstrate the effectiveness and scalability of QPM over a benchmark of five discrete-time stochastic processes with varying degrees of complexity, including a stochastic multi-agent system.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"57 ","pages":"Article 101606"},"PeriodicalIF":3.7,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143942252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-05-14DOI: 10.1016/j.nahs.2025.101608
Thomas Mejstrik , Vladimir Yu. Protasov
We investigate the stability of continuous-time linear switching systems with a guaranteed dwell time. It is known that the dwell time restrictions make the main methods for deciding stability such as Lyapunov functions and discretization inapplicable, at least in their standard forms. Our work focuses on adapting the discretization approach to address this limitation. The discretization is done merely by replacing arbitrary switching law with piecewise-constant functions with a fixed step size. We demonstrate that this classical method can be modified so that it not only becomes applicable under the dwell time constraints but also outperforms traditional methods for unconstrained systems. Namely, the discretization with the step size approximates the Lyapunov exponent with the precision , and the constant can be explicitly evaluated. This result is unexpected, as the approximation accuracy for systems without a guaranteed dwell time is linear in . Our methods implementation is efficient in dimensions up to 10 for arbitrary systems and up to several hundreds for positive systems. The numerical results are provided.
{"title":"Stability under dwell time constraints: Discretization revisited","authors":"Thomas Mejstrik , Vladimir Yu. Protasov","doi":"10.1016/j.nahs.2025.101608","DOIUrl":"10.1016/j.nahs.2025.101608","url":null,"abstract":"<div><div>We investigate the stability of continuous-time linear switching systems with a guaranteed dwell time. It is known that the dwell time restrictions make the main methods for deciding stability such as Lyapunov functions and discretization inapplicable, at least in their standard forms. Our work focuses on adapting the discretization approach to address this limitation. The discretization is done merely by replacing arbitrary switching law with piecewise-constant functions with a fixed step size. We demonstrate that this classical method can be modified so that it not only becomes applicable under the dwell time constraints but also outperforms traditional methods for unconstrained systems. Namely, the discretization with the step size <span><math><mi>h</mi></math></span> approximates the Lyapunov exponent with the precision <span><math><mrow><mi>C</mi><mspace></mspace><msup><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>, and the constant <span><math><mi>C</mi></math></span> can be explicitly evaluated. This result is unexpected, as the approximation accuracy for systems without a guaranteed dwell time is linear in <span><math><mi>h</mi></math></span>. Our methods implementation is efficient in dimensions up to 10 for arbitrary systems and up to several hundreds for positive systems. The numerical results are provided.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"57 ","pages":"Article 101608"},"PeriodicalIF":3.7,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143948255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-05-12DOI: 10.1016/j.nahs.2025.101605
Wenjing Wan , Zhao-Yan Li , Kai Zhang
This paper investigates the mean square output tracking control problem in heterogeneous multi-agent systems (HMASs) influenced by semi-Markovian switching topologies and multiple forms measurement noises. A novel distributed output feedback control scheme is proposed, ensuring robustness in environments characterized by stochastic topology changes and diverse noise types. Unlike previous methods, our research addresses both additive and multiplicative noises and general sojourn time distributions during topology switching, thereby providing a more general framework. The stability and convergence of the proposed approach are rigorously analyzed using Lyapunov-based techniques, and its efficacy is validated through two examples.
