Pub Date : 2025-10-07DOI: 10.1016/j.nahs.2025.101629
Eric Goubault, Sylvie Putot
We propose an approach for computing inner and outer-approximations of the sets of values that satisfy constraints expressed as arbitrarily quantified formulas. Such formulas arise for example when specifying important problems in control such as robustness, motion planning and controller comparison. We propose an interval-based method which allows for tight but tractable approximations. We demonstrate its applicability through a series of examples and benchmarks using a prototype implementation. Finally, we develop higher-order methods, particularly tractable order one methods which provide even tighter results.
{"title":"Inner and outer approximations of arbitrarily quantified reachability problems","authors":"Eric Goubault, Sylvie Putot","doi":"10.1016/j.nahs.2025.101629","DOIUrl":"10.1016/j.nahs.2025.101629","url":null,"abstract":"<div><div>We propose an approach for computing inner and outer-approximations of the sets of values that satisfy constraints expressed as arbitrarily quantified formulas. Such formulas arise for example when specifying important problems in control such as robustness, motion planning and controller comparison. We propose an interval-based method which allows for tight but tractable approximations. We demonstrate its applicability through a series of examples and benchmarks using a prototype implementation. Finally, we develop higher-order methods, particularly tractable order one methods which provide even tighter results.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101629"},"PeriodicalIF":3.7,"publicationDate":"2025-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145267873","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 : 2025-09-30DOI: 10.1016/j.nahs.2025.101644
Henk A.P. Blom
In MJLS literature the separation principle between filtering and control has been established in case the Markov mode switching process is fully observed, and the Euclidean state process is partially observed. In case the exact remains hidden, the separation principle has only been established under a linear filtering restriction. Since nonlinear filters can provide significant better estimates, the desire to extend the separation principle to MJLS with hidden is a long-standing challenge. The objective of this paper is to resolve this long-standing challenge in three steps. The first step is to transform the MJLS stochastic control problem into control under a quadratic performance criterion of a linear system driven by a martingale which is influenced by the control. The certainty equivalence (CE) condition known in literature applies to stochastic control of a linear system that is driven by a control independent martingale. Therefore, the second step is to relax this known CE condition such that it allows this control influence on the martingale. The third step is to prove that the relaxed CE condition is satisfied for the general MJLS control problem considered. The overall achievement is a CE control law for a partially observed MJLS, which assures the Separation Principle between filtering and control. The paper also shows that for the case that is fully observed and the exactremains hidden, that the novel CE control law differs significantly from the in literature well-developed Averaging MJLS control policy.
{"title":"Separation principle for stochastic control of continuous-time Markov jump linear systems under partial observations","authors":"Henk A.P. Blom","doi":"10.1016/j.nahs.2025.101644","DOIUrl":"10.1016/j.nahs.2025.101644","url":null,"abstract":"<div><div>In MJLS literature the separation principle between filtering and control has been established in case the Markov mode switching process <span><math><mrow><mo>{</mo><msub><mi>θ</mi><mi>t</mi></msub><mo>}</mo></mrow></math></span> is fully observed, and the Euclidean state process <span><math><mrow><mo>{</mo><msub><mi>x</mi><mi>t</mi></msub><mo>}</mo></mrow></math></span>is partially observed. In case the exact <span><math><mrow><mo>{</mo><msub><mi>θ</mi><mi>t</mi></msub><mo>}</mo></mrow></math></span>remains hidden, the separation principle has only been established under a linear filtering restriction. Since nonlinear filters can provide significant better estimates, the desire to extend the separation principle to MJLS with hidden <span><math><mrow><mo>{</mo><msub><mi>θ</mi><mi>t</mi></msub><mo>}</mo></mrow></math></span>is a long-standing challenge. The objective of this paper is to resolve this long-standing challenge in three steps. The first step is to transform the MJLS stochastic control problem into control under a