Pub Date : 2024-02-19DOI: 10.1016/j.nahs.2024.101478
Jie Zhang , Yingnan Pan , Liang Cao
In this paper, the fault-tolerant tracking control problem is addressed for switched nonlinear systems subject to time-varying output constraints and dead-zone input under arbitrary switching signal. An improved output-dependent barrier function with weight factors is presented to handle the output constraint issue, which eliminates the conservative design that converts the output constraints into the tracking error related constraints and relaxes the requirements for the initial value of the systems output. Meanwhile, the barrier function presented in this paper can be used for the time-varying/constant symmetric/asymmetric output constraints and can tackle both constrained and unconstrained cases. Besides, the performance of the systems is ensured when actuator faults and dead-zone input occur simultaneously. By establishing the new coordinate transformations, together with command filter technique and the backstepping approach, the presented adaptive control strategy ensures that all signals of the closed-loop systems are bounded. Finally, the validity of the presented method is demonstrated via two simulation examples.
{"title":"Command filter-based adaptive fault-tolerant tracking control for switched nonlinear systems with time-varying output constraints","authors":"Jie Zhang , Yingnan Pan , Liang Cao","doi":"10.1016/j.nahs.2024.101478","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101478","url":null,"abstract":"<div><p>In this paper, the fault-tolerant tracking control problem is addressed for switched nonlinear systems subject to time-varying output constraints and dead-zone input under arbitrary switching signal. An improved output-dependent barrier function with weight factors is presented to handle the output constraint issue, which eliminates the conservative design that converts the output constraints into the tracking error related constraints and relaxes the requirements for the initial value of the systems output. Meanwhile, the barrier function presented in this paper can be used for the time-varying/constant symmetric/asymmetric output constraints and can tackle both constrained and unconstrained cases. Besides, the performance of the systems is ensured when actuator faults and dead-zone input occur simultaneously. By establishing the new coordinate transformations, together with command filter technique and the backstepping approach, the presented adaptive control strategy ensures that all signals of the closed-loop systems are bounded. Finally, the validity of the presented method is demonstrated via two simulation examples.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139901381","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}
This paper studies the dwell-time-dependent stability analysis of impulsive systems by using a new time-square-dependent looped-functional. Based on the Lyapunov theory and two-sided looped-functional method, a time-square-dependent looped-functional is proposed, which fully utilizes the information of both the intervals and . Then, by applying Jensen’s inequality and free-matrix-based inequalities to deal with integral terms in the functional derivatives, sufficient stability conditions in the form of linear matrix inequality are derived for periodic and aperiodic impulsive systems. Finally, numerical examples and simulation tests are given to illustrate the effectiveness and superiority of the proposed method.
{"title":"Improved looped-functional approach for dwell-time-dependent stability analysis of impulsive systems","authors":"Hong-Bing Zeng, Wei-Min Wang, Wei Wang, Hui-Qin Xiao","doi":"10.1016/j.nahs.2024.101477","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101477","url":null,"abstract":"<div><p>This paper studies the dwell-time-dependent stability analysis of impulsive systems by using a new time-square-dependent looped-functional. Based on the Lyapunov theory and two-sided looped-functional method, a time-square-dependent looped-functional is proposed, which fully utilizes the information of both the intervals <span><math><mrow><mo>[</mo><msub><mrow><mi>t</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>,</mo><mi>t</mi><mo>]</mo></mrow></math></span> and <span><math><mrow><mo>[</mo><mi>t</mi><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>]</mo></mrow></math></span>. Then, by applying Jensen’s inequality and free-matrix-based inequalities to deal with integral terms in the functional derivatives, sufficient stability conditions in the form of linear matrix inequality are derived for periodic and aperiodic impulsive systems. Finally, numerical examples and simulation tests are given to illustrate the effectiveness and superiority of the proposed method.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139749258","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 : 2024-02-15DOI: 10.1016/j.nahs.2024.101476
Pierdomenico Pepe
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.
{"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><p>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.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"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}
Pub Date : 2024-02-14DOI: 10.1016/j.nahs.2024.101474
Junyan Xu , Yang Liu , Qingxin Meng , Jinde Cao , Mahmoud Abdel-Aty
This paper investigates the th moment exponential stability of impulsive stochastic delayed systems (ISDS). New stability criteria for ISDS are developed by applying the Razumikhin approach and a novel concept of average random impulsive estimation (ARIE). Stochastic impulsive strength, the time-varying delay in continuous dynamics, and the impulsive delay are considered simultaneously, and there are no imposed restrictions on their sizes. Utilizing ARIE, the proposed control scheme with stabilizing impulse can still ensure the stability of the whole system under the presence of impulsive perturbations at some impulsive instants, that is, it allows some impulsive intensities at impulsive instants are greater than 1 or a certain threshold which is more than 1. In addition, the requirement for the sign of time-derivative of Razumikhin function is also relaxed. Several illustrated examples are given to verify the effectiveness of our proposed results.
