Pub Date : 2024-01-13DOI: 10.1016/j.nahs.2024.101465
Elena Zattoni , Naohisa Otsuka , Anna Maria Perdon , Giuseppe Conte
This work deals with the problem of designing a feedback compensator that forces the output of a linear system with abrupt discontinuities in the state evolution and polytopic uncertainties to match that of a given model with the same features. First, the case in which the system and the model are initialized at zero and output matching is required to be exact is considered. Then, the case in which, for arbitrary initialization, output matching is required to be asymptotic for sufficiently slow sequences of the time instants wherein the state exhibits abrupt discontinuities is studied. In addition, on the assumption that the model is stable for sufficiently slow jump time sequences, also the further requirement that asymptotic output matching be achieved with stability of the compensated system is investigated. Constructive, directly checkable, solvability conditions for the problems addressed are derived by leveraging on appropriate structural notions and geometric tools. Algorithmic procedures for the synthesis of the compensators, when the solvability conditions are met, are devised. Some illustrative examples conclude the work.
{"title":"Model matching problems for impulsive linear systems with polytopic uncertainties","authors":"Elena Zattoni , Naohisa Otsuka , Anna Maria Perdon , Giuseppe Conte","doi":"10.1016/j.nahs.2024.101465","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101465","url":null,"abstract":"<div><p>This work deals with the problem of designing a feedback compensator that forces the output of a linear system with abrupt discontinuities in the state evolution and polytopic uncertainties to match that of a given model with the same features. First, the case in which the system and the model are initialized at zero and output matching is required to be exact is considered. Then, the case in which, for arbitrary initialization, output matching is required to be asymptotic for sufficiently slow sequences of the time instants wherein the state exhibits abrupt discontinuities is studied. In addition, on the assumption that the model is stable for sufficiently slow jump time sequences, also the further requirement that asymptotic output matching be achieved with stability of the compensated system is investigated. Constructive, directly checkable, solvability conditions for the problems addressed are derived by leveraging on appropriate structural notions and geometric tools. Algorithmic procedures for the synthesis of the compensators, when the solvability conditions are met, are devised. Some illustrative examples conclude the work.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2024-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1751570X24000025/pdfft?md5=5b0970aad840577006cc3297bdcce57f&pid=1-s2.0-S1751570X24000025-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139433962","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 : 2024-01-09DOI: 10.1016/j.nahs.2024.101464
Xu Cui , Qingxiang Zhang , Peng Yu , Fengwei Jing , Jin Guo
With the development of information technology, the amount of data transmitted in the network is getting larger and larger, and how to effectively utilize the communication resources has become the focus of a lot of research. In the framework of Finite Impulse Response (FIR) systems, this paper proposes a congruential summation-triggered communication scheme based on the cumulative effect of binary-valued observations to address the parameter identification problem, and its communication rate is derived. Then, the parameter estimation algorithm is designed under periodic input, and its strong convergence is proved, while an index is established to characterize the convergence performance of the algorithm. Furthermore, the trade-off problem between algorithm performance and communication resource is modeled as an optimization problem with constraints, and its explicit solution is given. Finally, numerical simulations are performed to verify the correctness and reasonableness of the algorithm.
