Pub Date : 2025-04-23DOI: 10.1016/j.jfranklin.2025.107632
Yuan Li , Xuebo Yang , Xiaolong Zheng , Zhongbo Chen , Jiatong Wang
The spacecraft rendezvous problem under external disturbances represents a significant and challenging research area. To enhance the accuracy of spacecraft rendezvous, this paper develops a model predictive control algorithm augmented by a function-adaptive law (FAL). The FAL is introduced to estimate and compensate for unknown disturbances in the aerospace environment effectively. A notable feature of this FAL is its integration with a robust command filtering (RCF) algorithm, which includes three key subtask modules: derivative excitation, noise suppression, and feedback correction. This meticulously designed structure enables the suppression of high-frequency components in the signal while accurately extracting its differential information. The paper provides a theoretical analysis of the recursive feasibility and stability of the designed model predictive controller and validates the controller’s effectiveness through a series of simulation experiments.
{"title":"Robust command filter-based model predictive control for spacecraft rendezvous","authors":"Yuan Li , Xuebo Yang , Xiaolong Zheng , Zhongbo Chen , Jiatong Wang","doi":"10.1016/j.jfranklin.2025.107632","DOIUrl":"10.1016/j.jfranklin.2025.107632","url":null,"abstract":"<div><div>The spacecraft rendezvous problem under external disturbances represents a significant and challenging research area. To enhance the accuracy of spacecraft rendezvous, this paper develops a model predictive control algorithm augmented by a function-adaptive law (FAL). The FAL is introduced to estimate and compensate for unknown disturbances in the aerospace environment effectively. A notable feature of this FAL is its integration with a robust command filtering (RCF) algorithm, which includes three key subtask modules: derivative excitation, noise suppression, and feedback correction. This meticulously designed structure enables the suppression of high-frequency components in the signal while accurately extracting its differential information. The paper provides a theoretical analysis of the recursive feasibility and stability of the designed model predictive controller and validates the controller’s effectiveness through a series of simulation experiments.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 8","pages":"Article 107632"},"PeriodicalIF":3.7,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-04-19DOI: 10.1016/j.jfranklin.2025.107685
Xinfeng Xu , Chun Liu , Liang Xu , Qiang Wang , Yizhen Meng
This paper investigates the optimal pursuit-evasion control (PEC) under zero-sum game for multiple quadrotor unmanned aerial vehicles (multi-QUAVs) with unknown dynamics, aiming to capture an evader QUAV (EQUAV). First, the pursuit-evasion error dynamics are constructed based on multi-pursuer QUAVs (multi-PQUAVs) and an EQUAV. Second, within the framework of a zero-sum game, adversarial strategies are designed for both the multi-PQUAVs and the EQUAV. By minimizing the cost function, the multi-PQUAVs aim to minimize the pursuit-evasion error, while the EQUAV seeks to maximize pursuit-evasion error. Third, an actor-critic neural network (NN) based on integral reinforcement learning (IRL) is developed to optimize the adversarial strategies of both the multi-PQUAVs and the EQUAV while updating their strategies toward the optimal approximate solution. The stability analysis demonstrates that the pursuit-evasion error, critic NN weight error, PQUAVs’ actor NN weight error, and EQUAV’s actor NN weight error are uniformly ultimately bounded. Finally, simulations validate the effectiveness and adaptability of the IRL-based optimal PEC algorithm under zero-sum game.
