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.

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

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

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

本质上还是个普通的分布式协议，加上了个期望速度补偿项，还有个啥暂时还不知道。

写了下程序，明白了，回来再补充下，最后一项就是自身与期望编队的误差。

接下来看一下事件触发机制。

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

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

B. Stability analysis

IV. Simulation

t = 30s 时的仿真效果

t = 50s 时的仿真效果

V. Conclusion