{"title":"FIR system identification under congruential summation-triggered communication scheme with binary observations","authors":"Xu Cui , Qingxiang Zhang , Peng Yu , Fengwei Jing , Jin Guo","doi":"10.1016/j.nahs.2024.101464","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101464","url":null,"abstract":"<div><p>With the development of information technology, the amount of data transmitted in the network is getting larger and larger, and how to effectively utilize the communication resources has become the focus of a lot of research. In the framework of Finite Impulse Response (FIR) systems, this paper proposes a congruential summation-triggered communication scheme based on the cumulative effect of binary-valued observations to address the parameter identification problem, and its communication rate is derived. Then, the parameter estimation algorithm is designed under periodic input, and its strong convergence is proved, while an index is established to characterize the convergence performance of the algorithm. Furthermore, the trade-off problem between algorithm performance and communication resource is modeled as an optimization problem with constraints, and its explicit solution is given. Finally, numerical simulations are performed to verify the correctness and reasonableness of the algorithm.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139406224","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 : 2023-12-28DOI: 10.1016/j.nahs.2023.101463
M. Di Ferdinando , S. Di Gennaro , A. Borri , G. Pola , P. Pepe
In this paper, the robust stabilization problem by means of quantized sampled-data event-based (QSE) controllers is investigated for nonlinear systems affected by state delays and unknown disturbances. In particular, a methodology for the design of robust QSE stabilizers is provided for control-affine nonlinear systems affected by unknown actuation disturbances and unknown measurement errors. Firstly, the notion of Steepest Descent Feedback (SDF), continuous or not, is suitably revised in order to deal with the robustification of event-based controllers. Then, Input-to-State Stability (ISS) redesign methodologies are used to provide the robustification term which is added to the SDF at hand in order to arbitrarily attenuate the effects of unknown external disturbances affecting the considered control scheme. A spline approximation approach is used in order to cope with the problem of the possible non-availability in the buffer of suitable past values of the system state required for the correct application of the proposed robust QSE controller. It is proved that there exist a suitably fast sampling and an accurate quantization of the input/output channels such that: the robust QSE implementation of SDFs, continuous or not, ensures the semi-global practical stability of the related closed-loop system, regardless of the above disturbances, provided that the observation errors affects marginally the new added control term. The stabilization in the sample-and-hold sense theory is used as a tool to prove the results. The provided results include the case of non-uniform quantization of the input/output channels and the case of aperiodic sampling. Applications are presented in order to validate the results.
{"title":"On the robustification of digital event-based stabilizers for nonlinear time-delay systems","authors":"M. Di Ferdinando , S. Di Gennaro , A. Borri , G. Pola , P. Pepe","doi":"10.1016/j.nahs.2023.101463","DOIUrl":"10.1016/j.nahs.2023.101463","url":null,"abstract":"<div><p>In this paper, the robust stabilization problem by means of quantized sampled-data event-based (QSE) controllers is investigated for nonlinear systems affected by state delays and unknown disturbances. In particular, a methodology for the design of robust QSE stabilizers is provided for control-affine nonlinear systems affected by unknown actuation disturbances and unknown measurement errors. Firstly, the notion of Steepest Descent Feedback (SDF), continuous or not, is suitably revised in order to deal with the robustification of event-based controllers. Then, Input-to-State Stability (ISS) redesign methodologies are used to provide the robustification term which is added to the SDF at hand in order to arbitrarily attenuate the effects of unknown external disturbances affecting the considered control scheme. A spline approximation approach is used in order to cope with the problem of the possible non-availability in the buffer of suitable past values of the system state required for the correct application of the proposed robust QSE controller. It is proved that there exist a suitably fast sampling and an accurate quantization of the input/output channels such that: the robust QSE implementation of SDFs, continuous or not, ensures the semi-global practical stability of the related closed-loop system, regardless of the above disturbances, provided that the observation errors affects marginally the new added control term. The stabilization in the sample-and-hold sense theory is used as a tool to prove the results. The provided results include the case of non-uniform quantization of the input/output channels and the case of aperiodic sampling. Applications are presented in order to validate the results.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1751570X23001346/pdfft?md5=33dde70ef24aeba6fcd430b039822d30&pid=1-s2.0-S1751570X23001346-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139061936","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 : 2023-12-28DOI: 10.1016/j.nahs.2023.101460
Armin Nurkanović , Jonathan Frey , Anton Pozharskiy , Moritz Diehl
The Finite Elements with Switch Detection (FESD) is a high-accuracy method for the numerical simulation and solution of optimal control problems subject to discontinuous ODEs. In this article, we extend the FESD method (Nurkanović et al., 2022) to the dynamic equations of multiple rigid bodies that exhibit state jumps due to impacts and Coulomb friction. This new method is referred to as FESD with Jumps (FESD-J). Starting from the standard Runge–Kutta equations, we let the integration step sizes be degrees of freedom. Additional constraints are introduced to ensure exact switch detection and to remove spurious degrees of freedom if no switches occur. Moreover, at the boundaries of each integration interval (finite element), we impose the impact equations in their complementarity form, at both the position and velocity level. They compute the normal and tangential impulses in case of contact making. Otherwise, they are reduced to the continuity conditions for the velocities. FESD-J treats multiple contacts, where each contact can have a different coefficient of restitution and friction. All methods introduced in this paper are implemented in the open-source software package NOSNOC (Nurkanović and Diehl, 2022). We illustrate the use of FESD-J in both simulation and optimal control examples.
