Pub Date : 2023-12-07DOI: 10.1016/j.nahs.2023.101452
Wenjing Xu , Kai Lu , Tao Zhang , Qiaomin Xiang
Investigating homoclinic trajectories and chaotic behaviors, is conducive to better understanding the fourteenth problem listed by Smale in his response to Arnold. This paper analytically detects coexisting homoclinic cycles without symmetry required in a class of three-dimensional (3D) piecewise systems, which is significantly different from the smooth case where a pair of homoclinic cycles with respect to one equilibrium point are generally symmetric. Moreover, it is rigorously shown that such coexisting cycles gives rise to chaos by means of analyzing a Poincaré map. An example finally is presented to illustrate the proposed results.
{"title":"Chaotic behaviors and coexisting homoclinic cycles in a class of 3D piecewise systems","authors":"Wenjing Xu , Kai Lu , Tao Zhang , Qiaomin Xiang","doi":"10.1016/j.nahs.2023.101452","DOIUrl":"https://doi.org/10.1016/j.nahs.2023.101452","url":null,"abstract":"<div><p><span>Investigating homoclinic trajectories and chaotic behaviors, is conducive to better understanding the fourteenth problem listed by Smale in his response to Arnold. This paper analytically detects coexisting homoclinic cycles without symmetry required in a class of three-dimensional (3D) piecewise systems, which is significantly different from the smooth case where a pair of homoclinic cycles with respect to one equilibrium point are generally symmetric. Moreover, it is rigorously shown that such coexisting cycles gives rise to chaos by means of analyzing a </span>Poincaré map. An example finally is presented to illustrate the proposed results.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138549415","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 : 2023-12-05DOI: 10.1016/j.nahs.2023.101454
Jiamin Jian , Peiyao Lai , Qingshuo Song , Jiaxuan Ye
In this work, we study the convergence rate of the -player Linear-Quadratic-Gaussian (LQG) game with a Markov chain common noise towards its asymptotic Mean Field Game. By postulating a Markovian structure via two auxiliary processes for the first and second moments of the Mean Field Game equilibrium and applying the fixed point condition in Mean Field Game, we first provide the characterization of the equilibrium measure in Mean Field Game with a finite-dimensional Riccati system of ODEs. Additionally, with an explicit coupling of the optimal trajectory of the -player game driven by dimensional Brownian motion and Mean Field Game counterpart driven by one-dimensional Brownian motion, we obtain the convergence rate with respect to 2-Wasserstein distance.
在这项研究中,我们研究了具有马尔可夫链普通噪声的N人线性-二次-高斯(LQG)博弈向其渐近平均场博弈的收敛速率。通过对平均场博弈均衡的第一矩和第二矩的两个辅助过程假设马尔可夫结构,并应用平均场博弈中的定点条件,我们首先用一个有限维 Riccati ODEs 系统提供了平均场博弈均衡度量的特征。此外,通过将 N 维布朗运动驱动的 N 人博弈最优轨迹与一维布朗运动驱动的平均场博弈最优轨迹明确耦合,我们得到了相对于 2-Wasserstein 距离的收敛率 O(N-1/2)。
{"title":"The convergence rate of the equilibrium measure for the hybrid LQG Mean Field Game","authors":"Jiamin Jian , Peiyao Lai , Qingshuo Song , Jiaxuan Ye","doi":"10.1016/j.nahs.2023.101454","DOIUrl":"https://doi.org/10.1016/j.nahs.2023.101454","url":null,"abstract":"<div><p><span>In this work, we study the convergence rate of the </span><span><math><mi>N</mi></math></span><span><span>-player Linear-Quadratic-Gaussian (LQG) game with a Markov chain common noise towards its asymptotic Mean Field Game. By postulating a Markovian structure via two auxiliary processes for the first and second moments of the Mean Field Game equilibrium and applying the fixed point condition in Mean Field Game, we first provide the characterization of the </span>equilibrium measure<span> in Mean Field Game with a finite-dimensional Riccati system of ODEs. Additionally, with an explicit coupling of the optimal trajectory of the </span></span><span><math><mi>N</mi></math></span>-player game driven by <span><math><mi>N</mi></math></span> dimensional Brownian motion and Mean Field Game counterpart driven by one-dimensional Brownian motion, we obtain the convergence rate <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> with respect to 2-Wasserstein distance.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138490572","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 : 2023-12-05DOI: 10.1016/j.nahs.2023.101456
Roberto Ambrosino, Raffaele Iervolino
The finite-time stabilizing control design problem for discrete-time conewise linear systems is tackled in this paper. Such a class of systems consists of the union of ordinary linear time-invariant subsystems, whose dynamics are defined in prescribed conical regions, constituting a conical partition of the state space. By imposing some cone-copositivity properties to a suitable piecewise quadratic function, two sufficient conditions are preliminarily derived concerning the system’s finite-time stability. By building on them, novel results are then presented for the system’s finite-time stabilization through a piecewise linear output feedback controller. Such results are based on the solution of feasibility problems involving sets of Linear Matrix Inequalities (LMIs). A numerical example illustrates the effectiveness of the proposed approach.
