Pub Date : 2025-05-01Epub Date: 2025-02-10DOI: 10.1016/j.nahs.2025.101580
Xiju Wu , Yue Zhang , Xinzhu Yan
In this paper, we investigate a stochastic hybrid epidemic model with alert effects and telegraph noise. The existence and uniqueness of global positive solution is discussed, and the sufficient conditions for the average persistence and ergodic stationary distribution are obtained. Furthermore, a sliding-mode controller is designed to prevent the large-scale spread of the epidemic. Finally, number simulations are employed to illustrate the theoretical analysis.
{"title":"Stationary distribution and sliding mode control on a stochastic hybrid epidemic model with telegraph noise","authors":"Xiju Wu , Yue Zhang , Xinzhu Yan","doi":"10.1016/j.nahs.2025.101580","DOIUrl":"10.1016/j.nahs.2025.101580","url":null,"abstract":"<div><div>In this paper, we investigate a stochastic hybrid epidemic model with alert effects and telegraph noise. The existence and uniqueness of global positive solution is discussed, and the sufficient conditions for the average persistence and ergodic stationary distribution are obtained. Furthermore, a sliding-mode controller is designed to prevent the large-scale spread of the epidemic. Finally, number simulations are employed to illustrate the theoretical analysis.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"56 ","pages":"Article 101580"},"PeriodicalIF":3.7,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143377025","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 : 2025-05-01Epub Date: 2024-12-10DOI: 10.1016/j.nahs.2024.101567
Yihong Tang, Yuan Liu, Qiang Ling
This paper investigates the finite bit rate stabilization of a switched linear system whose feedback packets are transmitted through a communication network with bounded time-varying delays. The unknown network delay and mode switching cause unavoidable asynchronous modes between the sensor and the controller, and greatly complicate the stabilization of that system. To resolve these issues, an event-triggering mechanism and a quantization method with a finite bit rate are proposed to sample, quantize and transmit the feedback signals. Furthermore, state estimation updating methods are designed to eliminate the effects of time-varying delays on state estimation errors. We derive sufficient stabilizing conditions in terms of average dwell time and feedback bit rate through determining the convergence rates of the Lyapunov function at sampling instants under different switching scenarios. Simulations are presented to verify the effectiveness of the proposed strategies.
{"title":"Finite bit rate stabilization of switched linear systems with bounded delay based on event-triggering control","authors":"Yihong Tang, Yuan Liu, Qiang Ling","doi":"10.1016/j.nahs.2024.101567","DOIUrl":"10.1016/j.nahs.2024.101567","url":null,"abstract":"<div><div>This paper investigates the finite bit rate stabilization of a switched linear system whose feedback packets are transmitted through a communication network with bounded time-varying delays. The unknown network delay and mode switching cause unavoidable asynchronous modes between the sensor and the controller, and greatly complicate the stabilization of that system. To resolve these issues, an event-triggering mechanism and a quantization method with a finite bit rate are proposed to sample, quantize and transmit the feedback signals. Furthermore, state estimation updating methods are designed to eliminate the effects of time-varying delays on state estimation errors. We derive sufficient stabilizing conditions in terms of average dwell time and feedback bit rate through determining the convergence rates of the Lyapunov function at sampling instants under different switching scenarios. Simulations are presented to verify the effectiveness of the proposed strategies.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"56 ","pages":"Article 101567"},"PeriodicalIF":3.7,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143144674","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 : 2025-05-01Epub Date: 2024-12-04DOI: 10.1016/j.nahs.2024.101557
André M. de Oliveira , Oswaldo L.V. Costa
This paper deals with the design of dynamic output feedback controllers for phase-type distributed semi-Markov jump linear systems. It is assumed that the state-space of the semi-Markov jump process can be written as the union of disjoint sets, called clusters, and that the only information available to the controller regarding the jumping process is which cluster it belongs to. We provide two sets of design conditions for the control problem, written in terms of bilinear matrix inequalities, which are associated with the observability and controllability Grammians (referred to as the “primal” and “dual” approaches, respectively). An iterative separation procedure, formulated as a sequence of linear matrix inequalities optimization problems, is proposed to reduce an upper bound of the norm of the system for both the primal and dual design conditions. We show that our conditions are not conservative in the sense that, for the Markov mode-dependent case, they also become necessary. Finally, we study the robust case, considering that the system matrices and transition rate matrix have polytopic uncertainties, and the observer-based control case, for which the conditions can be simplified and written directly as linear matrix inequalities. The paper concludes with an illustrative example in the context of systems subject to actuator and sensor faults.
