Pub Date : 2025-04-26DOI: 10.1016/j.nahs.2025.101600
Qian Fan , Zhiyan Shi , Bao Wang , Lei Jiang
This paper is concerned with the stability of nonlinear delayed systems with stochastic impulses, which are assumed to be triggered by renewal process, Poisson process, semi-Markov process and Markov process, respectively. Some sufficient conditions are achieved by using the method of Lyapunov function and the upgraded comparison principle. It is shown that the stability of the system containing both stable and unstable impulses can be achieved by using the structure of stochastic process. To show that the criteria are effective, a numerical example is provided.
{"title":"Input-to-state stability of nonlinear delayed systems with stochastic impulses","authors":"Qian Fan , Zhiyan Shi , Bao Wang , Lei Jiang","doi":"10.1016/j.nahs.2025.101600","DOIUrl":"10.1016/j.nahs.2025.101600","url":null,"abstract":"<div><div>This paper is concerned with the stability of nonlinear delayed systems with stochastic impulses, which are assumed to be triggered by renewal process, Poisson process, semi-Markov process and Markov process, respectively. Some sufficient conditions are achieved by using the method of Lyapunov function and the upgraded comparison principle. It is shown that the stability of the system containing both stable and unstable impulses can be achieved by using the structure of stochastic process. To show that the criteria are effective, a numerical example is provided.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"57 ","pages":"Article 101600"},"PeriodicalIF":3.7,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873859","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 : 2025-04-16DOI: 10.1016/j.nahs.2025.101598
Arnab Mapui, Santwana Mukhopadhyay
The main emphasis of this paper is to address the issue of event- and self-triggered impulsive control for the prescribed-time stability of impulsive systems. In the first part of the article, some Lyapunov-like sufficient conditions are derived to stabilize an impulsive system within the prescribed-time, where impulsive instants are obtained through an event-triggered mechanism. Unlike event-triggered control, event-triggered impulsive control executes solely when the event is generated. The second part of the article provides sufficient Lyapunov-like criteria for the prescribed-time stability of impulsive systems via a self-triggered mechanism. Contrary to the event-triggered impulsive control, where triggering instants are obtained through continuous or periodic monitoring of the event-triggering conditions, the proposed self-triggered impulsive control strategy can estimate the next triggering instant by the information available in the currently triggered instant. Moreover, it is demonstrated that the Zeno behavior can be excluded from both of the proposed mechanisms. Finally, two instances are provided to illustrate the theoretical results numerically and verify the veracity of the proposed methodologies.
{"title":"Lyapunov-like prescribed-time stability of impulsive systems via event & self-triggered impulsive control","authors":"Arnab Mapui, Santwana Mukhopadhyay","doi":"10.1016/j.nahs.2025.101598","DOIUrl":"10.1016/j.nahs.2025.101598","url":null,"abstract":"<div><div>The main emphasis of this paper is to address the issue of event- and self-triggered impulsive control for the prescribed-time stability of impulsive systems. In the first part of the article, some Lyapunov-like sufficient conditions are derived to stabilize an impulsive system within the prescribed-time, where impulsive instants are obtained through an event-triggered mechanism. Unlike event-triggered control, event-triggered impulsive control executes solely when the event is generated. The second part of the article provides sufficient Lyapunov-like criteria for the prescribed-time stability of impulsive systems via a self-triggered mechanism. Contrary to the event-triggered impulsive control, where triggering instants are obtained through continuous or periodic monitoring of the event-triggering conditions, the proposed self-triggered impulsive control strategy can estimate the next triggering instant by the information available in the currently triggered instant. Moreover, it is demonstrated that the Zeno behavior can be excluded from both of the proposed mechanisms. Finally, two instances are provided to illustrate the theoretical results numerically and verify the veracity of the proposed methodologies.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"57 ","pages":"Article 101598"},"PeriodicalIF":3.7,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143838386","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 : 2025-04-12DOI: 10.1016/j.nahs.2025.101599
Wu-Hua Chen, Hengliang Xiang
This paper studies an anti-disturbance impulsive control problem for a class of nonlinear systems with sampled measurements and input disturbances. It considers that the unknown input disturbances are generated by an exogenous system with additional disturbances. The goal is to construct an impulsive disturbance observer (IDO) to estimate the external disturbance and to use the disturbance estimate as a feed-forward compensator of the impulsive control so that the input disturbance can be rejected. Two types of design schemes are proposed in the linear matrix inequality framework. For the plants with sampled output measurements, a full-order IDO is constructed, under which both the state and the external disturbance can be estimated simultaneously. For the plants with state information available at impulse instants, a reduced-order IDO is designed, where only the estimation of the external disturbance is involved. Accordingly, the performance levels relative to the capability against the additional disturbance are respectively analyzed. Finally, an illustrative example is presented to demonstrate the validity of the results.
