Nonlinear Analysis-Hybrid Systems最新文献_第9页

On global exponential stability of discrete-time switching systems with dwell-time ranges: Novel induced LMIs for linear systems with delays 论具有停留时间范围的离散时间开关系统的全局指数稳定性有延迟线性系统的新诱导 LMI

IF 4.2 2区计算机科学

Nonlinear Analysis-Hybrid Systems Pub Date : 2024-02-15 DOI: 10.1016/j.nahs.2024.101476

Pierdomenico Pepe

{"title":"On global exponential stability of discrete-time switching systems with dwell-time ranges: Novel induced LMIs for linear systems with delays","authors":"Pierdomenico Pepe","doi":"10.1016/j.nahs.2024.101476","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101476","url":null,"abstract":"<div>In this paper, we provide necessary and sufficient Lyapunov conditions for discrete-time switching systems to be globally exponentially stable, when the switching signal obeys to a switches digraph and is subject to dwell-time constraints. In order to best exploit the information on switching-dwelling constraints, conditions are given by means of multiple Lyapunov functions. The number of involved Lyapunov functions is equal to the number of switching modes. To avoid a pileup of Lyapunov functions, we do not introduce dummy vertices that account for dwell-time ranges. For example, in the linear case, such a pileup corresponds to a pileup of decision matrices related to some linear matrix inequalities. A link between global exponential stability and exponential input-to-state stability is provided. The following result is proved: if, in the case of zero input, the discrete-time switching system is globally exponentially stable, and the functions describing the dynamics of the subsystems, with input, are suitably globally Lipschitz, then the switching system is exponentially input-to-state stable. Finally, exploiting the well known relationship between discrete-time systems with delays and discrete-time switching systems, the provided results are shown for the former systems, in the linear case. In particular, linear matrix inequalities, by which the global exponential stability of linear discrete-time systems with constrained time delays can be possibly established, are provided. The utility of these linear matrix inequalities is shown with a numerical example taken from the literature.</div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"52 ","pages":"Article 101476"},"PeriodicalIF":4.2,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1751570X2400013X/pdfft?md5=d5c33853de8186daf4484beef0600fa3&pid=1-s2.0-S1751570X2400013X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139737166","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}

引用次数: 0

Unified stability criteria for impulsive stochastic delayed systems 脉冲随机延迟系统的统一稳定性标准

IF 4.2 2区计算机科学

Nonlinear Analysis-Hybrid Systems Pub Date : 2024-02-14 DOI: 10.1016/j.nahs.2024.101474

Junyan Xu , Yang Liu , Qingxin Meng , Jinde Cao , Mahmoud Abdel-Aty

引用次数: 0

Saddle–node canard cycles in slow–fast planar piecewise linear differential systems 慢-快平面片断线性微分系统中的鞍节点卡纳循环

IF 4.2 2区计算机科学

Nonlinear Analysis-Hybrid Systems Pub Date : 2024-02-08 DOI: 10.1016/j.nahs.2024.101472

V. Carmona , S. Fernández-García , A.E. Teruel

{"title":"Saddle–node canard cycles in slow–fast planar piecewise linear differential systems","authors":"V. Carmona , S. Fernández-García , A.E. Teruel","doi":"10.1016/j.nahs.2024.101472","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101472","url":null,"abstract":"<div>By applying a singular perturbation approach, canard explosions exhibited by a general family of singularly perturbed planar Piecewise Linear (PWL) differential systems are analyzed. The performed study involves both hyperbolic and non-hyperbolic canard limit cycles appearing after both, a supercritical and a subcritical Hopf bifurcation. The obtained results are comparable with those obtained for smooth vector fields. In some sense, the manuscript can be understood as an extension towards the PWL framework of the results obtained for smooth systems by Dumortier and Roussarie in Mem. Am. Math. Soc. 1996, and Krupa and Szmolyan in J. Differ. Equ. 2001. In addition, some novel slow–fast behaviors are obtained. In particular, in the supercritical case, and under suitable conditions, it is proved that the limit cycles are organized along a curve exhibiting two folds. Each of these folds corresponds to a saddle–node bifurcation of canard limit cycles, one involving headless canard cycles, and the other involving canard cycles with head. This configuration also occurs in smooth systems with N-shaped fast nullcline. However, it has not been previously reported in the Van der Pol system. Our results provide justification for this observation.</div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"52 ","pages":"Article 101472"},"PeriodicalIF":4.2,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1751570X24000098/pdfft?md5=7093e1f1bae786ede295a3a6f74f22f2&pid=1-s2.0-S1751570X24000098-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139713863","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}