{"title":"H2 dynamic output feedback control of phase-type semi-Markov jump linear systems","authors":"André M. de Oliveira , Oswaldo L.V. Costa","doi":"10.1016/j.nahs.2024.101557","DOIUrl":"10.1016/j.nahs.2024.101557","url":null,"abstract":"<div><div>This paper deals with the design of <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> dynamic output feedback controllers for phase-type distributed semi-Markov jump linear systems. It is assumed that the state-space of the semi-Markov jump process can be written as the union of disjoint sets, called <em>clusters</em>, and that the only information available to the controller regarding the jumping process is which cluster it belongs to. We provide two sets of design conditions for the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> control problem, written in terms of bilinear matrix inequalities, which are associated with the observability and controllability Grammians (referred to as the “primal” and “dual” approaches, respectively). An iterative separation procedure, formulated as a sequence of linear matrix inequalities optimization problems, is proposed to reduce an upper bound of the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> norm of the system for both the primal and dual design conditions. We show that our conditions are not conservative in the sense that, for the Markov mode-dependent case, they also become necessary. Finally, we study the robust case, considering that the system matrices and transition rate matrix have polytopic uncertainties, and the observer-based control case, for which the conditions can be simplified and written directly as linear matrix inequalities. The paper concludes with an illustrative example in the context of systems subject to actuator and sensor faults.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"56 ","pages":"Article 101557"},"PeriodicalIF":3.7,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143144622","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 : 2025-05-01Epub Date: 2025-02-06DOI: 10.1016/j.nahs.2025.101579
Ran Tian, Jie Mei, Guangfu Ma
This paper addresses the issue of differential privacy-preserving in multi-agent systems (MASs) with the existence of misbehaving agents and antagonistic interactions over a signed digraph. Even with the existence of a maximum of faulty agents within the network, non-faulty agents pursue resilient bipartite consensus, with the requirement that their initial conditions can fulfill differential privacy. To this end, we propose the differentially private absolute weighted mean subsequence reduced (DP-AW-MSR) algorithm. Under the structurally balanced signed digraph with sufficient connectivity in terms of robustness, three essential properties of this algorithm are characterized: resilient bipartite consensus, accuracy and differential privacy. Numerical simulation is given to illustrate the effectiveness of our findings.
{"title":"Privacy-preserving resilient bipartite consensus of multi-agent systems: A differential privacy scheme","authors":"Ran Tian, Jie Mei, Guangfu Ma","doi":"10.1016/j.nahs.2025.101579","DOIUrl":"10.1016/j.nahs.2025.101579","url":null,"abstract":"<div><div>This paper addresses the issue of differential privacy-preserving in multi-agent systems (MASs) with the existence of misbehaving agents and antagonistic interactions over a signed digraph. Even with the existence of a maximum of <span><math><mi>f</mi></math></span> faulty agents within the network, non-faulty agents pursue resilient bipartite consensus, with the requirement that their initial conditions can fulfill differential privacy. To this end, we propose the differentially private absolute weighted mean subsequence reduced (DP-AW-MSR) algorithm. Under the structurally balanced signed digraph with sufficient connectivity in terms of robustness, three essential properties of this algorithm are characterized: resilient bipartite consensus, accuracy and differential privacy. Numerical simulation is given to illustrate the effectiveness of our findings.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"56 ","pages":"Article 101579"},"PeriodicalIF":3.7,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143329433","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 : 2025-05-01Epub Date: 2025-02-13DOI: 10.1016/j.nahs.2025.101583
Chunfeng Jiang , Shihua Fu , Carmen Del Vecchio , Biao Wang , Jianjun Wang , Jianli Zhao
This paper addresses the recurrent output tracking problem (ROTP) in Boolean networks (BNs), that is the property of systems output to intermittently and infinitely track a desired reference signal over long-term operation. Leveraging the semi-tensor product of matrices as the primary analytical tool, the study proposes solvability criteria for ROTP in both BNs and Boolean control networks (BCNs), and proposes algorithms to identify all states that enable recurrent tracking of the reference signal in these systems. Additionally, a truth matrix-based method is used to design state feedback controllers, ensuring ROTP solvability for BCNs initiating from such states. The study also explores the periodicity of the recurrent output tracking in B(C)Ns, demonstrating that the output tracking problem is a specific instance of the ROTP. The effectiveness of the proposed methods and results is validated through illustrative examples.
