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.

文章目录

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=[wij]∈RN×NW = [w_{ij}] \in \R^{N \times N}W=[wij]∈RN×N is adjacency matrix.

SSS is in-degree matrix.

Laplacian L=S−WL = S - WL=S−W

B. Problem description

xi(k+1)=xi(k)+vi(k)Tvi(k+1)=vi(k)+ui(k)T(1)\begin{aligned} x_i(k+1) &= x_i(k) + v_i(k) T \\ v_i(k+1) &= v_i(k) + u_i(k) T \\ \tag{1} \end{aligned}xi(k+1)vi(k+1)=xi(k)+vi(k)T=vi(k)+ui(k)T(1)

III. Main results

A. Event-triggered control protocol

ui(k)=K2∑j∈Niwij[Ak−kmi(Ψi(kmi−τ)−hi(kmi−τ))−Ak−kmi(Ψj(kmj−τ)−hj(kmj−τ))]+[hiv(k+1)−hiv(k)]/T+K1(Ψi(k)−hi(k))(7)\begin{aligned} u_i(k) &= K_2 \sum_{j\in N_i} w_{ij} [A^{k - k_m^i} (\varPsi_i(k_m^i - \tau) - h_i(k_m^i - \tau)) - A^{k - k_m^i} (\varPsi_j(k_m^j - \tau) - h_j(k_m^j - \tau))] \\ &+ [h_{iv} (k+1) - h_{iv}(k)] / T \\ &+ K_1 (\varPsi_i(k) - h_i(k)) \tag{7} \end{aligned}ui(k)=K2j∈Ni∑wij[Ak−kmi(Ψi(kmi−τ)−hi(kmi−τ))−Ak−kmi(Ψj(kmj−τ)−hj(kmj−τ))]+[hiv(k+1)−hiv(k)]/T+K1(Ψi(k)−hi(k))(7)

先简化一下
ui(k)=K2∑j∈Niwij[A(Ψi−hi)−A(Ψj−hj)]+[hiv(k+1)−hiv(k)]/T+K1(Ψi(k)−hi(k))(7)\begin{aligned} u_i(k) &= K_2 \sum_{j\in N_i} w_{ij} [A (\varPsi_i - h_i) - A (\varPsi_j - h_j)] \\ &+ [h_{iv} (k+1) - h_{iv}(k)] / T \\ &+ K_1 (\varPsi_i(k) - h_i(k)) \tag{7} \end{aligned}ui(k)=K2j∈Ni∑wij[A(Ψi−hi)−A(Ψj−hj)]+[hiv(k+1)−hiv(k)]/T+K1(Ψi(k)−hi(k))(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。

fi(k,ei(k))=∥ei(k)∥−cαk(8)f_i(k, e_i(k)) = \| e_i(k) \| - c \alpha^k \tag{8}fi(k,ei(k))=∥ei(k)∥−cαk(8)

ei(k)=Ak−kmi(Ψi(kmi−τ)−hi(kmi−τ))−(Ψi(k)−hi(k))e_i(k) = A^{k - k_m^i} (\varPsi_i(k_m^i - \tau) - h_i(k_m^i - \tau)) - (\varPsi_i(k) - h_i(k))ei(k)=Ak−kmi(Ψi(kmi−τ)−hi(kmi−τ))−(Ψi(k)−hi(k))

B. Stability analysis

IV. Simulation

t = 30s 时的仿真效果

t = 50s 时的仿真效果

V. Conclusion

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【Paper】2020_Event-Triggered Time-Varying Formation Control for Discrete-Time Multi-Agent Systems wit