{"title":"Unified stability criteria for impulsive stochastic delayed systems","authors":"Junyan Xu , Yang Liu , Qingxin Meng , Jinde Cao , Mahmoud Abdel-Aty","doi":"10.1016/j.nahs.2024.101474","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101474","url":null,"abstract":"<div><p>This paper investigates the <span><math><mi>p</mi></math></span>th moment exponential stability of impulsive stochastic delayed systems (ISDS). New stability criteria for ISDS are developed by applying the Razumikhin approach and a novel concept of average random impulsive estimation (ARIE). Stochastic impulsive strength, the time-varying delay in continuous dynamics, and the impulsive delay are considered simultaneously, and there are no imposed restrictions on their sizes. Utilizing ARIE, the proposed control scheme with stabilizing impulse can still ensure the stability of the whole system under the presence of impulsive perturbations at some impulsive instants, that is, it allows some impulsive intensities at impulsive instants are greater than 1 or a certain threshold which is more than 1. In addition, the requirement for the sign of time-derivative of Razumikhin function is also relaxed. Several illustrated examples are given to verify the effectiveness of our proposed results.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139733294","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 : 2024-02-08DOI: 10.1016/j.nahs.2024.101472
V. Carmona , S. Fernández-García , A.E. Teruel
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.
通过应用奇异扰动方法,分析了奇异扰动平面片断线性微分方程(PWL)微分方程一般族所表现出的卡式爆炸。研究涉及超临界和亚临界霍普夫分岔后出现的双曲和非双曲鸭式极限循环。所获得的结果与光滑矢量场的结果相当。从某种意义上讲,本手稿可以理解为杜莫蒂埃和鲁萨里在《美国数学会刊》(Mem. Am. Math.Math.Soc. 1996,以及 Krupa 和 Szmolyan 在 J. Differ.Equ.2001.此外,还获得了一些新的慢-快行为。特别是在超临界情况下,在合适的条件下,证明了极限循环是沿着一条表现出两个褶皱的曲线组织起来的。每个褶皱都对应于卡式极限循环的鞍节点分岔,一个涉及无头卡式循环,另一个涉及有头卡式循环。这种构型也出现在具有 N 型快速空折线的光滑系统中。然而,在范德波尔系统中,以前还没有报道过这种情况。我们的结果为这一观察提供了依据。
{"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><p>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.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"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}
Pub Date : 2024-02-06DOI: 10.1016/j.nahs.2024.101469
Jonas Breuling , Giuseppe Capobianco , Simon R. Eugster , Remco I. Leine
In 1983, Andersen proposed the RATTLE algorithm as an extension of the SHAKE algorithm. The RATTLE algorithm is a well-established method for simulating mechanical systems with perfect bilateral constraints. This paper further extends RATTLE for simulating nonsmooth mechanical systems with frictional unilateral constraints (i.e. frictional contact). With that, it satisfies the need for higher-order integration methods within the framework of nonsmooth contact dynamics in phases where the contact status does not change (i.e. no collisions/constant sliding states). In particular, the proposed method can simulate impact-free motions, such as persistent frictional contact, with second-order accurate positions and velocities and prohibits penetration by unilateral constraints on position level.
{"title":"A nonsmooth RATTLE algorithm for mechanical systems with frictional unilateral constraints","authors":"Jonas Breuling , Giuseppe Capobianco , Simon R. Eugster , Remco I. Leine","doi":"10.1016/j.nahs.2024.101469","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101469","url":null,"abstract":"<div><p>In 1983, Andersen proposed the RATTLE algorithm as an extension of the SHAKE algorithm. The RATTLE algorithm is a well-established method for simulating mechanical systems with perfect bilateral constraints. This paper further extends RATTLE for simulating nonsmooth mechanical systems with frictional unilateral constraints (i.e. frictional contact). With that, it satisfies the need for higher-order integration methods within the framework of nonsmooth contact dynamics in phases where the contact status does not change (i.e. no collisions/constant sliding states). In particular, the proposed method can simulate impact-free motions, such as persistent frictional contact, with second-order accurate positions and velocities and prohibits penetration by unilateral constraints on position level.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1751570X24000062/pdfft?md5=e7013b99c5c296c478a8e8de6cfc28ef&pid=1-s2.0-S1751570X24000062-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139699663","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 : 2024-02-06DOI: 10.1016/j.nahs.2024.101466
Yuki Shirai , Devesh K. Jha , Arvind U. Raghunathan , Diego Romeres
Stochastic and robust optimization of uncertain contact-rich systems is relatively unexplored. This paper presents a chance-constrained formulation for robust trajectory optimization during manipulation. In particular, we present chance-constrained optimization of Stochastic Discrete-time Linear Complementarity Systems (SDLCS). The optimization problem is formulated as a Mixed-Integer Quadratic Program with Chance Constraints (MIQPCC). In our formulation, we explicitly consider joint chance constraints for complementarity variables and states to capture the stochastic evolution of dynamics. Additionally, we demonstrate the use of our proposed approach for designing a Stochastic Model Predictive Controller (SMPC) with complementarity constraints for a planar pushing system. We evaluate the robustness of our optimized trajectories in simulation on several systems. The proposed approach outperforms some recent approaches for robust trajectory optimization for SDLCS.