quadratic performance criterion of a linear system driven by a martingale which is influenced by the control. The certainty equivalence (CE) condition known in literature applies to stochastic control of a linear system that is driven by a control independent martingale. Therefore, the second step is to relax this known CE condition such that it allows this control influence on the martingale. The third step is to prove that the relaxed CE condition is satisfied for the general MJLS control problem considered. The overall achievement is a CE control law for a partially observed MJLS, which assures the Separation Principle between filtering and control. The paper also shows that for the case that <span><math><mrow><mo>{</mo><msub><mi>x</mi><mi>t</mi></msub><mo>}</mo></mrow></math></span>is fully observed and the exact<span><math><mrow><mo>{</mo><msub><mi>θ</mi><mi>t</mi></msub><mo>}</mo></mrow></math></span>remains hidden, that the novel CE control law differs significantly from the in literature well-developed Averaging MJLS control policy.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101644"},"PeriodicalIF":3.7,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220775","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 : 2025-09-26DOI: 10.1016/j.nahs.2025.101647
Hoang Thi Duyen , Ky Quan Tran
This paper investigates -exponential stability – also known as exponential stability in the mean square – of neutral stochastic delay differential equations with impulsive perturbations. Our primary objective is to stabilize an impulsive-free system by appropriately designing impulsive controls. Unlike previous studies, we introduce new and verifiable criteria for -exponential stability. We further demonstrate that Euler–Maruyama-type approximations preserve -exponential stability provided that the step sizes are sufficiently small; explicit conditions on these step sizes are derived. Moreover, we detail the design of impulsive perturbations that achieve -exponential stabilization. Two examples are presented to validate the effectiveness of our criteria.
{"title":"L2-exponential stability and impulsive stabilization of neutral stochastic delay differential equations","authors":"Hoang Thi Duyen , Ky Quan Tran","doi":"10.1016/j.nahs.2025.101647","DOIUrl":"10.1016/j.nahs.2025.101647","url":null,"abstract":"<div><div>This paper investigates <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-exponential stability – also known as exponential stability in the mean square – of neutral stochastic delay differential equations with impulsive perturbations. Our primary objective is to stabilize an impulsive-free system by appropriately designing impulsive controls. Unlike previous studies, we introduce new and verifiable criteria for <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-exponential stability. We further demonstrate that Euler–Maruyama-type approximations preserve <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-exponential stability provided that the step sizes are sufficiently small; explicit conditions on these step sizes are derived. Moreover, we detail the design of impulsive perturbations that achieve <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-exponential stabilization. Two examples are presented to validate the effectiveness of our criteria.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101647"},"PeriodicalIF":3.7,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158732","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 : 2025-09-18DOI: 10.1016/j.nahs.2025.101642
Xiaoyun Wei , Xingwen Liu , Jun Yang , Tingjin Liu
This paper focuses on exponential stability analysis for discrete-time almost periodic piecewise nonlinear systems (APPNSs) with uncertain dwell time of subsystems. A discrete-time APPNS has a fundamental period, during which a finite number of subsystems that constitute the system are cyclically activated. Such systems can be modeled as switched systems with cyclically switching signals. With the assumption that the vector field of each subsystem of discrete-time APPNSs is continuously differentiable, a Lyapunov theorem is presented first to verify the exponential stability of discrete-time APPNSs. Then, a linearization method is employed and a mixed-mode time-varying homogeneous Lyapunov function is constructed to derive specific stability conditions expressed by linear matrix inequalities (LMIs). Note that this condition can verify the exponential stability of the considered nonlinear systems, as well as that of the corresponding linearized systems. Furthermore, the linearization method used here can be applied to general switched systems.
