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  • 狀態未知下Markov切換拓撲MASs自觸發控制

    Self-triggered control of multi-agent systems under Markov switching topologies and unknown states

    • 摘要: 本文考慮外界干擾和狀態未知綜合影響下帶有Markov切換拓撲的多智能體系統的一致性控制問題. 首先,設計基于新型觸發函數的自觸發機制,減少狀態觀測器和控制器的更新次數,其構造考慮外界干擾的影響,融入范數和積分累積的效應,有效地平衡觸發次數的減少和保持良好性能之間的關系;在此基礎上,設計自觸發降階狀態觀測器估計未知狀態,既可以實現狀態觀測誤差收斂到零,又可以實現狀態觀測器更新次數的減少. 其次,為了降低外界干擾對一致性控制效果的不利影響,構造干擾觀測器,實現干擾估計誤差有限時間收斂到零;同時基于自觸發狀態降階觀測器以及干擾觀測器設計了一致性控制器. 然后,利用Lyapunov理論分析多智能體系統在外界干擾和狀態未知影響下的均方一致性. 最后,利用數值對比仿真和多無人機仿真驗證設計的自觸發機制、自觸發狀態觀測器、干擾觀測器以及控制器的有效性.

       

      Abstract: In recent years, multi-agent systems (MASs) have been applied in many practical fields, including multi-vehicle and multi-robot systems. Research on consensus control of MASs has also received increasing attention. The purpose of consensus control for MASs is to drive the states of the agents to converge to a uniform value based on the local state information of the agents. To obtain a consensus on MASs, designing a distributed consensus control strategy is essential. In this study, the consensus control problem of MASs under an unknown state and external disturbance is investigated, where it behaves the Markov switching topology. To address unknown states and external disturbances, a reduced-order state observer and disturbance observer are each designed. To reduce controller update times and costs, a self-triggering mechanism is constructed. Based on the design of the reduced-order state observer, disturbance observer, and self-triggering mechanism, the consensus controller is then designed to obtain the mean-square consensus of the MASs under the Markov switching topology. The design details are as follows. First, a self-triggering mechanism is designed to predict the next triggering moment of the consensus controller. When developed, the monotonicity and positive characteristics of the exponential function are fully utilized, and an exponential term is used to increase the triggering threshold in the triggering function. Consequently, the self-triggering mechanism further reduces the number of controller updates. The estimated information of external disturbances is also considered. The mechanism also avoids using global information while simultaneously considering the balance between the immediate handling of adverse effects of external disturbances and the reduction of triggering times. Thus, a resource cost reduction is achieved. Our analysis reveals that the designed self-triggering mechanism can exclude the Zeno behavior. Second, a reduced-order observer is constructed to solve the problem of unknown states. To design it, the MAS model is transformed, and the control input and external disturbance are combined into a single variable. A new variable is then defined based on the state information of the followers, and a new form for the followers’ state is derived. Thus, a new model expression for MASs is obtained. Based on the above, the expression of the reduced-order model is obtained, and a reduced-order observer is designed to estimate the unknown state of the follower. Next, the observation error is proven to converge to zero. Third, based on the estimated information of the unknown state, a disturbance observer is designed to handle external disturbances. A Lyapunov function is designed for the estimation error. The estimation error is then determined to converge to zero. A consensus controller is designed based on the observers and self-triggering mechanism, and the mean-square consensus of the MASs is proven by Lyapunov theory. Finally, the effectiveness of the designed observer, self-triggering mechanism, and consensus controller is verified via both numerical and multi-UAV simulations.

       

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