{"title":"Chance-constrained optimization for contact-rich systems using mixed integer programming","authors":"Yuki Shirai , Devesh K. Jha , Arvind U. Raghunathan , Diego Romeres","doi":"10.1016/j.nahs.2024.101466","DOIUrl":"https://doi.org/10.1016/j.nahs.2024.101466","url":null,"abstract":"<div><p>Stochastic and robust optimization of uncertain contact-rich systems is relatively unexplored. This paper presents a chance-constrained formulation for robust trajectory optimization during manipulation. In particular, we present chance-constrained optimization of Stochastic Discrete-time Linear Complementarity Systems (SDLCS). The optimization problem is formulated as a Mixed-Integer Quadratic Program with Chance Constraints (MIQPCC). In our formulation, we explicitly consider joint chance constraints for complementarity variables and states to capture the stochastic evolution of dynamics. Additionally, we demonstrate the use of our proposed approach for designing a Stochastic Model Predictive Controller (SMPC) with complementarity constraints for a planar pushing system. We evaluate the robustness of our optimized trajectories in simulation on several systems. The proposed approach outperforms some recent approaches for robust trajectory optimization for SDLCS.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139694769","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 : 2024-02-06DOI: 10.1016/j.nahs.2024.101470
Bin Liu , Zhou-Teng Xie , Ping Li , Zhijie Sun
This paper studies the finite-time stability via -functions (-FTS) for impulsive dynamical systems (IDS). The notions of -functions, -FTS, and event--FTS are proposed for IDS. The -FTS is a type of well-defined finite-time stability which is expressed via -functions. The -FTS is decomposed into specific types through the decomposition of -functions. By establishing the comparison principles of FTS including -FTS and event--FTS, and by using the decompositions of -functions, the criteria on -FTS and event--FTS are derived for IDS. And with the help of the decompositions of -FTS, the settling time of the -FTS is effectively calculated. Moreover, two types of specific -FTS with fixed settling time, i.e., -FTS via resetting state to zero, and event--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 -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 -FTS criteria, including that an unstable continuous system may obtain FTS under a finite number of impulses.
{"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><p>This paper studies the finite-time stability via <span><math><mi>GKL</mi></math></span>-functions (<span><math><mi>GKL</mi></math></span>-FTS) for impulsive dynamical systems (IDS). The notions of <span><math><mi>GKL</mi></math></span>-functions, <span><math><mi>GKL</mi></math></span>-FTS, and event-<span><math><mi>GKL</mi></math></span>-FTS are proposed for IDS. The <span><math><mi>GKL</mi></math></span>-FTS is a type of well-defined finite-time stability which is expressed via <span><math><mi>GKL</mi></math></span>-functions. The <span><math><mi>GKL</mi></math></span>-FTS is decomposed into specific types through the decomposition of <span><math><mi>GKL</mi></math></span>-functions. By establishing the comparison principles of FTS including <span><math><mi>GKL</mi></math></span>-FTS and event-<span><math><mi>GKL</mi></math></span>-FTS, and by using the decompositions of <span><math><mi>GKL</mi></math></span>-functions, the criteria on <span><math><mi>GKL</mi></math></span>-FTS and event-<span><math><mi>GKL</mi></math></span>-FTS are derived for IDS. And with the help of the decompositions of <span><math><mi>GKL</mi></math></span>-FTS, the settling time of the <span><math><mi>GKL</mi></math></span>-FTS is effectively calculated. Moreover, two types of specific <span><math><mi>GKL</mi></math></span>-FTS with fixed settling time, i.e., <span><math><mi>GKL</mi></math></span>-FTS via resetting state to zero, and event-<span><math><mi>GKL</mi></math></span>-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 <span><math><mi>GKL</mi></math></span>-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 <span><math><mi>GKL</mi></math></span>-FTS criteria, including that an unstable continuous system may obtain FTS under a finite number of impulses.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"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}
Pub Date : 2024-02-01DOI: 10.1016/j.nahs.2024.101468
Quentin Le Lidec , Fabian Schramm , Louis Montaut , Cordelia Schmid , Ivan Laptev , Justin Carpentier
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.
{"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><p><span><span>Optimal control<span> (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 </span></span>dry friction and </span>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.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"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}
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.
{"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><p>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.</p><p>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.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"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}