{"title":"Integral reinforcement learning-based optimal pursuit-evasion control for multi-QUAVs: A zero-sum game approach","authors":"Xinfeng Xu , Chun Liu , Liang Xu , Qiang Wang , Yizhen Meng","doi":"10.1016/j.jfranklin.2025.107685","DOIUrl":"10.1016/j.jfranklin.2025.107685","url":null,"abstract":"<div><div>This paper investigates the optimal pursuit-evasion control (PEC) under zero-sum game for multiple quadrotor unmanned aerial vehicles (multi-QUAVs) with unknown dynamics, aiming to capture an evader QUAV (EQUAV). First, the pursuit-evasion error dynamics are constructed based on multi-pursuer QUAVs (multi-PQUAVs) and an EQUAV. Second, within the framework of a zero-sum game, adversarial strategies are designed for both the multi-PQUAVs and the EQUAV. By minimizing the cost function, the multi-PQUAVs aim to minimize the pursuit-evasion error, while the EQUAV seeks to maximize pursuit-evasion error. Third, an actor-critic neural network (NN) based on integral reinforcement learning (IRL) is developed to optimize the adversarial strategies of both the multi-PQUAVs and the EQUAV while updating their strategies toward the optimal approximate solution. The stability analysis demonstrates that the pursuit-evasion error, critic NN weight error, PQUAVs’ actor NN weight error, and EQUAV’s actor NN weight error are uniformly ultimately bounded. Finally, simulations validate the effectiveness and adaptability of the IRL-based optimal PEC algorithm under zero-sum game.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 8","pages":"Article 107685"},"PeriodicalIF":3.7,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143858787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-04-17DOI: 10.1016/j.jfranklin.2025.107690
Xiaolu Liu , Meiqi Gao , Liu Liu , Naifeng Gan
This paper studies the negative imaginary property for improper descriptor systems. Firstly, it is demonstrated that a descriptor system with a negative imaginary transfer function cannot be impulse-free, that is, the negative imaginary transfer function is improper. Then some necessary conditions and sufficient conditions are established to characterize the negative imaginary property of improper descriptor systems based on the quasi-Weierstrass form. Furthermore, the lossless negative imaginary property of improper descriptor systems is derived by the relationship between the lossless positive realness and the lossless negative imaginariness. Several examples are given to illustrate the obtained results. In addition, this paper presents a generalized Kalman–Yakubovich–Popov lemma for the negative imaginary property of descriptor systems, which is achieved independently of the relationship between positive realness and negative imaginariness.
{"title":"Negative imaginary lemmas for improper descriptor systems","authors":"Xiaolu Liu , Meiqi Gao , Liu Liu , Naifeng Gan","doi":"10.1016/j.jfranklin.2025.107690","DOIUrl":"10.1016/j.jfranklin.2025.107690","url":null,"abstract":"<div><div>This paper studies the negative imaginary property for improper descriptor systems. Firstly, it is demonstrated that a descriptor system with a negative imaginary transfer function cannot be impulse-free, that is, the negative imaginary transfer function is improper. Then some necessary conditions and sufficient conditions are established to characterize the negative imaginary property of improper descriptor systems based on the quasi-Weierstrass form. Furthermore, the lossless negative imaginary property of improper descriptor systems is derived by the relationship between the lossless positive realness and the lossless negative imaginariness. Several examples are given to illustrate the obtained results. In addition, this paper presents a generalized Kalman–Yakubovich–Popov lemma for the negative imaginary property of descriptor systems, which is achieved independently of the relationship between positive realness and negative imaginariness.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 8","pages":"Article 107690"},"PeriodicalIF":3.7,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143855775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-04-17DOI: 10.1016/j.jfranklin.2025.107683
Meng Zhou , Yan Wu , Jing Wang , Tarek Raïssi
This paper proposes a fault detection approach for the basic process of microbial growth in wastewater treatment, based on interval estimation technology. First, a nonlinear microbial growth model is converted into a Takagi–Sugeno (T–S) fuzzy system. Then, utilizing a T–S fuzzy structure, an observer is constructed based on an performance index. Furthermore, an ellipsoid bundle based set membership estimation algorithm is analyzed to synchronize interval estimation operations. In addition, interval residuals are computed from the generated interval state estimation and fault detection is performed for a wastewater treatment bioprocess with actuator faults or sensor faults. Finally, the feasibility of the proposed fault detection strategy for the wastewater treatment bioprocess is illustrated through numerical simulations.