{"title":"Exponential stability analysis of discrete-time almost periodic piecewise nonlinear systems","authors":"Xiaoyun Wei , Xingwen Liu , Jun Yang , Tingjin Liu","doi":"10.1016/j.nahs.2025.101642","DOIUrl":"10.1016/j.nahs.2025.101642","url":null,"abstract":"<div><div>This paper focuses on exponential stability analysis for discrete-time almost periodic piecewise nonlinear systems (APPNSs) with uncertain dwell time of subsystems. A discrete-time APPNS has a fundamental period, during which a finite number of subsystems that constitute the system are cyclically activated. Such systems can be modeled as switched systems with cyclically switching signals. With the assumption that the vector field of each subsystem of discrete-time APPNSs is continuously differentiable, a Lyapunov theorem is presented first to verify the exponential stability of discrete-time APPNSs. Then, a linearization method is employed and a mixed-mode time-varying homogeneous Lyapunov function is constructed to derive specific stability conditions expressed by linear matrix inequalities (LMIs). Note that this condition can verify the exponential stability of the considered nonlinear systems, as well as that of the corresponding linearized systems. Furthermore, the linearization method used here can be applied to general switched systems.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101642"},"PeriodicalIF":3.7,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145096590","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 : 2025-09-18DOI: 10.1016/j.nahs.2025.101643
Bhim Kumar, Muslim Malik
This paper investigates the finite-time stability and stabilization of impulsive positive switched delay systems defined on arbitrary time scales, using Lyapunov function-based methods. The finite-time stabilization problem is solved using state feedback controllers on time scales. Furthermore, the applicability of the proposed finite-time stability criteria is demonstrated for positive switched multi-agent delay systems by designing an event-triggered controller on time scales. The analysis extends the existing results to incorporate hybrid time domains with time-dependent switching and provide sufficient conditions for the system’s stability and stabilization within the specified time period. To demonstrate the results of this paper, several numerical and simulation-based examples are presented by considering continuous, discrete, and hybrid time domains simultaneously.
{"title":"Finite-time stability and stabilization of positive switched delay systems with non-instantaneous impulses on time scales and applications to multi-agent systems","authors":"Bhim Kumar, Muslim Malik","doi":"10.1016/j.nahs.2025.101643","DOIUrl":"10.1016/j.nahs.2025.101643","url":null,"abstract":"<div><div>This paper investigates the finite-time stability and stabilization of impulsive positive switched delay systems defined on arbitrary time scales, using Lyapunov function-based methods. The finite-time stabilization problem is solved using state feedback controllers on time scales. Furthermore, the applicability of the proposed finite-time stability criteria is demonstrated for positive switched multi-agent delay systems by designing an event-triggered controller on time scales. The analysis extends the existing results to incorporate hybrid time domains with time-dependent switching and provide sufficient conditions for the system’s stability and stabilization within the specified time period. To demonstrate the results of this paper, several numerical and simulation-based examples are presented by considering continuous, discrete, and hybrid time domains simultaneously.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101643"},"PeriodicalIF":3.7,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145096589","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 : 2025-09-12DOI: 10.1016/j.nahs.2025.101632
Mengyao Lu, Jingyuan Zhan, Liguo Zhang
This study addresses the boundary consensus problem of multi-agent systems, in which each agent is governed by hyperbolic partial differential equations. To reduce the controller update frequency, the event-triggered boundary controller is proposed for each agent based on the boundary state information of its neighbors and itself. Firstly, we present the well-posedness and consensus analysis under undirected communication graphs. By using Lyapunov approach and graph theory, we obtain the sufficient conditions associated with triggering parameters, Laplacian eigenvalues and boundary coefficient matrices for guaranteeing the asymptotic consensus and excluding Zeno behaviors. Next, we further consider the consensus problem under the directed communication topologies, and we also establish the sufficient conditions for ensuring the asymptotic consensus. Finally, we present a three-lane freeway traffic flow system described by Aw–Rascle–Zhang Equations as an example to demonstrate the effectiveness of the designed event-triggered boundary consensus controllers.