{"title":"FESD-J: Finite Elements with Switch Detection for numerical optimal control of rigid bodies with impacts and Coulomb friction","authors":"Armin Nurkanović , Jonathan Frey , Anton Pozharskiy , Moritz Diehl","doi":"10.1016/j.nahs.2023.101460","DOIUrl":"10.1016/j.nahs.2023.101460","url":null,"abstract":"<div><p><span><span>The Finite Elements with Switch Detection (FESD) is a high-accuracy method for the numerical simulation and solution of </span>optimal control<span> problems subject to discontinuous ODEs. In this article, we extend the FESD method (Nurkanović et al., 2022) to the dynamic equations of multiple rigid bodies that exhibit state jumps due to impacts and </span></span>Coulomb friction<span>. This new method is referred to as FESD with Jumps (FESD-J). Starting from the standard Runge–Kutta equations, we let the integration step sizes be degrees of freedom. Additional constraints are introduced to ensure exact switch detection and to remove spurious degrees of freedom if no switches occur. Moreover, at the boundaries of each integration interval (finite element), we impose the impact equations in their complementarity form, at both the position and velocity level. They compute the normal and tangential impulses in case of contact making. Otherwise, they are reduced to the continuity conditions for the velocities. FESD-J treats multiple contacts, where each contact can have a different coefficient of restitution and friction. All methods introduced in this paper are implemented in the open-source software package NOSNOC (Nurkanović and Diehl, 2022). We illustrate the use of FESD-J in both simulation and optimal control examples.</span></p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139061573","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 : 2023-12-26DOI: 10.1016/j.nahs.2023.101453
Yunzhe Men, Jian Sun
This paper deals with the control of a class of stochastic multi-timescale systems, called Markov jump singularly perturbed systems. The hidden semi-Markov model is introduced to handle the situation when system modes are unavailable in semi-Markov systems. Such a model is assumed deficient, that is, it lacks knowledge about the emission probability, transition probability, and probability density function of the sojourn time. It is a more general case compared with works conducted with perfect transition information. Depending on whether a fast or slow sampling rate is used, the resulting discrete-time singularly perturbed system is modeled differently, for both of which the controller design is conducted. Furthermore, criteria expressed in terms of linear matrix inequalities (LMIs) are developed that guarantee the -error mean-square stability. An approach to estimate the upper bound on -error with incomplete information is provided, meanwhile, the relationship between system performance and the upper of singular perturbation parameter is also presented. Finally, two simulation examples using real-world systems are provided to corroborate the validity as well as the practical merits of the results.