{"title":"Composite anti-disturbance impulsive control for a class of nonlinear systems via disturbance observers","authors":"Wu-Hua Chen, Hengliang Xiang","doi":"10.1016/j.nahs.2025.101599","DOIUrl":"10.1016/j.nahs.2025.101599","url":null,"abstract":"<div><div>This paper studies an anti-disturbance impulsive control problem for a class of nonlinear systems with sampled measurements and input disturbances. It considers that the unknown input disturbances are generated by an exogenous system with additional disturbances. The goal is to construct an impulsive disturbance observer (IDO) to estimate the external disturbance and to use the disturbance estimate as a feed-forward compensator of the impulsive control so that the input disturbance can be rejected. Two types of design schemes are proposed in the linear matrix inequality framework. For the plants with sampled output measurements, a full-order IDO is constructed, under which both the state and the external disturbance can be estimated simultaneously. For the plants with state information available at impulse instants, a reduced-order IDO is designed, where only the estimation of the external disturbance is involved. Accordingly, the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> performance levels relative to the capability against the additional disturbance are respectively analyzed. Finally, an illustrative example is presented to demonstrate the validity of the results.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"57 ","pages":"Article 101599"},"PeriodicalIF":3.7,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143823210","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 : 2025-03-28DOI: 10.1016/j.nahs.2025.101596
Cuiping Lu , Xiaodi Li
This paper concentrates on stabilization problem of nonlinear delay systems involved unknown parameters via adaptive impulsive observer-based saturated control (AIOSC). Different from the existing literature that only the system state reconstruction and parameter estimation problems are comprehensively and thoroughly studied, we simultaneously solve the stabilization problem of such system itself. In virtue of an improved set inclusion relationship related to the augmented vector, the saturated effects on both impulsive correction and continuous control are explored in the sense of unmeasurable states. The main challenge of this paper is that with the help of the modified convex combination method, the time-varying Lyapunov function-based method, and comparison principle, how to fully utilize the systematic information to construct an elastic constraint relationship among system structure, delay information, and impulsive time sequence, which makes system parameters adjust appropriately as needed. Moreover, the maximum estimation of attractive domain is obtained by a convex optimal problem. And two examples are presented to demonstrate the validity of results, where stabilization of Lorenz system involved unknown parameters is considered.
{"title":"Stabilization of nonlinear delay systems: Adaptive impulsive observer-based saturated control approach","authors":"Cuiping Lu , Xiaodi Li","doi":"10.1016/j.nahs.2025.101596","DOIUrl":"10.1016/j.nahs.2025.101596","url":null,"abstract":"<div><div>This paper concentrates on stabilization problem of nonlinear delay systems involved unknown parameters via adaptive impulsive observer-based saturated control (<em>AIOSC</em>). Different from the existing literature that only the system state reconstruction and parameter estimation problems are comprehensively and thoroughly studied, we simultaneously solve the stabilization problem of such system itself. In virtue of an improved set inclusion relationship related to the augmented vector, the saturated effects on both impulsive correction and continuous control are explored in the sense of unmeasurable states. The main challenge of this paper is that with the help of the modified convex combination method, the time-varying Lyapunov function-based method, and comparison principle, how to fully utilize the systematic information to construct an elastic constraint relationship among system structure, delay information, and impulsive time sequence, which makes system parameters adjust appropriately as needed. Moreover, the maximum estimation of attractive domain is obtained by a convex optimal problem. And two examples are presented to demonstrate the validity of results, where stabilization of Lorenz system involved unknown parameters is considered.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"57 ","pages":"Article 101596"},"PeriodicalIF":3.7,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143724107","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 : 2025-03-25DOI: 10.1016/j.nahs.2025.101595
Hankang Ji , Yuanyuan Li , Xueying Ding , Jianquan Lu
This paper studies the asymptotic synchronization of drive-response stochastic Boolean networks. We propose two coupled Boolean networks with stochastic sequences and then derive their algebraic forms using semi-tensor product property. Subsequently, a novel eigenvalue-based approach is introduced to establish necessary and sufficient conditions for the asymptotic synchronization of these networks. While prior synchronization results were typically derived from the powers of the transition probability matrix, our method requires only the eigenvalues of this matrix. Finally, several examples are provided to validate the results obtained.