{"title":"Event-triggered boundary consensus for multi-agent systems of hyperbolic balance laws","authors":"Mengyao Lu, Jingyuan Zhan, Liguo Zhang","doi":"10.1016/j.nahs.2025.101632","DOIUrl":"10.1016/j.nahs.2025.101632","url":null,"abstract":"<div><div>This study addresses the boundary consensus problem of multi-agent systems, in which each agent is governed by hyperbolic partial differential equations. To reduce the controller update frequency, the event-triggered boundary controller is proposed for each agent based on the boundary state information of its neighbors and itself. Firstly, we present the well-posedness and consensus analysis under undirected communication graphs. By using Lyapunov approach and graph theory, we obtain the sufficient conditions associated with triggering parameters, Laplacian eigenvalues and boundary coefficient matrices for guaranteeing the asymptotic consensus and excluding Zeno behaviors. Next, we further consider the consensus problem under the directed communication topologies, and we also establish the sufficient conditions for ensuring the asymptotic consensus. Finally, we present a three-lane freeway traffic flow system described by Aw–Rascle–Zhang Equations as an example to demonstrate the effectiveness of the designed event-triggered boundary consensus controllers.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101632"},"PeriodicalIF":3.7,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046681","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}
Deep neural networks (DNN) verification primarily focuses on qualitative verification, determining whether a DNN violates safety or robustness properties. This paper introduces a novel approach for quantitative verification of Feedforward Neural Networks (FFNN), transforming qualitative assessments into probabilistic evaluations. The resulting quantitative verification method not only can answer YES or NO questions but also can compute the probability of a property being violated. To do that, we introduce the concept of a probabilistic star (or shortly ProbStar), a new variant of the well-known star set, in which the predicate variables belong to a Gaussian distribution. We further propose an approach to compute the probability of a probabilistic star in high-dimensional space. Unlike existing works dealing with constrained input sets, our work considers the input set as a truncated multivariate normal (Gaussian) distribution, i.e., besides the constraints on the input variables, the input set has a probability of the constraints being satisfied. The input distribution is represented as a probabilistic star set and propagates through a network to construct the output reachable set containing multiple ProbStars, which are used to verify the safety or robustness properties of the network. In case a property is violated, the violation probability can be computed precisely by an exact verification algorithm or approximately by an over-approximate verification algorithm. Building on this foundation, we extend our quantitative verification framework to Learning-Enabled Cyber-Physical Systems (Le-CPS), where a piecewise linear FFNN controls a linear physical plant model. Our approach enables the construction of probabilistic reachable sets for Le-CPS, allowing for both qualitative Safe/Unsafe assessments and quantitative probability computations of property violations. We have implemented our verification framework in a tool named StarV and evaluated its effectiveness on benchmarks including HorizontalCAS and ACASXu networks, a rocket landing system, as well as advanced emergency braking and adaptive cruise control systems within the Le-CPS domain.
{"title":"Quantitative verification of learning-enabled systems using ProbStar reachability","authors":"Yuntao Li , Sung Woo Choi , Hideki Okamoto , Bardh Hoxha , Georgios Fainekos , Hoang-Dung Tran","doi":"10.1016/j.nahs.2025.101623","DOIUrl":"10.1016/j.nahs.2025.101623","url":null,"abstract":"<div><div>Deep neural networks (DNN) verification primarily focuses on <em>qualitative verification</em>, determining whether a DNN violates safety or robustness properties. This paper introduces a novel approach for <em>quantitative verification</em> of Feedforward Neural Networks (FFNN), transforming qualitative assessments into probabilistic evaluations. The resulting quantitative verification method not only can answer YES or NO questions but also can compute the probability of a property being violated. To do that, we introduce the concept of a probabilistic star (or shortly ProbStar), a new variant of the well-known star set, in which the predicate variables belong to a Gaussian distribution. We further propose an approach to compute the probability of a probabilistic star in high-dimensional space. Unlike existing works dealing with constrained input sets, our work considers the input set as a truncated multivariate normal (Gaussian) distribution, i.e., besides the constraints on the input variables, the input set has a probability of the constraints being satisfied. The input distribution is represented as a probabilistic star set and propagates through a network to construct the output reachable set containing multiple ProbStars, which are used to verify the safety or robustness properties of the network. In case a property is violated, the violation probability can be computed precisely by an exact verification algorithm or approximately by an over-approximate verification algorithm. Building on this foundation, we extend our quantitative verification framework to Learning-Enabled Cyber-Physical Systems (Le-CPS), where a piecewise linear FFNN controls a linear physical plant model. Our approach enables the construction of probabilistic reachable sets for Le-CPS, allowing for both qualitative Safe/Unsafe assessments and quantitative probability computations of property violations. We have implemented our verification framework in a tool named <em>StarV</em> and evaluated its effectiveness on benchmarks including HorizontalCAS and ACASXu networks, a rocket landing system, as well as advanced emergency braking and adaptive cruise control systems within the Le-CPS domain.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101623"},"PeriodicalIF":3.7,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046682","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 : 2025-09-11DOI: 10.1016/j.nahs.2025.101634
Mingyu Wang , Xiaofeng Zong , Xin Chen
This paper investigates the finite-time stability of a jump diffusion system with Brownian motion and random jump components. First, we establish a novel Lyapunov-type finite-time stability theorem, which provides a direct way for selecting an appropriate Lyapunov function. It is important to note that our finite-time stability result is significantly distinct from the case involving only Brownian motion. The presence of the jump term disrupts the continuity of the system’s solution paths, thereby introducing additional complexities in the analysis of finite-time stability. Subsequently, we employ this theorem to design a finite-time controller to ensure the finite-time stochastic stability of the tracking error in a drill-bit system. The proposed control strategy guarantees that the tracking error converges to the origin within finite time and remains there thereafter with probability one. Finally, simulation results are presented to validate the effectiveness of the proposed control law in achieving precise drill-bit tracking control.
