Nonlinear Analysis-Hybrid Systems最新文献

{"title":"Finite Elements with Switch Detection for numerical optimal control of nonsmooth dynamical systems with set-valued heaviside step functions","authors":"Armin Nurkanović ,&nbsp;Anton Pozharskiy ,&nbsp;Jonathan Frey ,&nbsp;Moritz Diehl","doi":"10.1016/j.nahs.2024.101518","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101518","url":null,"abstract":"<div><p>This paper develops high-accuracy methods for the numerical solution of optimal control problems subject to nonsmooth differential equations with set-valued Heaviside step functions. An important subclass of these systems are Filippov systems. By writing the Heaviside step function as the solution map of a linear program and using its optimality conditions, the initial nonsmooth system is rewritten into an equivalent Dynamic Complementarity System (DCS). The Finite Elements with Switch Detection (FESD) method (Nurkanović et al., 2024) was originally developed for Filippov systems transformed via Stewart’s reformulation into DCS (Stewart, 1990). This paper extends it to the above mentioned class of nonsmooth systems. The key ideas are to start with a standard Runge–Kutta method for the DCS and to let the integration step sizes to be degrees of freedom. Then, additional conditions are introduced to allow implicit but accurate switch detection and to remove possible spurious degrees of freedom when no switches occur. The theoretical properties of the FESD method are studied. The motivation for these developments is to obtain a computationally tractable formulation of nonsmooth optimal control problems. Numerical simulations and optimal control examples are used to illustrate the favorable properties of the proposed approach. All methods introduced in this paper are implemented in the open-source software package <span>nosnoc</span> (Nurkanović and Diehl, 2022).</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"54 ","pages":"Article 101518"},"PeriodicalIF":4.2,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1751570X24000554/pdfft?md5=70b77995cfbab380b741b9d892cf00bf&pid=1-s2.0-S1751570X24000554-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141291173","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}

{"title":"Dynamic event-triggered control of linear continuous-time systems using a positive systems approach","authors":"Safeyya Alyahia ,&nbsp;Corina Barbalata ,&nbsp;Michael Malisoff ,&nbsp;Frédéric Mazenc","doi":"10.1016/j.nahs.2024.101508","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101508","url":null,"abstract":"<div><p>We provide new dynamic event-triggered controls for continuous-time linear systems that contain additive uncertainties. We prove input-to-state stability properties that imply uniform global exponential stability when the additive uncertainties are zero. Significant novel features include (a) new dynamic extensions and new trigger rules that provide a new positive systems analog of significant prior dynamic event-triggered work of A. Girard and (b) our application to a BlueROV2 underwater vehicle model, where we provide significantly larger lower bounds on the inter-execution times, and usefully fewer trigger times, compared with standard dynamic event-triggered approaches that used the usual Euclidean norm, and as compared with static event-triggered controls that instead used positive systems approaches.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"54 ","pages":"Article 101508"},"PeriodicalIF":4.2,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141291174","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":"Stabilization of delayed semi-Markov jump neural networks with actuator faults: A quantized hybrid control approach","authors":"N. Aravinth ,&nbsp;R. Sakthivel ,&nbsp;N. Birundha devi ,&nbsp;Ardashir Mohammadzadeh ,&nbsp;S. Saat","doi":"10.1016/j.nahs.2024.101509","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101509","url":null,"abstract":"<div><p>The presented research is to focus on the issue of fault alarm-based quantized hybrid control strategy for semi-Markov jump neural networks subject to multiple vulnerable factors, namely, actuator faults, quantization effects and time-varying delays. Particularly, the fault-based alarm signal with a threshold value is proposed for controller switching and also for preventing false alarms. Precisely, a logarithmic quantizer is incorporated in the control design to adjust the transmission of signals and to enhance better robustness on system performance. Besides, a mixed <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> and passivity performance is employed in order to handle the traces of external disturbances. By proposing Lyapunov–Krasovskii functional involving time delays along with Wirtinger based integral inequality, the anticipated control gain parameters that confirm the stochastic stability of the addressed system can be determined with the assistance of linear matrix inequality. The excellent dynamic performances of the proposed control scheme are clarified through two numerical examples, whereas the stability of the system is restrained with the timely alert performance of the configured alarm signal.