{"title":"H∞ control of singularly perturbed systems using deficient hidden semi-Markov model","authors":"Yunzhe Men, Jian Sun","doi":"10.1016/j.nahs.2023.101453","DOIUrl":"https://doi.org/10.1016/j.nahs.2023.101453","url":null,"abstract":"<div><p>This paper deals with the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span><span><span> control of a class of stochastic multi-timescale systems, called Markov jump singularly perturbed systems. The hidden semi-Markov model is introduced to handle the situation when system modes are unavailable in semi-Markov systems. Such a model is assumed deficient, that is, it lacks knowledge about the emission probability, </span>transition probability<span><span><span>, and probability density function<span> of the sojourn time. It is a more general case compared with works conducted with perfect transition information. Depending on whether a fast or slow sampling rate is used, the resulting discrete-time singularly perturbed system is modeled differently, for both of which the </span></span>controller design is conducted. Furthermore, criteria expressed in terms of </span>linear matrix inequalities (LMIs) are developed that guarantee the </span></span><span><math><mi>δ</mi></math></span>-error mean-square stability. An approach to estimate the upper bound on <span><math><mi>δ</mi></math></span><span>-error with incomplete information is provided, meanwhile, the relationship between system performance and the upper of singular perturbation parameter is also presented. Finally, two simulation examples using real-world systems are provided to corroborate the validity as well as the practical merits of the results.</span></p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139050139","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 : 2023-12-20DOI: 10.1016/j.nahs.2023.101461
Jinlong Yuan , Shuang Zhao , Dongyao Yang , Chongyang Liu , Changzhi Wu , Tao Zhou , Sida Lin , Yuduo Zhang , Wanli Cheng
The modeling of microbial fed-batch fermentation with switching operators to product 1,3-propanediol (1,3-PD) still maintains a challenge because it is strongly of nonlinearity and uncertainty. Machine learning methods for learning such models have become a hot research topic, but the interpretability of existing techniques remains a challenging problem. Recently, the Koopman operator, which is a linear operator governing the eigenfunction evolution along trajectories of a nonlinear dynamical system with switching operators, has been studied for modeling complex dynamics. In this paper, we propose a Koopman modeling method based on an interpretable Koopman operator. The predominant merit of using the Koopman operator is to offer a linear infinite dimensional description of a nonlinear dynamical system with switching operators. In the proposed method, an enhanced learning-based extended dynamic mode decomposition (enhanced-EDMD) algorithm based on a novel eigenfunction construction method is proposed to obtain a finite-dimensional approximation of the Koopman operator. The convergence analysis of the enhanced-EDMD algorithm is also studied. Furthermore, to maximize the productivity of 1,3-PD and minimize the total variation in the optimal control within a time frame, an algorithm combining the model predictive control method with the enhanced learning-based EDMD (denoted by MPC-Enhanced-EDMD), based on gradient-based optimization and exact penalty function method, is proposed for devising optimal feeding rate of glycerol evolving with time. Numerical simulations are conducted by demonstrating the effectiveness of the enhanced-EDMD algorithm on the dynamics prediction and the MPC-Enhanced-EDMD method on the optimal feeding rates of glycerol.
{"title":"Koopman modeling and optimal control for microbial fed-batch fermentation with switching operators","authors":"Jinlong Yuan , Shuang Zhao , Dongyao Yang , Chongyang Liu , Changzhi Wu , Tao Zhou , Sida Lin , Yuduo Zhang , Wanli Cheng","doi":"10.1016/j.nahs.2023.101461","DOIUrl":"10.1016/j.nahs.2023.101461","url":null,"abstract":"<div><p><span>The modeling of microbial fed-batch fermentation with switching operators to product 1,3-propanediol (1,3-PD) still maintains a challenge because it is strongly of nonlinearity and uncertainty. Machine learning methods<span><span> for learning such models have become a hot research topic, but the interpretability of existing techniques remains a challenging problem. Recently, the Koopman operator, which is a </span>linear operator governing the </span></span>eigenfunction<span><span><span> evolution along trajectories of a nonlinear dynamical system with switching operators, has been studied for modeling complex dynamics. In this paper, we propose a Koopman modeling method based on an interpretable Koopman operator. The predominant merit of using the Koopman operator is to offer a linear infinite dimensional description of a nonlinear dynamical system with switching operators. In the proposed method, an enhanced learning-based extended dynamic mode decomposition (enhanced-EDMD) algorithm based on a novel eigenfunction construction method is proposed to obtain a finite-dimensional approximation of the Koopman operator. The convergence analysis of the enhanced-EDMD algorithm is also studied. Furthermore, to maximize the productivity of 1,3-PD and minimize the total variation in the </span>optimal control within a time frame, an algorithm combining the </span>model predictive control method with the enhanced learning-based EDMD (denoted by MPC-Enhanced-EDMD), based on gradient-based optimization and exact penalty function method, is proposed for devising optimal feeding rate of glycerol evolving with time. Numerical simulations are conducted by demonstrating the effectiveness of the enhanced-EDMD algorithm on the dynamics prediction and the MPC-Enhanced-EDMD method on the optimal feeding rates of glycerol.</span></p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138820115","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 : 2023-12-18DOI: 10.1016/j.nahs.2023.101459
Félix A. Miranda-Villatoro
We study a set-valued maximal monotone coupling law achieving robust output convergence in heterogeneous networks of dynamical systems with uncertainties and persistent disturbances. The coupling consists of an adaptable strategy built from normal cones to convex time-dependent sets (hard-threshold maps). To guarantee the convergence of the output mismatches to a neighborhood of the origin, only connectivity of the intrinsic graph is required (knowledge of the graph algebraic connectivity is not required), whereas only the output of the associated systems is used. Numerical simulations illustrate the effectiveness of the proposed coupling scheme.