{"title":"Finite-time stability of jump diffusion system and its application in drill-bit tracking control","authors":"Mingyu Wang , Xiaofeng Zong , Xin Chen","doi":"10.1016/j.nahs.2025.101634","DOIUrl":"10.1016/j.nahs.2025.101634","url":null,"abstract":"<div><div>This paper investigates the finite-time stability of a jump diffusion system with Brownian motion and random jump components. First, we establish a novel Lyapunov-type finite-time stability theorem, which provides a direct way for selecting an appropriate Lyapunov function. It is important to note that our finite-time stability result is significantly distinct from the case involving only Brownian motion. The presence of the jump term disrupts the continuity of the system’s solution paths, thereby introducing additional complexities in the analysis of finite-time stability. Subsequently, we employ this theorem to design a finite-time controller to ensure the finite-time stochastic stability of the tracking error in a drill-bit system. The proposed control strategy guarantees that the tracking error converges to the origin within finite time and remains there thereafter with probability one. Finally, simulation results are presented to validate the effectiveness of the proposed control law in achieving precise drill-bit tracking control.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101634"},"PeriodicalIF":3.7,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046680","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 : 2025-09-10DOI: 10.1016/j.nahs.2025.101633
Shaowen Miao , Aiwen Lai , Jan Komenda , Sébastien Lahaye
In this paper, we address the problem of initial-state detectability (I-detectability) for timed discrete-event systems modeled by time-interval automata (TIAs). An I-observer, defined over a timed event set, is developed to check both strong and weak I-detectability. Additionally, an I-detector structure is designed as an alternative method for verifying strong I-detectability, which is more efficient than the I-observer in certain cases. In addition, we are the first to formally define the concepts of strong and weak timed initial-state detectability (-I-detectability) within the framework of timed discrete-event systems. Specifically, I-detectability necessitates that the initial state of a system can be detected after a finite number of observations. From another perspective, -I-detectability entails that the initial state can be ascertained after a delay of time units. Under the assumption that every cycle in the TIA has strictly positive weight, we establish that a TIA is -I-detectable if and only if it satisfies the condition of being I-detectable. Finally, we introduce an algebraic method to compute the upper bound of time that needs to elapse before the initial state can be determined in an I-detectable TIA.