{"title":"Cooperative output feedback tracking control of heterogeneous multi-agent systems with semi-Markovian switching topologies and multiple measurement noises","authors":"Wenjing Wan , Zhao-Yan Li , Kai Zhang","doi":"10.1016/j.nahs.2025.101605","DOIUrl":"10.1016/j.nahs.2025.101605","url":null,"abstract":"<div><div>This paper investigates the mean square output tracking control problem in heterogeneous multi-agent systems (HMASs) influenced by semi-Markovian switching topologies and multiple forms measurement noises. A novel distributed output feedback control scheme is proposed, ensuring robustness in environments characterized by stochastic topology changes and diverse noise types. Unlike previous methods, our research addresses both additive and multiplicative noises and general sojourn time distributions during topology switching, thereby providing a more general framework. The stability and convergence of the proposed approach are rigorously analyzed using Lyapunov-based techniques, and its efficacy is validated through two examples.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"57 ","pages":"Article 101605"},"PeriodicalIF":3.7,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-04-28DOI: 10.1016/j.nahs.2025.101602
Marco Florentino , Tiago Carvalho
In this paper we establish conditions in order to obtain a set of trajectories of -dimensional piecewise smooth vector fields that preserves measure even in the case where sliding motion is allowed. The key hypothesis is the occurrence of a sliding–escaping connection. As consequence, classical results from the ergodic theory of dynamical systems can be adapted for the context of piecewise smooth vector fields, just as the Poincaré’s Recurrence Theorem and the Birkhoff’s Theorem. Also, we apply the results for previous models of the literature.
{"title":"Piecewise smooth vector fields with sliding motion preserving measure","authors":"Marco Florentino , Tiago Carvalho","doi":"10.1016/j.nahs.2025.101602","DOIUrl":"10.1016/j.nahs.2025.101602","url":null,"abstract":"<div><div>In this paper we establish conditions in order to obtain a set of trajectories of <span><math><mi>n</mi></math></span>-dimensional piecewise smooth vector fields that preserves measure even in the case where sliding motion is allowed. The key hypothesis is the occurrence of a sliding–escaping connection. As consequence, classical results from the ergodic theory of dynamical systems can be adapted for the context of piecewise smooth vector fields, just as the Poincaré’s Recurrence Theorem and the Birkhoff’s Theorem. Also, we apply the results for previous models of the literature.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"57 ","pages":"Article 101602"},"PeriodicalIF":3.7,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143879020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-04-26DOI: 10.1016/j.nahs.2025.101603
Fei Wang , Jun-e Feng , Biao Wang
This paper presents a systematic mathematical analysis of the network reconstruction problem based on the algebraic model of networked evolutionary games, focusing on two data scenarios: (1) players’ payoff and strategy data, and (2) only players’ strategy data. Begin with the first scenario, the players’ payoff functions are transformed into a system of linear equations concerning neighbors using the payoff vector of the fundamental network game. Then the necessary and sufficient conditions for reconstructing the player network from the payoff functions are provided. In the second scenario, by considering the myopic best response and the unconditional imitation updating rules, the conditions under which the fundamental network game ensures that the strategy dynamic equations contain information about all player neighbors are investigated. Moreover, criteria for determining neighbors from these strategy dynamic equations are proposed. Finally, two examples demonstrate the network reconstruction process.
{"title":"Reconstructing networks from the algebraic model of networked evolutionary games","authors":"Fei Wang , Jun-e Feng , Biao Wang","doi":"10.1016/j.nahs.2025.101603","DOIUrl":"10.1016/j.nahs.2025.101603","url":null,"abstract":"<div><div>This paper presents a systematic mathematical analysis of the network reconstruction problem based on the algebraic model of networked evolutionary games, focusing on two data scenarios: (1) players’ payoff and strategy data, and (2) only players’ strategy data. Begin with the first scenario, the players’ payoff functions are transformed into a system of linear equations concerning neighbors using the payoff vector of the fundamental network game. Then the necessary and sufficient conditions for reconstructing the player network from the payoff functions are provided. In the second scenario, by considering the myopic best response and the unconditional imitation updating rules, the conditions under which the fundamental network game ensures that the strategy dynamic equations contain information about all player neighbors are investigated. Moreover, criteria for determining neighbors from these strategy dynamic equations are proposed. Finally, two examples demonstrate the network reconstruction process.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"57 ","pages":"Article 101603"},"PeriodicalIF":3.7,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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