{"title":"Recurrent output tracking of Boolean networks","authors":"Chunfeng Jiang , Shihua Fu , Carmen Del Vecchio , Biao Wang , Jianjun Wang , Jianli Zhao","doi":"10.1016/j.nahs.2025.101583","DOIUrl":"10.1016/j.nahs.2025.101583","url":null,"abstract":"<div><div>This paper addresses the recurrent output tracking problem (ROTP) in Boolean networks (BNs), that is the property of systems output to intermittently and infinitely track a desired reference signal over long-term operation. Leveraging the semi-tensor product of matrices as the primary analytical tool, the study proposes solvability criteria for ROTP in both BNs and Boolean control networks (BCNs), and proposes algorithms to identify all states that enable recurrent tracking of the reference signal in these systems. Additionally, a truth matrix-based method is used to design state feedback controllers, ensuring ROTP solvability for BCNs initiating from such states. The study also explores the periodicity of the recurrent output tracking in B(C)Ns, demonstrating that the output tracking problem is a specific instance of the ROTP. The effectiveness of the proposed methods and results is validated through illustrative examples.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"56 ","pages":"Article 101583"},"PeriodicalIF":3.7,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143402959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-05-01Epub Date: 2024-12-09DOI: 10.1016/j.nahs.2024.101559
Jian Xiang , Ruggero Lanotte , Simone Tini , Stephen Chong , Massimo Merro
This paper contributes a formal framework for quantitative analysis of bounded sensor attacks on cyber–physical systems, using the formalism of differential dynamic logic. Given a precondition and postcondition of a system, we formalize two quantitative safety notions, quantitative forward and backward safety, which respectively express (1) how strong the strongest postcondition of the system is with respect to the specified postcondition, and (2) how strong the specified precondition is with respect to the weakest precondition of the system needed to ensure the specified postcondition holds. We introduce two notions, forward and backward robustness, to characterize the robustness of a system against sensor attacks as the loss of safety. To reason about robustness, we introduce two simulation distances, forward and backward simulation distances, which are defined based on the behavioral distances between the original system and the system with compromised sensors. Forward and backward distances, respectively, characterize upper bounds of the degree of forward and backward safety loss caused by the sensor attacks. We verify the two simulation distances by expressing them as modalities, i.e., formulas of differential dynamic logic, and develop an ad-hoc proof system to reason with such formulas. We showcase our formal notions and reasoning techniques on two non-trivial case studies: an autonomous vehicle that needs to avoid collision and a water tank system.
{"title":"Measuring robustness in cyber-physical systems under sensor attacks","authors":"Jian Xiang , Ruggero Lanotte , Simone Tini , Stephen Chong , Massimo Merro","doi":"10.1016/j.nahs.2024.101559","DOIUrl":"10.1016/j.nahs.2024.101559","url":null,"abstract":"<div><div>This paper contributes a formal framework for quantitative analysis of bounded sensor attacks on cyber–physical systems, using the formalism of differential dynamic logic. Given a precondition and postcondition of a system, we formalize two quantitative safety notions, quantitative forward and backward safety, which respectively express (1) how strong the strongest postcondition of the system is with respect to the specified postcondition, and (2) how strong the specified precondition is with respect to the weakest precondition of the system needed to ensure the specified postcondition holds. We introduce two notions, forward and backward robustness, to characterize the robustness of a system against sensor attacks as the loss of safety. To reason about robustness, we introduce two simulation distances, forward and backward simulation distances, which are defined based on the behavioral distances between the original system and the system with compromised sensors. Forward and backward distances, respectively, characterize upper bounds of the degree of forward and backward safety loss caused by the sensor attacks. We verify the two simulation distances by expressing them as modalities, i.e., formulas of differential dynamic logic, and develop an ad-hoc proof system to reason with such formulas. We showcase our formal notions and reasoning techniques on two non-trivial case studies: an autonomous vehicle that needs to avoid collision and a water tank system.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"56 ","pages":"Article 101559"},"PeriodicalIF":3.7,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143144671","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 : 2025-05-01Epub Date: 2025-01-09DOI: 10.1016/j.nahs.2024.101571
Yushen Huang , Ertai Luo , Stanley Bak, Yifan Sun
In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast to previous methods, our approach is able to tightly capture the non-convexity of the reachable set. Building up on our main result, we show how our reachability algorithm can be extended to handle linear time-varying systems as well as linear systems with time-varying parameters. Moreover, our approach opens up new possibilities for reachability analysis of linear time-invariant systems, nonlinear systems, and hybrid systems. We compare our approach to other state of the art methods, with superior tightness on two benchmarks including a 9-dimensional vehicle platooning system. Moreover, as part of the journal extension, we investigate through a polynomial zonotope with special structure named multi-affine zonotopes and its optimization problem. We provide the corresponding optimization algorithm and experiment over the examples obtained from two benchmark systems, showing the efficiency and scalability comparing to the state of the art method for handling such type of set representation.
