Nonlinear Analysis-Hybrid Systems最新文献

{"title":"FESD-J: Finite Elements with Switch Detection for numerical optimal control of rigid bodies with impacts and Coulomb friction","authors":"Armin Nurkanović ,&nbsp;Jonathan Frey ,&nbsp;Anton Pozharskiy ,&nbsp;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":"52 ","pages":"Article 101460"},"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}

{"title":"H∞ control of singularly perturbed systems using deficient hidden semi-Markov model","authors":"Yunzhe Men,&nbsp;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":"52 ","pages":"Article 101453"},"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}

{"title":"Koopman modeling and optimal control for microbial fed-batch fermentation with switching operators","authors":"Jinlong Yuan ,&nbsp;Shuang Zhao ,&nbsp;Dongyao Yang ,&nbsp;Chongyang Liu ,&nbsp;Changzhi Wu ,&nbsp;Tao Zhou ,&nbsp;Sida Lin ,&nbsp;Yuduo Zhang ,&nbsp;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":"52 ","pages":"Article 101461"},"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}

{"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":"52 ","pages":"Article 101459"},"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}

{"title":"Duality of controllability and observability in proportional equal conflict timed continuous Petri Nets","authors":"J.L. García-Malacara ,&nbsp;César Arzola ,&nbsp;Antonio Ramírez-Treviño ,&nbsp;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":"52 ","pages":"Article 101455"},"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}

{"title":"Semi-global asymptotic state agreement of nonlinear multi-agent systems with communication delays under directed switching topologies","authors":"Zhanxiu Wang ,&nbsp;Zhenghong Jin ,&nbsp;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":"52 ","pages":"Article 101458"},"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}

{"title":"Secured consensus control for multi-agent systems under DoS attacks: Coding–decoding communication protocol","authors":"Tingting Ru ,&nbsp;Hong Lin ,&nbsp;Chenxiao Cai","doi":"10.1016/j.nahs.2023.101445","DOIUrl":"https://doi.org/10.1016/j.nahs.2023.101445","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"52 ","pages":"Article 101445"},"PeriodicalIF":4.2,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138557652","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}

{"title":"Chaotic behaviors and coexisting homoclinic cycles in a class of 3D piecewise systems","authors":"Wenjing Xu ,&nbsp;Kai Lu ,&nbsp;Tao Zhang ,&nbsp;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":"52 ","pages":"Article 101452"},"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}

{"title":"The convergence rate of the equilibrium measure for the hybrid LQG Mean Field Game","authors":"Jiamin Jian ,&nbsp;Peiyao Lai ,&nbsp;Qingshuo Song ,&nbsp;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":"52 ","pages":"Article 101454"},"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}

{"title":"Finite-time stabilization of discrete-time conewise linear systems","authors":"Roberto Ambrosino,&nbsp;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":"52 ","pages":"Article 101456"},"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}