{"title":"Finite-time stabilization of discrete-time conewise linear systems","authors":"Roberto Ambrosino, Raffaele Iervolino","doi":"10.1016/j.nahs.2023.101456","DOIUrl":"https://doi.org/10.1016/j.nahs.2023.101456","url":null,"abstract":"<div><p>The finite-time stabilizing control design problem for discrete-time conewise linear systems is tackled in this paper. Such a class of systems consists of the union of ordinary linear time-invariant subsystems, whose dynamics are defined in prescribed conical regions, constituting a conical partition of the state space. By imposing some cone-copositivity properties to a suitable piecewise quadratic function, two sufficient conditions are preliminarily derived concerning the system’s finite-time stability. By building on them, novel results are then presented for the system’s finite-time stabilization through a piecewise linear output feedback controller. Such results are based on the solution of feasibility problems involving sets of Linear Matrix Inequalities (LMIs). A numerical example illustrates the effectiveness of the proposed approach.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1751570X23001279/pdfft?md5=625bbbf054a010bf192f5e47a1e74f94&pid=1-s2.0-S1751570X23001279-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138490574","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 : 2023-12-05DOI: 10.1016/j.nahs.2023.101457
Siyuan Zhang , Jun Zhao
This paper addresses the bumpless transfer control for switched nonlinear delayed systems with exogenous perturbations via the interval type-2 fuzzy model. We firstly establish a novel characterization of bumpless transfer performance, which provides a framework to the bumpless transfer control of switched nonlinear systems. By using the multiple Lyapunov-Krasovskii functionals and the state-dependent switching strategy, sufficient conditions for asymptotically stability with bumpless transfer performance are obtained. More incisively, different from the existing results where the bumpless transfer control design conditions do not involve the information of membership functions, we adopt the piecewise-linear-membership-function technique to remove this limitation. Correspondingly, novel membership-function-dependent bumpless transfer criteria are derived, under which the state-dependent switching law and bumpless transfer controllers are jointly designed. Finally, a tunnel diode circuit model is exploited to verify the applicability and validity of the developed method.
{"title":"Membership-function-dependent H∞ bumpless transfer control for switched interval type-2 fuzzy systems with time-delay","authors":"Siyuan Zhang , Jun Zhao","doi":"10.1016/j.nahs.2023.101457","DOIUrl":"https://doi.org/10.1016/j.nahs.2023.101457","url":null,"abstract":"<div><p>This paper addresses the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span><span> bumpless transfer control for switched nonlinear delayed systems with exogenous perturbations via the interval type-2 fuzzy model. We firstly establish a novel characterization of bumpless transfer performance, which provides a framework to the bumpless transfer control of switched nonlinear systems. By using the multiple Lyapunov-Krasovskii functionals and the state-dependent switching strategy, sufficient conditions for asymptotically stability with </span><span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> bumpless transfer performance are obtained. More incisively, different from the existing results where the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> bumpless transfer control design conditions do not involve the information of membership functions, we adopt the piecewise-linear-membership-function technique to remove this limitation. Correspondingly, novel membership-function-dependent <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> bumpless transfer criteria are derived, under which the state-dependent switching law and <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span><span> bumpless transfer controllers are jointly designed. Finally, a tunnel diode circuit model is exploited to verify the applicability and validity of the developed method.</span></p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138490573","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}
This paper deals with hybrid dynamical systems in the context of cybersecurity and Cyber–Physical Systems. It is shown how the design of a cipher, called self-synchronizing stream cipher, can be recast as control-theoretic issues, in particular left inversion, flatness and structural analysis. From an automatic control point of view, the main contribution lies in a methodology to construct generic flat LPV systems. Beyond pure control theoretic matters, the design also addresses computational complexity and security concerns. Those considerations motivate a hybrid architecture involving switched automata. A Proof-Of-Concept example illustrates the design of a statistical self-synchronizing stream cipher and the way how it operates to encrypt data flows.
