{"title":"Periodic intermittent control for almost sure stability of stochastic strict-feedback semi-Markov jump systems","authors":"Chang Gao , Yu Xiao , Hao Dong , Beibei Guo","doi":"10.1016/j.nahs.2024.101524","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101524","url":null,"abstract":"<div><p>In this paper, we investigate the issue of almost sure stability (ASS) for a class of stochastic strict-feedback semi-Markov jump systems (SSSJSs) under periodic intermittent control (PIC). This control method and dynamic properties are studied for the first time in strict-feedback systems. First of all, based on the structural properties of the SSSJSs, virtual controllers are designed step by step and eventually deduced into the actual controller. Furthermore, by using stochastic analysis theory and multiple Lyapunov function method, we obtain sufficient conditions for ASS via PIC, which have a close relationship with control width and control period. By virtue of multiple Lyapunov functions that depend on the system states, the conservatism caused by mode-independent cases can be reduced effectively. Finally, the effectiveness of the presented results is illustrated by simulation examples.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"54 ","pages":"Article 101524"},"PeriodicalIF":3.7,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141542968","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 by delay feedback control for highly nonlinear switched stochastic systems with non-differentiable delay","authors":"Ying Zhao , Quanxin Zhu","doi":"10.1016/j.nahs.2024.101525","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101525","url":null,"abstract":"<div><p>The authors consider the stabilization of highly nonlinear switched stochastic systems with non-differentiable delay by delay feedback control. In this paper, switching signals of highly nonlinear switched stochastic systems are non-random which are different from the previous literature. Moreover, the time-varying delay of highly nonlinear switched stochastic systems is non-differentiable, while the time-varying delay of feedback control is constant or differentiable. By using the Lyapunov functional method and the mode-dependent average dwell time approach, we have established the delay-dependent stabilization criteria of highly nonlinear switched stochastic delay systems by delay feedback control. Finally, two numerical examples are provided to show the effectiveness of the developed theoretical results.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"54 ","pages":"Article 101525"},"PeriodicalIF":3.7,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141542967","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":"Ergodicity for population dynamics by pure-jump noise with switching","authors":"Zhenzhong Zhang , Wenze Chen , Hanlu Yang , Jinying Tong , Xin Zhao","doi":"10.1016/j.nahs.2024.101521","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101521","url":null,"abstract":"<div><p>In this paper we consider the long time behavior for an <span><math><mi>n</mi></math></span>-dimensional population model driven by truncated <span><math><mi>α</mi></math></span>-stable processes for interacting species. Some sufficient conditions for ergodicity or transience for our systems are given. This paper discloses the different jump measures impact on such pure-jumps population dynamics.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"54 ","pages":"Article 101521"},"PeriodicalIF":3.7,"publicationDate":"2024-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141485682","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}
Stacey R. Smith? , Tyler Meadows , Gail S.K. Wolkowicz
{"title":"Competition in the nutrient-driven self-cycling fermentation process","authors":"Stacey R. Smith? , Tyler Meadows , Gail S.K. Wolkowicz","doi":"10.1016/j.nahs.2024.101519","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101519","url":null,"abstract":"<div><p>Self-cycling fermentation is an automated process used for culturing microorganisms. We consider a model of <span><math><mi>n</mi></math></span> distinct species competing for a single non-reproducing nutrient in a self-cycling fermentor in which the nutrient level is used as the decanting condition. The model is formulated in terms of impulsive ordinary differential equations. We prove that two species are able to coexist in the fermentor under certain conditions. We also provide numerical simulations that suggest coexistence of three species is possible and that competitor-mediated coexistence can occur in this case. These results are in contrast to the chemostat, the continuous analogue, where multiple species cannot coexist on a single nonreproducing nutrient.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"54 ","pages":"Article 101519"},"PeriodicalIF":3.7,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1751570X24000566/pdfft?md5=e254b98cebab802142bedb00cec1d2ef&pid=1-s2.0-S1751570X24000566-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141485683","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}
Hongjie Pang , Jun Cheng , Huaicheng Yan , Dan Zhang , Wenhai Qi
{"title":"Asynchronous model predictive control of LPV systems with stochastic communication protocol","authors":"Hongjie Pang , Jun Cheng , Huaicheng Yan , Dan Zhang , Wenhai Qi","doi":"10.1016/j.nahs.2024.101522","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101522","url":null,"abstract":"<div><p>This study is dedicated to exploring the challenge of asynchronous resilient robust model predictive control (RMPC) for linear parameter-varying (LPV) systems operating under a stochastic communication protocol (SCP). In contrast to the conventional Markov-based SCP, a novel sojourn probability-based SCP is introduced to regulate packet transmissions. This innovative approach simplifies the determination of transition probabilities and lessens the computational burden. Acknowledging the challenges associated with observing sojourn probability information, a mode detector is employed to describe the connection between mode discrepancies. To address parameter uncertainties, a novel detected-mode-based resilient control law is formulated to ensure the mean-square stability of the LPV system within the resilient RMPC framework. Additionally, an online algorithm for resilient RMPC is presented, grounded in an auxiliary optimization problem. Ultimately, the effectiveness of the proposed control strategy is validated via a high-purity distillation process model.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"54 ","pages":"Article 101522"},"PeriodicalIF":3.7,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141485684","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}
Aya Younes, Félix Miranda-Villatoro, Bernard Brogliato
{"title":"Trajectory tracking in linear complementarity systems with and without state jumps: A passivity approach","authors":"Aya Younes, Félix Miranda-Villatoro, Bernard Brogliato","doi":"10.1016/j.nahs.2024.101520","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101520","url":null,"abstract":"<div><p>This work is largely concerned with trajectory tracking in linear complementarity systems (LCS). The main analytical tool for stability analysis and control design is passivity and the associated linear matrix inequalities (LMIs) for feedback passification. Cases with and without state-jumps, with and without parametric uncertainties, are analyzed. Theoretical findings are illustrated with examples from circuits with set-valued, nonsmooth electronic components, networks with unilateral interactions, and mechanical system with unilateral spring.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"54 ","pages":"Article 101520"},"PeriodicalIF":3.7,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141438966","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}
Armin Nurkanović , Anton Pozharskiy , Jonathan Frey , Moritz Diehl
{"title":"Finite Elements with Switch Detection for numerical optimal control of nonsmooth dynamical systems with set-valued heaviside step functions","authors":"Armin Nurkanović , Anton Pozharskiy , Jonathan Frey , 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 , Corina Barbalata , Michael Malisoff , 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}
N. Aravinth , R. Sakthivel , N. Birundha devi , Ardashir Mohammadzadeh , S. Saat
{"title":"Stabilization of delayed semi-Markov jump neural networks with actuator faults: A quantized hybrid control approach","authors":"N. Aravinth , R. Sakthivel , N. Birundha devi , Ardashir Mohammadzadeh , 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}
Shuting Zhang , Xueying Ding , Jianquan Lu , Jungang Lou , Yang Liu
{"title":"Output-feedback stabilization of probabilistic Boolean control networks","authors":"Shuting Zhang , Xueying Ding , Jianquan Lu , Jungang Lou , 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}