引用次数: 0

A nonsmooth RATTLE algorithm for mechanical systems with frictional unilateral constraints 具有摩擦单边约束的机械系统的非平滑 RATTLE 算法

IF 4.2 2区计算机科学

Nonlinear Analysis-Hybrid Systems Pub Date : 2024-02-06 DOI: 10.1016/j.nahs.2024.101469

Jonas Breuling , Giuseppe Capobianco , Simon R. Eugster , Remco I. Leine

引用次数: 0

Chance-constrained optimization for contact-rich systems using mixed integer programming 利用混合整数编程对接触丰富的系统进行机会受限优化

IF 4.2 2区计算机科学

Nonlinear Analysis-Hybrid Systems Pub Date : 2024-02-06 DOI: 10.1016/j.nahs.2024.101466

Yuki Shirai , Devesh K. Jha , Arvind U. Raghunathan , Diego Romeres

引用次数: 0

Finite-time stability via GKL-functions for impulsive dynamical systems 通过 GKL 函数实现脉冲动力系统的有限时间稳定性

IF 4.2 2区计算机科学

Nonlinear Analysis-Hybrid Systems Pub Date : 2024-02-06 DOI: 10.1016/j.nahs.2024.101470

Bin Liu , Zhou-Teng Xie , Ping Li , Zhijie Sun

{"title":"Finite-time stability via GKL-functions for impulsive dynamical systems","authors":"Bin Liu , Zhou-Teng Xie , Ping Li , Zhijie Sun","doi":"10.1016/j.nahs.2024.101470","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101470","url":null,"abstract":"<div>This paper studies the finite-time stability via <math><mi>GKL</mi></math>-functions (<math><mi>GKL</mi></math>-FTS) for impulsive dynamical systems (IDS). The notions of <math><mi>GKL</mi></math>-functions, <math><mi>GKL</mi></math>-FTS, and event-<math><mi>GKL</mi></math>-FTS are proposed for IDS. The <math><mi>GKL</mi></math>-FTS is a type of well-defined finite-time stability which is expressed via <math><mi>GKL</mi></math>-functions. The <math><mi>GKL</mi></math>-FTS is decomposed into specific types through the decomposition of <math><mi>GKL</mi></math>-functions. By establishing the comparison principles of FTS including <math><mi>GKL</mi></math>-FTS and event-<math><mi>GKL</mi></math>-FTS, and by using the decompositions of <math><mi>GKL</mi></math>-functions, the criteria on <math><mi>GKL</mi></math>-FTS and event-<math><mi>GKL</mi></math>-FTS are derived for IDS. And with the help of the decompositions of <math><mi>GKL</mi></math>-FTS, the settling time of the <math><mi>GKL</mi></math>-FTS is effectively calculated. Moreover, two types of specific <math><mi>GKL</mi></math>-FTS with fixed settling time, i.e., <math><mi>GKL</mi></math>-FTS via resetting state to zero, and event-<math><mi>GKL</mi></math>-FTS via Zeno behaviour, are provided. And four examples with numerical simulations are presented to demonstrate the effectiveness of the results. It is shown that the <math><mi>GKL</mi></math>-FTS criteria are less conservative in relaxing the FTS conditions of IDS in the literature. And specific effects of impulses on FTS are given in these <math><mi>GKL</mi></math>-FTS criteria, including that an unstable continuous system may obtain FTS under a finite number of impulses.</div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"52 ","pages":"Article 101470"},"PeriodicalIF":4.2,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139694768","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}

引用次数: 0

Leveraging randomized smoothing for optimal control of nonsmooth dynamical systems 利用随机平滑技术实现非平滑动力系统的优化控制

IF 4.2 2区计算机科学

Nonlinear Analysis-Hybrid Systems Pub Date : 2024-02-01 DOI: 10.1016/j.nahs.2024.101468

Quentin Le Lidec , Fabian Schramm , Louis Montaut , Cordelia Schmid , Ivan Laptev , Justin Carpentier