{"title":"Flatness and structural analysis for the design of stream ciphers involving hybrid automata","authors":"Hamid Boukerrou , Gilles Millérioux , Marine Minier , Taha Boukhobza","doi":"10.1016/j.nahs.2023.101443","DOIUrl":"https://doi.org/10.1016/j.nahs.2023.101443","url":null,"abstract":"<div><p><span>This paper deals with hybrid dynamical systems in the context of cybersecurity and Cyber–Physical Systems. It is shown how the design of a cipher, called self-synchronizing stream cipher, can be recast as control-theoretic issues, in particular left inversion, flatness and structural analysis. From an automatic control point of view, the main contribution lies in a methodology to construct generic flat </span>LPV systems. Beyond pure control theoretic matters, the design also addresses computational complexity and security concerns. Those considerations motivate a hybrid architecture involving switched automata. A Proof-Of-Concept example illustrates the design of a statistical self-synchronizing stream cipher and the way how it operates to encrypt data flows.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138480188","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 : 2023-11-27DOI: 10.1016/j.nahs.2023.101444
Yihao Xu , Alexandre Seuret , Kun Liu , Senchun Chai
The recent literature on event-triggered control has demonstrated the potential of dynamic periodic event-triggered control. Compared to continuous-time event-triggering rules, the benefit of considering periodic event-triggered control is to avoid the Zeno phenomenon, which refers to the situation when there are an infinite number of updates in a bounded interval of time. The idea of periodic event-triggered control is to trigger the control law only at known allowable periodic sampling instants. In this paper, our objective is to relax the constraint on the periodicity of the allowable sampling instants and to adapt this framework to the dynamic event-triggered control, which has not been considered in the literature, as far as we are aware of. Following the successful efforts to assess the stability of aperiodic sampled-data control, here we propose a generic framework to emulate aperiodic dynamic event-triggered control law for linear systems, for which the allowable sampling instants are not necessarily equidistant. Such an analysis is made possible thanks to the looped-functionals framework, which gives the flexibility to consider the periodic/aperiodic static/dynamic event-triggered control in a single formulation. Finally, the efficiency of the proposed results is illustrated through the study of two academic examples.
{"title":"Aperiodic dynamic event-triggered control for linear systems: A looped-functional approach","authors":"Yihao Xu , Alexandre Seuret , Kun Liu , Senchun Chai","doi":"10.1016/j.nahs.2023.101444","DOIUrl":"https://doi.org/10.1016/j.nahs.2023.101444","url":null,"abstract":"<div><p>The recent literature on event-triggered control has demonstrated the potential of dynamic periodic event-triggered control. Compared to continuous-time event-triggering rules, the benefit of considering periodic event-triggered control is to avoid the Zeno phenomenon, which refers to the situation when there are an infinite number of updates in a bounded interval of time. The idea of periodic event-triggered control is to trigger the control law only at known allowable periodic sampling instants. In this paper, our objective is to relax the constraint on the periodicity of the allowable sampling instants and to adapt this framework to the dynamic event-triggered control, which has not been considered in the literature, as far as we are aware of. Following the successful efforts to assess the stability of aperiodic sampled-data control, here we propose a generic framework to emulate aperiodic dynamic event-triggered control law for linear systems, for which the allowable sampling instants are not necessarily equidistant. Such an analysis is made possible thanks to the looped-functionals framework, which gives the flexibility to consider the periodic/aperiodic static/dynamic event-triggered control in a single formulation. Finally, the efficiency of the proposed results is illustrated through the study of two academic examples.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1751570X23001152/pdfft?md5=3df4260f020038dec4e8a77a13200378&pid=1-s2.0-S1751570X23001152-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138453661","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 : 2023-11-08DOI: 10.1016/j.nahs.2023.101442
Yuan Tian , Chunxue Li , Jing Liu
Competition is a common biological relationship in nature, especially for some fish species. For different situations and different purposes in a two populations competitive system, we propose three novel mathematical models of two-fish competition with linear correlation feedback control. The first scenario considers undesirable competition in the system, and the purpose of control is to avoid the extinction of the inferior population. By discussing the existence and stability of the order-1 periodic solution, an effective method is provided for the realization of the fixed-period control and stabilization of the system, and the parameter optimization design is realized with the goal of minimizing the control cost. The second scenario considers the coexistence of two fish populations, and the purpose of control is transformed into harvesting of both populations. By analyzing the existence of the order-1 and order-2 periodic solutions, the dynamic characteristics and complexity of the control system are enriched, and the optimal design of parameters is realized with the goal of maximizing the economic benefits. The third scenario considers the phenomenon of equal competition between the two populations. The purpose of control is to avoid the extinction of one of the populations due to the large number of one population. By analyzing the existence of the order-1 and order-2 periodic solutions, the dynamical characteristics of the system are further enriched. Finally, numerical simulations are carried out for the three scenarios to illustrate the theoretical results and the feasibility of the control. The control strategy based on linear dependent feedback proposed in this paper provides an effective way to realize the coexistence of two populations competing systems.