{"title":"Fault detection for wastewater treatment bioprocesses based on ellipsoid bundles","authors":"Meng Zhou , Yan Wu , Jing Wang , Tarek Raïssi","doi":"10.1016/j.jfranklin.2025.107683","DOIUrl":"10.1016/j.jfranklin.2025.107683","url":null,"abstract":"<div><div>This paper proposes a fault detection approach for the basic process of microbial growth in wastewater treatment, based on interval estimation technology. First, a nonlinear microbial growth model is converted into a Takagi–Sugeno (T–S) fuzzy system. Then, utilizing a T–S fuzzy structure, an observer is constructed based on an <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> performance index. Furthermore, an ellipsoid bundle based set membership estimation algorithm is analyzed to synchronize interval estimation operations. In addition, interval residuals are computed from the generated interval state estimation and fault detection is performed for a wastewater treatment bioprocess with actuator faults or sensor faults. Finally, the feasibility of the proposed fault detection strategy for the wastewater treatment bioprocess is illustrated through numerical simulations.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 8","pages":"Article 107683"},"PeriodicalIF":3.7,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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.jfranklin.2025.107687
Chen Yang, Wei Tang, Yin Sheng, Zhigang Zeng
In this paper, the tracking consensus of timescale-type nonlinear multiagent systems is investigated. First, the finite-time reachability of the designed integral sliding manifold is achieved through a discontinuous controller. Second, combining the proposed dynamic event-triggered strategy, sufficient condition for practical tracking consensus is obtained by constructing non-negative functions and applying inequality techniques. In addition, in combination with time scale calculus theory, Zeno behavior is excluded. The framework for sliding mode control (SMC) of timescale-type multiagent systems is constructed to generalize previous continuous-time SMC and discrete-time SMC results. Ultimately, the feasibility of the obtained theoretical results is validated through two numerical simulations.
{"title":"Consensus of nonlinear multiagent systems on time scales via event-triggered sliding mode control","authors":"Chen Yang, Wei Tang, Yin Sheng, Zhigang Zeng","doi":"10.1016/j.jfranklin.2025.107687","DOIUrl":"10.1016/j.jfranklin.2025.107687","url":null,"abstract":"<div><div>In this paper, the tracking consensus of timescale-type nonlinear multiagent systems is investigated. First, the finite-time reachability of the designed integral sliding manifold is achieved through a discontinuous controller. Second, combining the proposed dynamic event-triggered strategy, sufficient condition for practical tracking consensus is obtained by constructing non-negative functions and applying inequality techniques. In addition, in combination with time scale calculus theory, Zeno behavior is excluded. The framework for sliding mode control (SMC) of timescale-type multiagent systems is constructed to generalize previous continuous-time SMC and discrete-time SMC results. Ultimately, the feasibility of the obtained theoretical results is validated through two numerical simulations.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 8","pages":"Article 107687"},"PeriodicalIF":3.7,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143848588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-04-15DOI: 10.1016/j.jfranklin.2025.107680
Zhaoping Du, Jiarong Li, Hui Ye, Jianzhen Li
In this paper, the problem of integral sliding mode control (ISMC) for a class of nonlinear networked cascade control systems (NCCSs) with multiple delays is studied. Due to the limited communication bandwidth between the networked nodes, there are multiple delays in transmission, which lead to the NCCS performance degraded or even unstable. Firstly, the model of NCCS with nonlinear disturbance and multiple delays is constructed where ISMC is introduced into this system for the first time. This paper presents sufficient condition for ensuring system stability by utilizing Lyapunov functions and linear matrix inequality (LMI) techniques. Subsequently, a collaborative design approach is employed to determine the key parameters of the state feedback primary controller and the integral sliding mode secondary controller. In order to validate the effectiveness of the proposed method, simulation experiments are conducted on a thermal power plant model. The simulation results demonstrate that the system can enter the sliding mode surface and maintain stable operation within a finite time, effectively applying the ISMC in continuous NCCS with multiple delays.
{"title":"Integral sliding mode control for nonlinear networked cascade control systems with multiple delays","authors":"Zhaoping Du, Jiarong Li, Hui Ye, Jianzhen Li","doi":"10.1016/j.jfranklin.2025.107680","DOIUrl":"10.1016/j.jfranklin.2025.107680","url":null,"abstract":"<div><div>In this paper, the problem of integral sliding mode control (ISMC) for a class of nonlinear networked cascade control systems (NCCSs) with multiple delays is studied. Due to the limited communication bandwidth between the networked nodes, there are multiple delays in transmission, which lead to the NCCS performance degraded or even unstable. Firstly, the model of NCCS with nonlinear disturbance and multiple delays is constructed where ISMC is introduced into this system for the first time. This paper presents sufficient condition for ensuring system stability by utilizing Lyapunov functions and linear matrix inequality (LMI) techniques. Subsequently, a collaborative design approach is employed to determine the key parameters of the state feedback primary controller and the integral sliding mode secondary controller. In order to validate the effectiveness of the proposed method, simulation experiments are conducted on a thermal power plant model. The simulation results demonstrate that the system can enter the sliding mode surface and maintain stable operation within a finite time, effectively applying the ISMC in continuous NCCS with multiple delays.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 8","pages":"Article 107680"},"PeriodicalIF":3.7,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143838947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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.jfranklin.2025.107689
Zeyuan Wang, Mohammed Chadli
This paper proposes a novel distributed fault estimation framework for a class of nonlinear multi-agent systems (MASs), addressing time-varying multiplicative and additive faults in both actuators and sensors. To address these challenges, the Takagi–Sugeno (T-S) system model is employed, incorporating unmeasurable decision variables, which introduces more complexity compared to known decision variables. This study pioneers the one-sided Lipschitz approach in this context, offering significant advancements over the traditional Lipschitz method. A two-step design process is presented to estimate system states, faults, and external disturbances through an th-order proportional-integral observer and a constrained least squares estimator, which is data-driven. Agents can update their observers by using relative residual outputs derived from neighboring information, enhancing both fault and state estimation accuracy. Furthermore, a dynamic event-triggered communication protocol enables efficient output sharing and reduces communication costs. The observer design conditions are formulated as an optimization problem constrained by linear matrix inequalities, ensuring robust H-infinity performance. Simulation results validate the effectiveness of the proposed method for robust fault estimation in nonlinear MASs.