{"title":"Leveraging randomized smoothing for optimal control of nonsmooth dynamical systems","authors":"Quentin Le Lidec , Fabian Schramm , Louis Montaut , Cordelia Schmid , Ivan Laptev , Justin Carpentier","doi":"10.1016/j.nahs.2024.101468","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101468","url":null,"abstract":"<div>Optimal control (OC) algorithms such as differential dynamic programming (DDP) take advantage of the derivatives of the dynamics to control physical systems efficiently. Yet, these algorithms are prone to failure when dealing with non-smooth dynamical systems. This can be attributed to factors such as the existence of discontinuities in the dynamics derivatives or the presence of non-informative gradients. On the contrary, reinforcement learning (RL) algorithms have shown better empirical results in scenarios exhibiting non-smooth effects (contacts, frictions, etc.). Our approach leverages recent works on randomized smoothing (RS) to tackle non-smoothness issues commonly encountered in optimal control and provides key insights on the interplay between RL and OC through the prism of RS methods. This naturally leads us to introduce the randomized Differential Dynamic Programming (RDDP) algorithm accounting for deterministic but non-smooth dynamics in a very sample-efficient way. The experiments demonstrate that our method can solve classic robotic problems with dry friction and frictional contacts, where classical OC algorithms are likely to fail, and RL algorithms require, in practice, a prohibitive number of samples to find an optimal solution.</div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"52 ","pages":"Article 101468"},"PeriodicalIF":4.2,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139675293","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}

引用次数: 0

Data-driven abstraction-based control synthesis 基于数据驱动抽象的控制合成

IF 4.2 2区计算机科学

Nonlinear Analysis-Hybrid Systems Pub Date : 2024-01-29 DOI: 10.1016/j.nahs.2024.101467

Milad Kazemi , Rupak Majumdar , Mahmoud Salamati , Sadegh Soudjani , Ben Wooding

{"title":"Data-driven abstraction-based control synthesis","authors":"Milad Kazemi , Rupak Majumdar , Mahmoud Salamati , Sadegh Soudjani , Ben Wooding","doi":"10.1016/j.nahs.2024.101467","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101467","url":null,"abstract":"<div>This paper studies formal synthesis of controllers for continuous-space systems with unknown dynamics to satisfy requirements expressed as linear temporal logic formulas. Formal abstraction-based synthesis schemes rely on a precise mathematical model of the system to build a finite abstract model, which is then used to design a controller. The abstraction-based schemes are not applicable when the dynamics of the system are unknown. We propose a data-driven approach that computes a growth bound of the system using a finite number of trajectories. The computed growth bound together with the sampled trajectories are then used to construct the abstraction and synthesise a controller.Our approach casts the computation of a growth bound as a robust convex optimisation program (RCP). Since the unknown dynamics appear in the optimisation, we formulate a scenario convex program (SCP) corresponding to the RCP using a finite number of sampled trajectories. We establish a sample complexity result that gives a lower bound for the number of sampled trajectories to guarantee the correctness of the growth bound computed from the SCP with a given confidence. Our sample complexity result requires knowing a possibly conservative bound on the Lipschitz constant of the system. We also provide a sample complexity result for the satisfaction of the specification on the system in closed loop with the designed controller for a given confidence. Our data-driven synthesised controller can provide guarantees on satisfaction of both finite and infinite-horizon specifications. We show that our data-driven approach can be readily used as a model-free abstraction refinement scheme by modifying the formulation of the system’s growth bounds and providing similar sample complexity results. The performance of our approach is shown on three case studies.</div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"52 ","pages":"Article 101467"},"PeriodicalIF":4.2,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1751570X24000049/pdfft?md5=7da196d9d946e935867e0b56bbbc21a9&pid=1-s2.0-S1751570X24000049-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139653626","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}

引用次数: 0

Model matching problems for impulsive linear systems with polytopic uncertainties 具有多态不确定性的脉冲线性系统的模型匹配问题

IF 4.2 2区计算机科学

Nonlinear Analysis-Hybrid Systems Pub Date : 2024-01-13 DOI: 10.1016/j.nahs.2024.101465

Elena Zattoni , Naohisa Otsuka , Anna Maria Perdon , Giuseppe Conte

{"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>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.</div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"52 ","pages":"Article 101465"},"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}

引用次数: 0

FIR system identification under congruential summation-triggered communication scheme with binary observations 具有二进制观测结果的全同求和触发通信方案下的 FIR 系统识别

IF 4.2 2区计算机科学

Nonlinear Analysis-Hybrid Systems Pub Date : 2024-01-09 DOI: 10.1016/j.nahs.2024.101464

Xu Cui , Qingxiang Zhang , Peng Yu , Fengwei Jing , Jin Guo

引用次数: 0