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"54 ","pages":"Article 101509"},"PeriodicalIF":4.2,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141242352","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":"Output-feedback stabilization of probabilistic Boolean control networks","authors":"Shuting Zhang ,&nbsp;Xueying Ding ,&nbsp;Jianquan Lu ,&nbsp;Jungang Lou ,&nbsp;Yang Liu","doi":"10.1016/j.nahs.2024.101505","DOIUrl":"10.1016/j.nahs.2024.101505","url":null,"abstract":"<div><p>To simulate a more realistic and uncertain system model, this paper innovatively studies the output feedback control strategy to stabilize probabilistic Boolean control networks (PBCNs). This is the first time that output feedback method is used to solve stability problems in PBCNs. Compared with the traditional state feedback, observing output states is more direct and efficient. Firstly, a condition for the output-feedback stabilization in the sense of minimum time is explored. A sufficient and necessary condition is then provided to determine time-invariant output-feedback stabilizers. Afterwards, two constructive algorithms for design time-invariant output-feedback controllers are proposed. To comprehensively solve the output feedback stabilization problems, this paper explores two sufficient conditions for obtaining stabilizers under time-varying feedback control inputs, which provides more feasibility and significance for solving biomedical problems.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"53 ","pages":"Article 101505"},"PeriodicalIF":4.2,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171781","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":"Numerical solutions of optimal stopping problems for a class of hybrid stochastic systems","authors":"Philip A. Ernst ,&nbsp;Xiaohang Ma ,&nbsp;Masoud H. Nazari ,&nbsp;Hongjiang Qian ,&nbsp;Le Yi Wang ,&nbsp;George Yin","doi":"10.1016/j.nahs.2024.101507","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101507","url":null,"abstract":"<div><p>This paper is devoted to numerically solving a class of optimal stopping problems for stochastic hybrid systems involving both continuous states and discrete events. The motivation for solving this class of problems stems from quickest event detection problems of stochastic hybrid systems in broad application domains. We solve the optimal stopping problems numerically by constructing feasible algorithms using Markov chain approximation techniques. The key tasks we undertake include designing and constructing discrete-time Markov chains that are locally consistent with switching diffusions, proving the convergence of suitably scaled sequences, and obtaining convergence for the cost and value functions. Finally, numerical results are provided to demonstrate the performance of the algorithms.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"53 ","pages":"Article 101507"},"PeriodicalIF":4.2,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141068846","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":"Event-triggered stochastic consensus of multiagent systems over random antagonistic network in a compound noisy environment","authors":"Jinxin Shang ,&nbsp;Yingxue Du ,&nbsp;Zhi Liu ,&nbsp;Ancai Zhang ,&nbsp;Yan Zhang ,&nbsp;Tianwei Zhou","doi":"10.1016/j.nahs.2024.101506","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101506","url":null,"abstract":"<div><p>This article investigates an event-triggered strategy to deal with the bipartite consensus issue for stochastic multiagent systems (SMASs) in a communication noisy environment. The communication network can be modeled by a random signed graph and the communication noise is compound noises (additive noise and multiplicative noise). The stochastic event-triggered bipartite consensus control protocol for SMASs with compound noises is presented by the stochastic approximation (SA) method. Due to the control gain is time-varying and agent-dependent, the implementation of event-triggered control protocol may cause out-sync of the control gain. Meanwhile, the coexistence of stochastic antagonistic information and compound noises causes it hard to turn the noises term into an error equation, which leads to the fact that the traditional error transition method is invalid for our underlying system. To deal with these challenges, the state’s boundedness for each agent is first constructed by the Lyapunov method, and then the event-triggered bipartite consensus can be demonstrated via a new semi-decomposition technique. Finally, the effectiveness of the proposed SA controller is verified by two examples.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"53 ","pages":"Article 101506"},"PeriodicalIF":4.2,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141068847","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":"Observer-based asynchronously intermittent decentralized control of large-scale systems","authors":"Ruogu Wang ,&nbsp;Xuanrong Yang ,&nbsp;Jing Shi","doi":"10.1016/j.nahs.2024.101503","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101503","url":null,"abstract":"<div><p>This paper focuses on observer-based asynchronously intermittent decentralized control of large-scale linear systems. The controller and observer of each subsystem are assumed to work and rest simultaneously, whereas the controllers and observers in different subsystems have independently and asynchronously intermittent working/resting time. By designing a piece-wise continuous auxiliary timer and using it to construct a switching vertex-Lyapunov function for each subsystem, we provide linear matrix inequality (LMI) conditions to determine the minimal allowable control rate of the intermittent controller that preserves the stability of the closed-loop system. We also present the design of an observer-based decentralized controller via LMIs. Finally, a simulation example illustrates the validity of the results.