{"title":"Distributed event-triggered fault estimation for Takagi–Sugeno multi-agent systems with unmeasurable decision variables","authors":"Zeyuan Wang, Mohammed Chadli","doi":"10.1016/j.jfranklin.2025.107689","DOIUrl":"10.1016/j.jfranklin.2025.107689","url":null,"abstract":"<div><div>This paper proposes a novel distributed fault estimation framework for a class of nonlinear multi-agent systems (MASs), addressing time-varying multiplicative and additive faults in both actuators and sensors. To address these challenges, the Takagi–Sugeno (T-S) system model is employed, incorporating unmeasurable decision variables, which introduces more complexity compared to known decision variables. This study pioneers the one-sided Lipschitz approach in this context, offering significant advancements over the traditional Lipschitz method. A two-step design process is presented to estimate system states, faults, and external disturbances through an <span><math><mi>ℓ</mi></math></span>th-order proportional-integral observer and a constrained least squares estimator, which is data-driven. Agents can update their observers by using relative residual outputs derived from neighboring information, enhancing both fault and state estimation accuracy. Furthermore, a dynamic event-triggered communication protocol enables efficient output sharing and reduces communication costs. The observer design conditions are formulated as an optimization problem constrained by linear matrix inequalities, ensuring robust H-infinity performance. Simulation results validate the effectiveness of the proposed method for robust fault estimation in nonlinear MASs.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 8","pages":"Article 107689"},"PeriodicalIF":3.7,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143838946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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.jfranklin.2025.107688
Tiange Yang , Yuanyuan Zou , Jinfeng Liu , Shaoyuan Li , Xiaohu Zhao
This paper addresses the multi-agent control problem in the context of global temporal logic tasks, considering agents with heterogeneous capabilities. These global tasks involve not only absolute and relative temporal and spatial constraints, but also group behaviors, including task completion times, agent capabilities, and task interdependencies such as the need for synchronous execution. The global tasks are formally formulated into global signal temporal logic (STL) formulae, and a synchronous robustness metric is designed to evaluate the synchronization quality with real values. A mixed-integer linear programming (MILP) encoding method is further proposed to realize task-satisfied motion planning with high synchronicity and minimum control efforts. The encoding method uses a logarithmic number of binary variables to fully capture synchronous robustness, leading to only linear computational complexity. Simulations are conducted to demonstrate the efficiency of the proposed control strategy.
