Z. Yan, L. Han, X. Li, X. Dong, Q. Li and Z. Ren, “Event-Triggered Time-Varying Formation Control for Discrete-Time Multi-Agent Systems with Communication Delays,” 2020 Chinese Automation Congress (CAC), 2020, pp. 6707-6711, doi: 10.1109/CAC51589.2020.9326758.

文章目錄

• I. Introduction
• II. Preliminaries
• • A. Graph theory and notations
  • B. Problem description
• III. Main results
• • A. Event-triggered control protocol
  • B. Stability analysis
• IV. Simulation
• V. Conclusion

I. Introduction

II. Preliminaries

A. Graph theory and notations

$W=[w_{ij}]\in {\mathbb{R}}^{N\times N}$ is adjacency matrix.

$S$ is in-degree matrix.

Laplacian $L=S?W$

B. Problem description

$$\begin{array}{rl}{x}_i(k+1)& =x_i(k)+v_i(k)T\\ v_i(k+1)& =v_i(k)+u_i(k)T\end{array}\text{\hspace{1em}(1)}$$

III. Main results

A. Event-triggered control protocol

$$\begin{array}{rl}{u}_i(k)& =K_2\sum _{j\in N_i}{w}_{ij}[A^{k?k_m^i}({\Psi }_i(k_m^i?\tau )?h_i(k_m^i?\tau ))?A^{k?k_m^i}({\Psi }_j(k_m^j?\tau )?h_j(k_m^j?\tau ))]\\ & +[h_{iv}(k+1)?h_{iv}(k)]/T\\ & +K_1({\Psi }_i(k)?h_i(k))\end{array}\text{\hspace{1em}(7)}$$

先簡化一下
$$\begin{array}{rl}{u}_i(k)& =K_2\sum _{j\in N_i}{w}_{ij}[A({\Psi }_i?h_i)?A({\Psi }_j?h_j)]\\ & +[h_{iv}(k+1)?h_{iv}(k)]/T\\ & +K_1({\Psi }_i(k)?h_i(k))\end{array}\text{\hspace{1em}(7)}$$

本質上還是個普通的分布式協議，加上了個期望速度補償項，還有個啥暫時還不知道。

寫了下程序，明白了，回來再補充下，最后一項就是自身與期望編隊的誤差。

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接下來看一下事件觸發機制。

$$f_i(k,e_i(k))=\Vert e_i(k)\Vert ?c{\alpha }^k\text{\hspace{1em}(8)}$$

$e_i(k)=A^{k?k_m^i}({\Psi }_i(k_m^i?\tau )?h_i(k_m^i?\tau ))?({\Psi }_i(k)?h_i(k))$

B. Stability analysis

IV. Simulation

t = 30s 時的仿真效果

t = 50s 時的仿真效果

V. Conclusion

總結

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