{"title":"Reachability analysis for linear systems with uncertain parameters using polynomial zonotopes","authors":"Yushen Huang , Ertai Luo , Stanley Bak, Yifan Sun","doi":"10.1016/j.nahs.2024.101571","DOIUrl":"10.1016/j.nahs.2024.101571","url":null,"abstract":"<div><div>In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast to previous methods, our approach is able to tightly capture the non-convexity of the reachable set. Building up on our main result, we show how our reachability algorithm can be extended to handle linear time-varying systems as well as linear systems with time-varying parameters. Moreover, our approach opens up new possibilities for reachability analysis of linear time-invariant systems, nonlinear systems, and hybrid systems. We compare our approach to other state of the art methods, with superior tightness on two benchmarks including a 9-dimensional vehicle platooning system. Moreover, as part of the journal extension, we investigate through a polynomial zonotope with special structure named multi-affine zonotopes and its optimization problem. We provide the corresponding optimization algorithm and experiment over the examples obtained from two benchmark systems, showing the efficiency and scalability comparing to the state of the art method for handling such type of set representation.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"56 ","pages":"Article 101571"},"PeriodicalIF":3.7,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143144673","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 : 2025-05-01Epub Date: 2025-02-12DOI: 10.1016/j.nahs.2025.101582
Yue Zhang, Xin Ai, Zhenlei Li, Jie Gao
In this paper, the piecewise-smooth functional response function and distributed delay are used to describe the memory effect of predators and capture law when the abundance of prey changes greatly in ecosystems more realistically. A singular piecewise-smooth prey–predator model with distributed delay is studied. Considering the growth and loss rate of the predator much smaller than that of the prey, the model is described by a fast–slow system that mathematically leads to a singular perturbation problem. The dynamic behavior of the fast–slow system with distributed delay, piecewise smooth is novel and interesting. The system undergoes a Hopf bifurcation where the interior equilibrium becomes unstable leading to a stable limit cycle. As the perturbation parameter decreases, the co-existence equilibrium has a transition from the unstable node to the stable node which leads multiple relaxation oscillations occurring. This study reveals the occurrence of boundary equilibrium bifurcations, enriching the understanding of predator–prey dynamics. In addition, a sliding mode controller is designed in the fast–slow predator–prey system to make the periodic trajectory tend to the internal equilibrium point. Taking the predator–prey relationship between insect and bird as an example, numerical simulations are provided to verify the theoretical results.
{"title":"Bifurcation analysis and sliding mode control of a singular piecewise-smooth prey–predator model with distributed delay","authors":"Yue Zhang, Xin Ai, Zhenlei Li, Jie Gao","doi":"10.1016/j.nahs.2025.101582","DOIUrl":"10.1016/j.nahs.2025.101582","url":null,"abstract":"<div><div>In this paper, the piecewise-smooth functional response function and distributed delay are used to describe the memory effect of predators and capture law when the abundance of prey changes greatly in ecosystems more realistically. A singular piecewise-smooth prey–predator model with distributed delay is studied. Considering the growth and loss rate of the predator much smaller than that of the prey, the model is described by a fast–slow system that mathematically leads to a singular perturbation problem. The dynamic behavior of the fast–slow system with distributed delay, piecewise smooth is novel and interesting. The system undergoes a Hopf bifurcation where the interior equilibrium becomes unstable leading to a stable limit cycle. As the perturbation parameter decreases, the co-existence equilibrium has a transition from the unstable node to the stable node which leads multiple relaxation oscillations occurring. This study reveals the occurrence of boundary equilibrium bifurcations, enriching the understanding of predator–prey dynamics. In addition, a sliding mode controller is designed in the fast–slow predator–prey system to make the periodic trajectory tend to the internal equilibrium point. Taking the predator–prey relationship between insect and bird as an example, numerical simulations are provided to verify the theoretical results.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"56 ","pages":"Article 101582"},"PeriodicalIF":3.7,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387469","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 : 2025-02-01Epub Date: 2024-11-12DOI: 10.1016/j.nahs.2024.101553
Yilun Wu, Anna Tur, Peichen Ye
Switching phenomena are ubiquitous in real-world applications. An -player hybrid pollution-control problem is considered with switching behavior and uncertain game duration. The payoff functional with a random duration is converted to a payoff functional in the infinite horizon, which is discounted by a heterogeneous discounting function. By applying Pontryagin’s maximum principle and analyzing the structure of the adjoint variable, the sustainable equilibria in cooperative and noncooperative games are uniquely determined. The convergence of the corresponding state variable in cooperative and noncooperative games is proved. Furthermore, a unique state trajectory represented by a hybrid limit cycle is found to compute the players’ payoffs in cooperative and noncooperative scenarios. Finally, a reasonable, cooperative solution that employs the Shapley value as a single-point solution is proposed. All results are derived analytically and demonstrated with a numerical example.