{"title":"Multi-agent control synthesis from global temporal logic tasks with synchronous satisfaction requirements","authors":"Tiange Yang , Yuanyuan Zou , Jinfeng Liu , Shaoyuan Li , Xiaohu Zhao","doi":"10.1016/j.jfranklin.2025.107688","DOIUrl":"10.1016/j.jfranklin.2025.107688","url":null,"abstract":"<div><div>This paper addresses the multi-agent control problem in the context of global temporal logic tasks, considering agents with heterogeneous capabilities. These global tasks involve not only absolute and relative temporal and spatial constraints, but also group behaviors, including task completion times, agent capabilities, and task interdependencies such as the need for synchronous execution. The global tasks are formally formulated into global signal temporal logic (STL) formulae, and a synchronous robustness metric is designed to evaluate the synchronization quality with real values. A mixed-integer linear programming (MILP) encoding method is further proposed to realize task-satisfied motion planning with high synchronicity and minimum control efforts. The encoding method uses a logarithmic number of binary variables to fully capture synchronous robustness, leading to only linear computational complexity. Simulations are conducted to demonstrate the efficiency of the proposed control strategy.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 8","pages":"Article 107688"},"PeriodicalIF":3.7,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143851485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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.jfranklin.2025.107686
Tianpeng Fan, Hongxiao Hu, Quan Wan, Zhongguo Li, Zhengtao Ding
In multi-agent systems (MASs), the time to reach a consensus is an important factor in characterising system performance and control strategy. The linear protocol has a fast convergence rate when the initial error is large but slows significantly as the error decreases. Therefore, this paper combines the linear protocol with two finite-time protocols, and a switching strategy is designed to achieve fast finite-time consensus. First, when the connection topology is undirected, it is proved that the continuous finite-time consensus protocol is unnecessary, with the fastest convergence achieved by switching directly from the linear protocol to the discontinuous finite-time protocol. Two switching thresholds are provided. Subsequently, the results are extended to detail-balanced and leader-following graphs. Notably, in the leader-following case, the graph only needs to be connected without requiring strongly connected or detail-balanced. The proposed approach significantly reduces the time required for MAS consensus and eliminates the need for additional parameter calculations.
{"title":"Fast finite-time consensus strategy for multi-agent systems based on switching of different protocols","authors":"Tianpeng Fan, Hongxiao Hu, Quan Wan, Zhongguo Li, Zhengtao Ding","doi":"10.1016/j.jfranklin.2025.107686","DOIUrl":"10.1016/j.jfranklin.2025.107686","url":null,"abstract":"<div><div>In multi-agent systems (MASs), the time to reach a consensus is an important factor in characterising system performance and control strategy. The linear protocol has a fast convergence rate when the initial error is large but slows significantly as the error decreases. Therefore, this paper combines the linear protocol with two finite-time protocols, and a switching strategy is designed to achieve fast finite-time consensus. First, when the connection topology is undirected, it is proved that the continuous finite-time consensus protocol is unnecessary, with the fastest convergence achieved by switching directly from the linear protocol to the discontinuous finite-time protocol. Two switching thresholds are provided. Subsequently, the results are extended to detail-balanced and leader-following graphs. Notably, in the leader-following case, the graph only needs to be connected without requiring strongly connected or detail-balanced. The proposed approach significantly reduces the time required for MAS consensus and eliminates the need for additional parameter calculations.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 8","pages":"Article 107686"},"PeriodicalIF":3.7,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143838945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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.jfranklin.2025.107684
Yining Chen , Guoting Wang , Yongle Guo , Linying Xiang , Dandan Li , Zhiqiang Zuo
We investigate the consensus problem for a network of infinite-dimensional agents with directed switching topology. Different from the general parabolic-type agents, networked wave PDEs which are suitable to model a group of flexible spacecrafts are addressed in this paper. Under mild conditions, a boundary control protocol is proposed for the underlying system. Subsequently, a novel common Lyapunov function is constructed to guarantee consensus and detailed analysis of theoretical findings is obtained. The well-posedness is further considered with the help of semigroup theory and inductive method. Moreover, a numerical example is exhibited to support the derived results.
{"title":"Consensus of wave PDE agents under switching graphs","authors":"Yining Chen , Guoting Wang , Yongle Guo , Linying Xiang , Dandan Li , Zhiqiang Zuo","doi":"10.1016/j.jfranklin.2025.107684","DOIUrl":"10.1016/j.jfranklin.2025.107684","url":null,"abstract":"<div><div>We investigate the consensus problem for a network of infinite-dimensional agents with directed switching topology. Different from the general parabolic-type agents, networked wave PDEs which are suitable to model a group of flexible spacecrafts are addressed in this paper. Under mild conditions, a boundary control protocol is proposed for the underlying system. Subsequently, a novel common Lyapunov function is constructed to guarantee consensus and detailed analysis of theoretical findings is obtained. The well-posedness is further considered with the help of semigroup theory and inductive method. Moreover, a numerical example is exhibited to support the derived results.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 8","pages":"Article 107684"},"PeriodicalIF":3.7,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143825604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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