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"53 ","pages":"Article 101503"},"PeriodicalIF":4.2,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140905563","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":"Optimal control strategies for stormwater detention ponds","authors":"Martijn A. Goorden ,&nbsp;Kim G. Larsen ,&nbsp;Jesper E. Nielsen ,&nbsp;Thomas D. Nielsen ,&nbsp;Weizhu Qian ,&nbsp;Michael R. Rasmussen ,&nbsp;Jiří Srba ,&nbsp;Guohan Zhao","doi":"10.1016/j.nahs.2024.101504","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101504","url":null,"abstract":"<div><p>Stormwater detention ponds are essential stormwater management solutions that regulate the urban catchment discharge towards streams. Their purposes are to reduce the hydraulic load to avoid stream erosion, as well as to minimize the degradation of the natural waterbody by direct discharge of pollutants. Currently, static controllers are widely implemented for detention pond outflow regulation in engineering practice, i.e., the outflow discharge is capped at a fixed value. Such a passive discharge setting fails to exploit the full potential of the overall water system, hence further improvements are needed. We apply formal methods to synthesize (i.e., derive automatically) optimal active controllers. We model the stormwater detention pond, including the urban catchment area and the rain forecasts with its uncertainty, as hybrid Markov decision processes. Subsequently, we use the tool <span>Uppaal</span> <span>Stratego</span> to synthesize using Q-learning a control strategy maximizing the retention time for pollutant sedimentation (optimality) while also minimizing the duration of emergency overflow in the detention pond (safety). These strategies are synthesized for both an off-line and on-line settings. Simulation results for an existing pond show that <span>Uppaal</span> <span>Stratego</span> can learn optimal strategies that significantly reduce emergency overflows. For off-line controllers, a scenario with low rain periods shows a 26% improvement of pollutant sedimentation with respect to static control, and a scenario with high rain periods shows a reduction of overflow probability of 10%–19% for static control to lower than 5%, while pollutant sedimentation has only declined by 7% compared to static-control. For on-line controllers, one scenario with heavy rain shows a 95% overflow duration reduction and a 29% pollutant sedimentation improvement compared to static control.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"53 ","pages":"Article 101504"},"PeriodicalIF":4.2,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1751570X24000414/pdfft?md5=200e71aa2ed9483ffd9ff6f45ee3a527&pid=1-s2.0-S1751570X24000414-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140905564","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}

{"title":"State estimation of the semilinear wave equation over the limited capacity communication channel","authors":"Maxim V. Dolgopolik ,&nbsp;Alexander L. Fradkov ,&nbsp;Boris Andrievsky","doi":"10.1016/j.nahs.2024.101500","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101500","url":null,"abstract":"<div><p>In the paper the problem of state estimation of the nonlinear spatially-distributed system described by semilinear wave equations over the limited capacity communication channel is considered under the assumption that the boundary derivative is measured with the sampling and the external boundary control input is perfectly known. The Luenberger-type observer is designed based on the Speed-gradient method with an energy-like objective functional. An upper bound for the observer error in terms of the data transmission error and channel data rate (capacity) is derived and two data transmission procedures are numerically studied to find the admissible data transmission bounds. The key contribution of this paper is the extension of the previously existing results to the cases when the measurements and signal transmission in the control system cannot be available instantly and the finite capacity of the communication channels should be taken into account. The study of such cases is important for the observation and control of PDEs since the instant processing of infinite dimensional PDE data is problematic. The novelty of the results is threefold. Firstly, the state observer for distributed systems described by semilinear wave equations under limited channel data rate (capacity) is designed. Secondly, first time analytic bound for estimation error is obtained. Thirdly, first time the adaptive coding procedure is introduced and numerically studied for distributed systems.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"53 ","pages":"Article 101500"},"PeriodicalIF":4.2,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140879825","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":"A node-pinning and state-flipped approach to partial synchronization of Boolean Networks","authors":"Leihao Du ,&nbsp;Zhipeng Zhang ,&nbsp;Chengyi Xia","doi":"10.1016/j.nahs.2024.101501","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101501","url":null,"abstract":"<div><p>In this paper, the partial synchronization of general Boolean Networks is studied from the perspective of nodes and states by using the semi-tensor product of matrices. First, by introducing the Hamming distances and its algebraic expression, the partial synchronization of general Boolean Networks can be transformed into an ensemble stability problem. Second, through optimizing the pinning strategy, the conditions for achieving partial synchronization of general Boolean Networks are developed, and the algorithm for finding the optimal pinning nodes is given. Subsequently, to further simplify the above condition, the related pinning node strategy is further optimized and combined by introducing state-flipped mechanism, which makes the general Boolean Networks partially synchronous under no condition, and requires the less number of nodes to be pinned compared to the previous works. Meanwhile, the corresponding algorithm for seeking the optimal pinning nodes is designed in the context of flipping the state only once. Finally, the obtained results are validated by several specific numerical examples. In summary, the current work can further enrich and improve the study of partial synchronization problems in Boolean Networks.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"53 ","pages":"Article 101501"},"PeriodicalIF":4.2,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140879818","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}