本文研究了由时间间隔自动机（TIAs）建模的时间离散事件系统的初始状态可检测性问题。在一个定时事件集上定义了一个i -观测器，用于检查强和弱i -可探测性。此外，设计了一个i检测器结构作为验证强i可探测性的替代方法，在某些情况下，它比i观察者更有效。此外，我们首次在时间离散事件系统的框架内正式定义了强和弱时间初始状态可探测性（t - i -可探测性）的概念。具体来说，i -可探测性要求系统的初始状态可以在有限次观测后被探测到。从另一个角度来看，T- i可探测性意味着在延迟T个时间单位后可以确定初始状态。在假定TIA中的每个周期都有严格正权的前提下，我们建立了TIA是t - i可检测的当且仅当它满足i可检测的条件。最后，我们引入了一种代数方法来计算在i可检测的TIA中确定初始状态所需时间的上界。
{"title":"Timed initial-state detectability of discrete-event systems by algebraic method","authors":"Shaowen Miao , Aiwen Lai , Jan Komenda , Sébastien Lahaye","doi":"10.1016/j.nahs.2025.101633","DOIUrl":"10.1016/j.nahs.2025.101633","url":null,"abstract":"<div><div>In this paper, we address the problem of initial-state detectability (I-detectability) for timed discrete-event systems modeled by time-interval automata (TIAs). An I-observer, defined over a timed event set, is developed to check both strong and weak I-detectability. Additionally, an I-detector structure is designed as an alternative method for verifying strong I-detectability, which is more efficient than the I-observer in certain cases. In addition, we are the first to formally define the concepts of strong and weak timed initial-state detectability (<span><math><mi>T</mi></math></span>-I-detectability) within the framework of timed discrete-event systems. Specifically, I-detectability necessitates that the initial state of a system can be detected after a finite number of observations. From another perspective, <span><math><mi>T</mi></math></span>-I-detectability entails that the initial state can be ascertained after a delay of <span><math><mi>T</mi></math></span> time units. Under the assumption that every cycle in the TIA has strictly positive weight, we establish that a TIA is <span><math><mi>T</mi></math></span>-I-detectable if and only if it satisfies the condition of being I-detectable. Finally, we introduce an algebraic method to compute the upper bound of time that needs to elapse before the initial state can be determined in an I-detectable TIA.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101633"},"PeriodicalIF":3.7,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145027221","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 : 2025-09-09DOI: 10.1016/j.nahs.2025.101630
Vishnu Murali, Ashutosh Trivedi, Majid Zamani
A barrier certificate, defined over the states of a dynamical system, is a real-valued function whose zero level set characterizes an inductively verifiable state invariant separating reachable states from unsafe ones. When combined with powerful decision procedures — such as sum-of-squares programming (SOS) or satisfiability-modulo-theory solvers (SMT) — barrier certificates enable an automated deductive verification approach to safety. The barrier certificate approach has been extended to refute LTL and -regular specifications by separating consecutive transitions of corresponding -automata in the hope of denying all accepting runs. Unsurprisingly, such tactics are bound to be conservative as refutation of recurrence properties requires reasoning about ranking functions to prove liveness as well. This paper introduces the notion of closure certificates as a natural extension of barrier certificates from state invariants to transition invariants. We show how one may use ranking function arguments over such certificates to verify discrete-time dynamical systems against Linear Temporal logic formulae. We augment these definitions with SOS and SMT based characterization for automating the search of closure certificates and demonstrate their effectiveness over some case studies.
{"title":"Closure certificates","authors":"Vishnu Murali, Ashutosh Trivedi, Majid Zamani","doi":"10.1016/j.nahs.2025.101630","DOIUrl":"10.1016/j.nahs.2025.101630","url":null,"abstract":"<div><div>A <em>barrier certificate</em>, defined over the states of a dynamical system, is a real-valued function whose zero level set characterizes an inductively verifiable <em>state invariant</em> separating reachable states from unsafe ones. When combined with powerful decision procedures — such as sum-of-squares programming (SOS) or satisfiability-modulo-theory solvers (SMT) — barrier certificates enable an automated deductive verification approach to safety. The barrier certificate approach has been extended to refute LTL and <span><math><mi>ω</mi></math></span>-regular specifications by separating consecutive transitions of corresponding <span><math><mi>ω</mi></math></span>-automata in the hope of denying all accepting runs. Unsurprisingly, such tactics are bound to be conservative as refutation of <em>recurrence properties</em> requires reasoning about ranking functions to prove liveness as well. This paper introduces the notion of <em>closure certificates</em> as a natural extension of barrier certificates from state invariants to transition invariants. We show how one may use ranking function arguments over such certificates to verify discrete-time dynamical systems against Linear Temporal logic formulae. We augment these definitions with SOS and SMT based characterization for automating the search of closure certificates and demonstrate their effectiveness over some case studies.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101630"},"PeriodicalIF":3.7,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020290","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}
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