{"title":"Non-smooth competitive systems and complex dynamics induced by linearly dependent feedback control","authors":"Yuan Tian , Chunxue Li , Jing Liu","doi":"10.1016/j.nahs.2023.101442","DOIUrl":"https://doi.org/10.1016/j.nahs.2023.101442","url":null,"abstract":"<div><p>Competition is a common biological relationship in nature, especially for some fish species. For different situations and different purposes in a two populations competitive system, we propose three novel mathematical models of two-fish competition with linear correlation feedback control. The first scenario considers undesirable competition in the system, and the purpose of control is to avoid the extinction of the inferior population. By discussing the existence and stability of the order-1 periodic solution, an effective method is provided for the realization of the fixed-period control and stabilization of the system, and the parameter optimization design is realized with the goal of minimizing the control cost. The second scenario considers the coexistence of two fish populations, and the purpose of control is transformed into harvesting of both populations. By analyzing the existence of the order-1 and order-2 periodic solutions, the dynamic characteristics and complexity of the control system are enriched, and the optimal design of parameters is realized with the goal of maximizing the economic benefits. The third scenario considers the phenomenon of equal competition between the two populations. The purpose of control is to avoid the extinction of one of the populations due to the large number of one population. By analyzing the existence of the order-1 and order-2 periodic solutions, the dynamical characteristics of the system are further enriched. Finally, numerical simulations are carried out for the three scenarios to illustrate the theoretical results and the feasibility of the control. The control strategy based on linear dependent feedback proposed in this paper provides an effective way to realize the coexistence of two populations competing systems.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92135693","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 : 2023-11-03DOI: 10.1016/j.nahs.2023.101437
Lichen Ding, Kazumune Hashimoto, Shigemasa Takai
In this paper, we investigate the problem of mitigating epidemics by applying an event-triggered control strategy. We consider a susceptible–infected–removed–susceptible (SIRS) model, which builds upon the foundational SIR model by accounting for reinfection cases. The event-triggered control strategy is formulated based on the condition in which the control input (e.g., the level of public measures) is updated only when the fraction of the infected subjects changes over a designed threshold. To synthesize the event-triggered controller, we leverage the notion of a symbolic model, which represents an abstracted expression of the transition system associated with the SIRS model under the event-triggered control strategy. Then, by employing safety and reachability games, two event-triggered controllers are synthesized to ensure a desired specification, which is more sophisticated than the one given in previous works. The effectiveness of the proposed approach is illustrated through numerical simulations.
{"title":"Synthesis of event-triggered controllers for SIRS epidemic models","authors":"Lichen Ding, Kazumune Hashimoto, Shigemasa Takai","doi":"10.1016/j.nahs.2023.101437","DOIUrl":"https://doi.org/10.1016/j.nahs.2023.101437","url":null,"abstract":"<div><p>In this paper, we investigate the problem of mitigating epidemics by applying an event-triggered control strategy. We consider a susceptible–infected–removed–susceptible (SIRS) model, which builds upon the foundational SIR model by accounting for reinfection cases. The event-triggered control strategy is formulated based on the condition in which the control input (e.g., the level of public measures) is updated <em>only when</em> the fraction of the infected subjects changes over a designed threshold. To synthesize the event-triggered controller, we leverage the notion of a symbolic model, which represents an abstracted expression of the transition system associated with the SIRS model under the event-triggered control strategy. Then, by employing safety and reachability games, two event-triggered controllers are synthesized to ensure a desired specification, which is more sophisticated than the one given in previous works. The effectiveness of the proposed approach is illustrated through numerical simulations.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91963724","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 : 2023-10-31DOI: 10.1016/j.nahs.2023.101440
Qian Shen , Shengyuan Xu , Yihan Chen
This note investigates the H∞ filtering for a kind of discrete-time switched systems ruled by cyclic switching regularities. By virtue of the cyclic manipulation of dwell-time (DT) switching and average dwell-time (ADT) switching reported in the literature, an innovative switching strategy of cycle-dependent persistent dwell-time (CPDT) property is first developed referring to the original persistent dwell-time (PDT) scheme. Further, to overcome the cycle-dependent DT constraint appearing in the CPDT switching, cycle-dependent ADT is sub-regionally injected into the suffering areas, which is different from the full-regional injection of ADT into the PDT switching in the literature. In this way, the CPDT switching is advanced to the cycle-dependent average persistent dwell-time switching, which can bring more flexibility to the switching design. Based on the newly introduced switching mechanisms, quasi-time-dependent (QTD) stability and l2-gain criteria are formulated for discrete-time cyclic switched systems to guide the design of intended QTD full-order filters, through which the produced filter error systems perform as expected in terms of the stability and H∞ noise attenuation capability. At last, the validities and advantages of the obtained filtering solutions are expounded by specific illustrative examples.
