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動態事件觸發下的一階非線性多智能體系統設定時間一致性

Dynamic event-triggered predefined-time consensus for first-order nonlinear multiagent systems

  • 摘要: 為了保證多智能體系統收斂速度快的同時節約通信資源,針對一階非線性多智能體系統提出了動態事件觸發設定時間一致性算法. 相較于傳統的有限時間和固定時間控制算法,設定時間控制算法引入時變函數,可以保證系統在任意預設時間內均可達到一致性. 同時,設定時間控制算法的收斂時間上界不依賴于系統初始狀態、拓撲結構和控制參數,可以根據用戶需求任意提前設置. 故設定時間控制算法解決了計算冗雜的問題,同時可以保證控制精度. 為了進一步減少觸發次數,在現有的靜態事件觸發控制算法的基礎上引入新的動態變量,進而設計出動態事件觸發算法. 動態變量隨時間改變,可以降低觸發次數,從而減少控制器更新頻率和執行機構的磨損程度. 鑒于非線性系統廣泛存在于實際應用場景中,基于非線性系統設計的控制算法更具有一般性. 最后,通過數值仿真驗證動態事件觸發設定時間一致性算法的有效性. 綜上,本文所提出的動態事件觸發設定時間一致性算法可以保證一階非線性系統在任意設定時間內實現一致性,并且減少觸發次數,更可能應用于實際工程.

     

    Abstract: To ensure fast convergence speed and save communication resources, a dynamic event-triggered predefined-time consensus algorithm is proposed for nonlinear multiagent systems in this study. First, the input controller of each agent is developed using a time-varying function to ensure the realization of the predefined-time consensus. Afterward, the measurement error, based on a hyperbolic tangent function, is proposed to exclude the occurrence of Zeno behavior. Finally, a trigger function is established based on the measurement error, and internal dynamic variables are introduced to propose a dynamic event-triggered control protocol, which can reduce triggering times. In view of the widespread presence of nonlinear systems in practical scenarios, the control algorithm based on the developed first-order nonlinear multiagent system is generalized. For the predefined-time control algorithm, a time-varying function is introduced to ensure that the system can achieve consensus at the predefined time. Compared with the conventional finite-time and fixed-time control algorithms, the upper bound of convergence time does not depend on the initial state, topology information, and control parameters but can be arbitrarily set in advance as per the actual needs of users. Thus, the predefined-time control algorithm reduces the computation complexity and ensures control accuracy to a great extent. To further reduce the triggering times, the dynamic event-triggered control algorithm is improved by introducing a novel dynamic variable based on the existing static event-triggered control algorithm. This dynamic variable can be adjusted in real-time with the systems and is always greater than 0. Using the proposed dynamic event-triggered algorithm greatly reduces the triggering times, and Zeno behavior can be eliminated. Therefore, the dynamic event-triggered control algorithm plays an important role in reducing the number of controller updates and actuator wear. Above all, the proposed dynamic event-triggered predefined-time consensus algorithm can not only ensure the convergence speed but also reduce the update frequency of the controller and eventually achieve the consensus in a predefined time without Zeno behavior. Because the control input and measurement error are developed by using the hyperbolic tangent function and the hyperbolic tangent function can solve nondifferential problems caused by discontinuous functions, the nondifferential problems can be excluded. Finally, the effectiveness of the proposed dynamic event-triggered predefined-time consensus algorithm and theoretical analysis results are confirmed using numerical simulations. To sum up, this dynamic event-triggered predefined-time consensus algorithm can ensure the consensus of first-order nonlinear mutiagent systems in arbitrary setting time, and reduce the trigger times, which is more likely to be applied to practical engineering.

     

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