{"title":"Necessary and sufficient conditions for asymptotic synchronization of drive-response coupled stochastic Boolean networks","authors":"Hankang Ji , Yuanyuan Li , Xueying Ding , Jianquan Lu","doi":"10.1016/j.nahs.2025.101595","DOIUrl":"10.1016/j.nahs.2025.101595","url":null,"abstract":"<div><div>This paper studies the asymptotic synchronization of drive-response stochastic Boolean networks. We propose two coupled Boolean networks with stochastic sequences and then derive their algebraic forms using semi-tensor product property. Subsequently, a novel eigenvalue-based approach is introduced to establish necessary and sufficient conditions for the asymptotic synchronization of these networks. While prior synchronization results were typically derived from the powers of the transition probability matrix, our method requires only the eigenvalues of this matrix. Finally, several examples are provided to validate the results obtained.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"57 ","pages":"Article 101595"},"PeriodicalIF":3.7,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143696741","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 : 2025-03-20DOI: 10.1016/j.nahs.2025.101597
Gabriela Lígia Reis , Pedro Henrique Silva Coutinho , Iury Bessa , Rodrigo Farias Araújo
This paper deals with the event-triggered gain-scheduling control of nonlinear systems based on the differential algebraic representation (DAR) approach. Since the parameters of the gain-scheduled controller depend on the sampled state information, a mismatch is induced between the controller and the DAR of the plant. To deal with this issue, we propose a novel dynamic event-triggered control strategy with a compensation term for the mismatch. Then, we propose a co-design condition, in the form of linear matrix inequalities (LMIs), to design the gain-scheduling controller and the event-triggering mechanism. We show that Zeno behavior is avoided with the proposed event-triggering mechanism. Moreover, as the LMI conditions are derived by constraining the region of validity of the DAR, we estimate the region of attraction of the closed-loop equilibrium lying inside this region of validity. Finally, a multi-objective optimization problem is provided to enlarge the estimate of the region of attraction and minimize the number of transmissions. Numerical simulations illustrate the advantages of the proposed condition in reducing conservativeness when compared to related work, as well as reducing the number of events.
{"title":"Dynamic event-triggered control for nonlinear systems via differential algebraic representation","authors":"Gabriela Lígia Reis , Pedro Henrique Silva Coutinho , Iury Bessa , Rodrigo Farias Araújo","doi":"10.1016/j.nahs.2025.101597","DOIUrl":"10.1016/j.nahs.2025.101597","url":null,"abstract":"<div><div>This paper deals with the event-triggered gain-scheduling control of nonlinear systems based on the differential algebraic representation (DAR) approach. Since the parameters of the gain-scheduled controller depend on the sampled state information, a mismatch is induced between the controller and the DAR of the plant. To deal with this issue, we propose a novel dynamic event-triggered control strategy with a compensation term for the mismatch. Then, we propose a co-design condition, in the form of linear matrix inequalities (LMIs), to design the gain-scheduling controller and the event-triggering mechanism. We show that Zeno behavior is avoided with the proposed event-triggering mechanism. Moreover, as the LMI conditions are derived by constraining the region of validity of the DAR, we estimate the region of attraction of the closed-loop equilibrium lying inside this region of validity. Finally, a multi-objective optimization problem is provided to enlarge the estimate of the region of attraction and minimize the number of transmissions. Numerical simulations illustrate the advantages of the proposed condition in reducing conservativeness when compared to related work, as well as reducing the number of events.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"57 ","pages":"Article 101597"},"PeriodicalIF":3.7,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143684570","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 is about state estimation in a timed probabilistic setting. A reference model, namely a labeled timed probabilistic automaton, is used for this purpose and an a posteriori probability vector is defined based on a sequence of observations and their associated time stamps that have been collected thus far. The observable language of the considered system is assumed to be live. The main contribution of the paper is to introduce and characterize some basic detectability notions for timed stochastic systems: (i) event detectability, which implies that the system becomes detectable at the time instant of each new observation but may lose the detectability property between two observations, and (ii) silent detectability, which implies that the system becomes detectable when no observation is collected within an arbitrary large duration. Relaxed notions of detectability are also studied: first, assuming that, given a threshold, the a priori probability that an observed timed sequence leads to an exact reconstruction of the state, is larger than or equal to that threshold; second, by replacing the estimation of single states by the estimation of classes formed by several states.