{"title":"Robust output convergence of heterogeneous networks via nonsmooth hard-threshold couplings","authors":"Félix A. Miranda-Villatoro","doi":"10.1016/j.nahs.2023.101459","DOIUrl":"https://doi.org/10.1016/j.nahs.2023.101459","url":null,"abstract":"<div><p>We study a set-valued maximal monotone<span><span> coupling law achieving robust output convergence in heterogeneous networks of </span>dynamical systems<span> with uncertainties and persistent disturbances. The coupling consists of an adaptable strategy built from normal cones to convex time-dependent sets (hard-threshold maps). To guarantee the convergence of the output mismatches to a neighborhood of the origin, only connectivity of the intrinsic graph is required (knowledge of the graph algebraic connectivity is not required), whereas only the output of the associated systems is used. Numerical simulations illustrate the effectiveness of the proposed coupling scheme.</span></span></p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138713403","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 : 2023-12-15DOI: 10.1016/j.nahs.2023.101455
J.L. García-Malacara , César Arzola , Antonio Ramírez-Treviño , C. Renato Vázquez
Controllability and observability properties have been widely studied in Timed Continuous Petri Nets (s), a class of piecewise affine systems, in order to analyze and control crowded discrete event systems. This work studies the concept of duality applied to s as a vehicle to establish links between controllability and observability, i.e., a synergy to improve the understanding of these properties and to enlarge the class of nets that can be analyzed. To achieve this, we study the concepts of rank-controllability and rank-observability. They capture structural conditions for controllability and observability. Afterwards, the computation of dual nets for Fork-Attribution (), Choice-Free (), Join-Free (), and Proportional Equal Conflict () s subclasses are presented. By using the dual definition, several relations between the primal’s controllability and its dual’s observability are stated. Particularly, in rank-controllability and rank-observability are dual properties. In consistent and strongly connected , , and nets, the rank-observability of the dual is sufficient for the rank-controllability of the primal. The opposite implication holds for and if the self-loop places, added by the dual construction methodology, are measurable.