切换现象在实际应用中无处不在。本文考虑了一个 n 人混合污染控制问题，该问题具有切换行为和不确定的博弈持续时间。随机持续时间的报酬函数被转换为无限视界的报酬函数，并通过异质贴现函数进行贴现。通过应用庞特里亚金最大原则和分析邻接变量的结构，唯一确定了合作博弈和非合作博弈中的可持续均衡。证明了合作博弈和非合作博弈中相应状态变量的收敛性。此外，还找到了一个由混合极限循环代表的唯一状态轨迹，用于计算合作和非合作情况下博弈者的报酬。最后，还提出了一种合理的合作解，它采用夏普利值作为单点解。所有结果都是通过分析得出的，并通过一个数值示例进行了演示。
{"title":"Sustainable solution for hybrid differential game with regime shifts and random duration","authors":"Yilun Wu, Anna Tur, Peichen Ye","doi":"10.1016/j.nahs.2024.101553","DOIUrl":"10.1016/j.nahs.2024.101553","url":null,"abstract":"<div><div>Switching phenomena are ubiquitous in real-world applications. An <span><math><mi>n</mi></math></span>-player hybrid pollution-control problem is considered with switching behavior and uncertain game duration. The payoff functional with a random duration is converted to a payoff functional in the infinite horizon, which is discounted by a heterogeneous discounting function. By applying Pontryagin’s maximum principle and analyzing the structure of the adjoint variable, the sustainable equilibria in cooperative and noncooperative games are uniquely determined. The convergence of the corresponding state variable in cooperative and noncooperative games is proved. Furthermore, a unique state trajectory represented by a hybrid limit cycle is found to compute the players’ payoffs in cooperative and noncooperative scenarios. Finally, a reasonable, cooperative solution that employs the Shapley value as a single-point solution is proposed. All results are derived analytically and demonstrated with a numerical example.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"55 ","pages":"Article 101553"},"PeriodicalIF":3.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142657595","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 : 2025-02-01Epub Date: 2024-10-23DOI: 10.1016/j.nahs.2024.101549
Do Duc Thuan
In this paper, the problem of positivity and stability for linear time-invariant implicit dynamic equations is generally studied. We provide necessary and sufficient conditions for positivity of these equations. This characterization can be considered as a unification and generalization for some previous results. On the other hand, we study the exponential stability of positive implicit dynamic equations. Previously, this issue was not completely addressed. By using Krein–Rutman theorem, we show that a positive implicit dynamic equation on a time scale is uniformly exponentially stable if and only if the characteristic polynomial of the matrix pair defining the equation has all its coefficients of the same sign.
{"title":"Exponential stability of positive implicit dynamic equations with constant coefficients","authors":"Do Duc Thuan","doi":"10.1016/j.nahs.2024.101549","DOIUrl":"10.1016/j.nahs.2024.101549","url":null,"abstract":"<div><div>In this paper, the problem of positivity and stability for linear time-invariant implicit dynamic equations is generally studied. We provide necessary and sufficient conditions for positivity of these equations. This characterization can be considered as a unification and generalization for some previous results. On the other hand, we study the exponential stability of positive implicit dynamic equations. Previously, this issue was not completely addressed. By using Krein–Rutman theorem, we show that a positive implicit dynamic equation on a time scale is uniformly exponentially stable if and only if the characteristic polynomial of the matrix pair defining the equation has all its coefficients of the same sign.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"55 ","pages":"Article 101549"},"PeriodicalIF":3.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530119","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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