{"title":"Detectability notions for a class of finite labeled Markovian systems","authors":"Dimitri Lefebvre , Carla Seatzu , Christoforos N. Hadjicostis , Alessandro Giua","doi":"10.1016/j.nahs.2025.101586","DOIUrl":"10.1016/j.nahs.2025.101586","url":null,"abstract":"<div><div>This paper is about state estimation in a timed probabilistic setting. A reference model, namely a labeled timed probabilistic automaton, is used for this purpose and an a posteriori probability vector is defined based on a sequence of observations and their associated time stamps that have been collected thus far. The observable language of the considered system is assumed to be live. The main contribution of the paper is to introduce and characterize some basic detectability notions for timed stochastic systems: (i) <em>event detectability</em>, which implies that the system becomes detectable at the time instant of each new observation but may lose the detectability property between two observations, and (ii) <em>silent detectability</em>, which implies that the system becomes detectable when no observation is collected within an arbitrary large duration. Relaxed notions of detectability are also studied: first, assuming that, given a threshold, the a priori probability that an observed timed sequence leads to an exact reconstruction of the state, is larger than or equal to that threshold; second, by replacing the estimation of single states by the estimation of classes formed by several states.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"57 ","pages":"Article 101586"},"PeriodicalIF":3.7,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143563098","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}
This paper is a pilot study on the fixed-time stability of switched chaotic systems via the intermittent control. Some novel fixed-time stability theorems that generalize some previous related research works and have a broad application prospect, are proposed. According to the proposed fixed-time stability theorems, a new intermittent switching controller for reducing information transmission and saving control energy is provided to achieve the fixed-time stability of the considered switched chaotic systems. In addition, numerical simulations are conducted to verify the correctness of resulting conclusion.
{"title":"Fixed-time intermittent control for a class of switched chaotic systems","authors":"Luxia Han, Runzi Luo, Panpan Zhang, Xianzhou Liu, Shuai Liu, Zijun Song","doi":"10.1016/j.nahs.2025.101587","DOIUrl":"10.1016/j.nahs.2025.101587","url":null,"abstract":"<div><div>This paper is a pilot study on the fixed-time stability of switched chaotic systems via the intermittent control. Some novel fixed-time stability theorems that generalize some previous related research works and have a broad application prospect, are proposed. According to the proposed fixed-time stability theorems, a new intermittent switching controller for reducing information transmission and saving control energy is provided to achieve the fixed-time stability of the considered switched chaotic systems. In addition, numerical simulations are conducted to verify the correctness of resulting conclusion.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"56 ","pages":"Article 101587"},"PeriodicalIF":3.7,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509190","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 : 2025-02-22DOI: 10.1016/j.nahs.2025.101585
Mengmeng Zhang, Quanxin Zhu
It is universally acknowledged that noise can stabilize systems. Given an unstable impulsive system, can it be stabilized by Lévy noise? In this article, we mainly discuss the stochastic stabilization of unstable impulsive systems via Lévy noise. First, the conditions for -moment exponential stability of unstable impulsive systems under continuous-time feedback control with Lévy noise are derived using the Lyapunov function method. Second, the almost sure exponentially stable conditions for the unstable impulsive systems under discrete-time feedback control with Lévy noise are derived through the comparison method. Additionally, several new stochastic stabilization strategies are proposed to design stochastic discrete-time feedback control for deriving almost sure exponentially stable results through stochastic analysis. Finally, two examples and their relevant simulation figures are given to check the validity of the results.