{"title":"Duality of controllability and observability in proportional equal conflict timed continuous Petri Nets","authors":"J.L. García-Malacara , César Arzola , Antonio Ramírez-Treviño , C. Renato Vázquez","doi":"10.1016/j.nahs.2023.101455","DOIUrl":"https://doi.org/10.1016/j.nahs.2023.101455","url":null,"abstract":"<div><p><span>Controllability and observability properties have been widely studied in Timed Continuous Petri Nets (</span><span><math><mrow><mi>T</mi><mi>C</mi><mi>P</mi><mi>N</mi></mrow></math></span>s), a class of <em>piecewise affine systems</em><span>, in order to analyze and control crowded discrete event systems. This work studies the concept of duality applied to </span><span><math><mrow><mi>T</mi><mi>C</mi><mi>P</mi><mi>N</mi></mrow></math></span>s as a vehicle to establish links between controllability and observability, i.e., a synergy to improve the understanding of these properties and to enlarge the class of nets that can be analyzed. To achieve this, we study the concepts of rank-controllability and rank-observability. They capture structural conditions for controllability and observability. Afterwards, the computation of dual nets for Fork-Attribution (<span><math><mrow><mi>F</mi><mi>A</mi></mrow></math></span>), Choice-Free (<span><math><mrow><mi>C</mi><mi>F</mi></mrow></math></span>), Join-Free (<span><math><mrow><mi>J</mi><mi>F</mi></mrow></math></span>), and Proportional Equal Conflict (<span><math><mrow><mi>P</mi><mi>E</mi><mi>Q</mi></mrow></math></span>) <span><math><mrow><mi>T</mi><mi>C</mi><mi>P</mi><mi>N</mi></mrow></math></span>s subclasses are presented. By using the dual definition, several relations between the primal’s controllability and its dual’s observability are stated. Particularly, in <span><math><mrow><mi>F</mi><mi>A</mi></mrow></math></span> rank-controllability and rank-observability are dual properties. In consistent and strongly connected <span><math><mrow><mi>C</mi><mi>F</mi></mrow></math></span>, <span><math><mrow><mi>J</mi><mi>F</mi></mrow></math></span>, and <span><math><mrow><mi>P</mi><mi>E</mi><mi>Q</mi></mrow></math></span> nets, the rank-observability of the dual is sufficient for the rank-controllability of the primal. The opposite implication holds for <span><math><mrow><mi>C</mi><mi>F</mi></mrow></math></span> and <span><math><mrow><mi>P</mi><mi>E</mi><mi>Q</mi></mrow></math></span> if the self-loop places, added by the dual construction methodology, are measurable.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138678473","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 : 2023-12-13DOI: 10.1016/j.nahs.2023.101458
Zhanxiu Wang , Zhenghong Jin , Hua Li
This paper investigates the semi-global state agreement problem for continuous-time nonlinear multi-agent systems with communication delays under direct and switching topologies. A systematic solution to the semi-global state agreement is presented and based on which a sufficient and necessary condition on the control laws is obtained, as long as the direct and switching communication topologies satisfy a mild joint connectivity assumption. Illustrative simulations are provided to validate the efficacy of the proposed theoretical results.
{"title":"Semi-global asymptotic state agreement of nonlinear multi-agent systems with communication delays under directed switching topologies","authors":"Zhanxiu Wang , Zhenghong Jin , Hua Li","doi":"10.1016/j.nahs.2023.101458","DOIUrl":"https://doi.org/10.1016/j.nahs.2023.101458","url":null,"abstract":"<div><p>This paper investigates the semi-global state agreement problem for continuous-time nonlinear multi-agent systems with communication delays under direct and switching topologies. A systematic solution to the semi-global state agreement is presented and based on which a sufficient and necessary condition<span> on the control laws is obtained, as long as the direct and switching communication topologies satisfy a mild joint connectivity assumption. Illustrative simulations are provided to validate the efficacy of the proposed theoretical results.</span></p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138582361","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 : 2023-12-08DOI: 10.1016/j.nahs.2023.101445
Tingting Ru , Hong Lin , Chenxiao Cai
This paper focuses on the leader following consensus control problem for multi-agent systems (MASs) subject to denial-of-service (DoS) attacks. First, a sliding mode observer is developed to estimate each agent state, actuator, and sensor fault. Then, a coding–decoding communication protocol is proposed to enhance the communication security between agents. Based on the sliding mode observer and communication protocol, a leader-following consensus controller is designed to guarantee the consensus and input-to-state stability of MASs under DoS attacks. Finally, the effectiveness of the developed controller is verified by a simulation example.
本文重点研究了受到拒绝服务(DoS)攻击的多代理系统(MAS)的领导者跟随共识控制问题。首先,开发了一种滑模观测器来估计每个代理的状态、执行器和传感器故障。然后,提出了一种编码-解码通信协议,以增强代理之间的通信安全。在滑模观测器和通信协议的基础上,设计了一种领导者-跟随者共识控制器,以保证在 DoS 攻击下 MAS 的共识和输入-状态稳定性。最后,通过一个仿真实例验证了所开发控制器的有效性。
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