{"title":"H∞ filtering for discrete-time cyclic switched systems: Relaxed cycle-dependent persistent dwell-time constraints with averaging treatment","authors":"Qian Shen , Shengyuan Xu , Yihan Chen","doi":"10.1016/j.nahs.2023.101440","DOIUrl":"https://doi.org/10.1016/j.nahs.2023.101440","url":null,"abstract":"<div><p>This note investigates the <em>H</em><sub>∞</sub> filtering for a kind of discrete-time switched systems ruled by cyclic switching regularities. By virtue of the cyclic manipulation of dwell-time (DT) switching and average dwell-time (ADT) switching reported in the literature, an innovative switching strategy of cycle-dependent persistent dwell-time (CPDT) property is first developed referring to the original persistent dwell-time (PDT) scheme. Further, to overcome the cycle-dependent DT constraint appearing in the CPDT switching, cycle-dependent ADT is sub-regionally injected into the suffering areas, which is different from the full-regional injection of ADT into the PDT switching in the literature. In this way, the CPDT switching is advanced to the cycle-dependent average persistent dwell-time switching, which can bring more flexibility to the switching design. Based on the newly introduced switching mechanisms, quasi-time-dependent (QTD) stability and <em>l</em><sub>2</sub>-gain criteria are formulated for discrete-time cyclic switched systems to guide the design of intended QTD full-order filters, through which the produced filter error systems perform as expected in terms of the stability and <em>H</em><sub>∞</sub><span> noise attenuation capability. At last, the validities and advantages of the obtained filtering solutions are expounded by specific illustrative examples.</span></p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92043315","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 : 2023-10-27DOI: 10.1016/j.nahs.2023.101441
Junfeng Zhang , Tarek Raïssi , Qiang Li , Di Wu
This paper presents a distributed fault detection filter (FDF) for positive semi-Markovian jump systems (PSMJSs) based on an adaptive event-triggered mechanism (AETM) scheme. A novel AETM is first proposed for the systems. A weighted fault model is introduced to assist the estimation of the original fault. Utilizing stochastic copositive Lyapunov function (CLF), a distributed FDF whose parameters are designed by virtue of linear programming (LP), is proposed. Under the designed filter, the positivity and stochastic stability with -gain performance of a fault detection system is reached. The contribution of this paper contains three aspects: (i) An AETM is constructed for the considered systems, (ii) A distributed FDF is designed for the systems, and (iii) The hybrid -gain performance is achieved with respect to the disturbance and the fault. Two illustrative examples are given for verifying the validity of the results.
{"title":"Distributed adaptive event-triggered fault detection filter of positive semi-Markovian jump systems","authors":"Junfeng Zhang , Tarek Raïssi , Qiang Li , Di Wu","doi":"10.1016/j.nahs.2023.101441","DOIUrl":"https://doi.org/10.1016/j.nahs.2023.101441","url":null,"abstract":"<div><p><span><span>This paper presents a distributed fault detection filter (FDF) for positive semi-Markovian jump systems (PSMJSs) based on an adaptive event-triggered mechanism (AETM) scheme. A novel AETM is first proposed for the systems. A weighted fault model is introduced to assist the estimation of the original fault. Utilizing stochastic copositive </span>Lyapunov function (CLF), a distributed FDF whose parameters are designed by virtue of linear programming (LP), is proposed. Under the designed filter, the positivity and stochastic stability with </span><span><math><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>/</mo><mi>L</mi><mtext>_</mtext></mrow></math></span>-gain performance of a fault detection system is reached. The contribution of this paper contains three aspects: (i) An AETM is constructed for the considered systems, (ii) A distributed FDF is designed for the systems, and (iii) The hybrid <span><math><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>/</mo><mi>L</mi><mtext>_</mtext></mrow></math></span>-gain performance is achieved with respect to the disturbance and the fault. Two illustrative examples are given for verifying the validity of the results.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92043314","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}