{"title":"Stabilization of unstable impulsive systems via stochastic discrete-time feedback control with Lévy noise","authors":"Mengmeng Zhang, Quanxin Zhu","doi":"10.1016/j.nahs.2025.101585","DOIUrl":"10.1016/j.nahs.2025.101585","url":null,"abstract":"<div><div>It is universally acknowledged that noise can stabilize systems. Given an unstable impulsive system, can it be stabilized by Lévy noise? In this article, we mainly discuss the stochastic stabilization of unstable impulsive systems via Lévy noise. First, the conditions for <span><math><mi>p</mi></math></span>-moment exponential stability of unstable impulsive systems under continuous-time feedback control with Lévy noise are derived using the Lyapunov function method. Second, the almost sure exponentially stable conditions for the unstable impulsive systems under discrete-time feedback control with Lévy noise are derived through the comparison method. Additionally, several new stochastic stabilization strategies are proposed to design stochastic discrete-time feedback control for deriving almost sure exponentially stable results through stochastic analysis. Finally, two examples and their relevant simulation figures are given to check the validity of the results.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"56 ","pages":"Article 101585"},"PeriodicalIF":3.7,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143463429","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}
The paper proposes a new sparse star set representation and extends the recent star reachability method to verify the robustness of vanilla, long short-term memory (LSTM), and gated recurrent units (GRU) recurrent neural networks (RNNs) for safety-critical applications. RNNs are a popular machine learning method for various applications, but they are vulnerable to adversarial attacks, where slightly perturbing the input sequence can lead to an unexpected result. Recent notable techniques for verifying RNNs include unrolling and invariant inference approaches. The first method has scaling issues since unrolling an RNN creates a large feedforward neural network. The second method, using invariant sets, has better scalability but can produce unknown results due to the accumulation of over-approximation errors over time. This paper introduces a complementary verification method for RNNs that is both sound and complete. A relaxation parameter can be used to convert the method into a fast over-approximation method that still provides soundness guarantees. The vanilla RNN verification method is designed to be used with NNV, a tool for verifying deep neural networks and learning-enabled cyber–physical systems, while the verification approach of LSTM and GRU RNNs are implemented on StarV. Compared to state-of-the-art methods for verifying a vanilla RNN, the extended exact reachability method is faster, and the over-approximation method is to faster. Although the sparse star set is slow compared to state-of-the-art methods, it was able to verify more robust cases in general than them.
{"title":"Reachability analysis of recurrent neural networks","authors":"Sung Woo Choi , Yuntao Li , Xiaodong Yang , Tomoya Yamaguchi , Bardh Hoxha , Georgios Fainekos , Danil Prokhorov , Hoang-Dung Tran","doi":"10.1016/j.nahs.2025.101581","DOIUrl":"10.1016/j.nahs.2025.101581","url":null,"abstract":"<div><div>The paper proposes a new sparse star set representation and extends the recent star reachability method to verify the robustness of vanilla, long short-term memory (LSTM), and gated recurrent units (GRU) recurrent neural networks (RNNs) for safety-critical applications. RNNs are a popular machine learning method for various applications, but they are vulnerable to adversarial attacks, where slightly perturbing the input sequence can lead to an unexpected result. Recent notable techniques for verifying RNNs include unrolling and invariant inference approaches. The first method has scaling issues since unrolling an RNN creates a large feedforward neural network. The second method, using invariant sets, has better scalability but can produce unknown results due to the accumulation of over-approximation errors over time. This paper introduces a complementary verification method for RNNs that is both sound and complete. A relaxation parameter can be used to convert the method into a fast over-approximation method that still provides soundness guarantees. The vanilla RNN verification method is designed to be used with NNV, a tool for verifying deep neural networks and learning-enabled cyber–physical systems, while the verification approach of LSTM and GRU RNNs are implemented on <em>StarV</em>. Compared to state-of-the-art methods for verifying a vanilla RNN, the extended exact reachability method is <span><math><mrow><mn>10</mn><mo>×</mo></mrow></math></span> faster, and the over-approximation method is <span><math><mrow><mn>100</mn><mo>×</mo></mrow></math></span> to <span><math><mrow><mn>5000</mn><mo>×</mo></mrow></math></span> faster. Although the sparse star set is slow compared to state-of-the-art methods, it was able to verify more robust cases in general than them.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"56 ","pages":"Article 101581"},"PeriodicalIF":3.7,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143453561","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号