SCIENCE CHINA Information Sciences, Volume 64 , Issue 3 : 132205(2021) https://doi.org/10.1007/s11432-019-2815-7

## Observer-based self-triggered control for time-varying formation of multi-agent systems

• AcceptedFeb 9, 2020
• PublishedFeb 7, 2021
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### Acknowledgment

This work was partially supported by Fundamental Research Funds for the Central Universities (Grant No. FRF-GF-17-B46), National Natural Science Foundation of China (Grant Nos. 61703037, 61921004), and National Postdoctoral Program for Innovative Talents (Grant No. BX20200081). The authors would like to thank the anonymous associate editor and reviewers for their comments and suggestions.

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• Figure 1

Undirected interaction topology emph G.

• Figure 2

(Color online) Formation error $z_i(t)$ $(i=1,2,\ldots,8)$ under the distributed event-triggered strategy with continuous communication. (a) $z_{i1}$ of each agent when $t\in[0,1]$; (b) $z_{i1}$ of each agent when $t\in[1.4,1.5]$; (c) $z_{i2}$ of each agent when $t\in[0,1]$; (d) $z_{i2}$ of each agent when $t\in[1.4,1.5]$; (e) $z_{i3}$ of each agent when $t\in[0,1]$; (f) $z_{i3}$ of each agent when $t\in[1.4,1.5]$.

• Figure 3

(Color online) Measurement error $e_i(t)$ $(i=1,2,\ldots,8)$ under the distributed event-triggered strategy with continuous communication. (a) $\|e_{i1}\|$ of each agent when $t\in[0,1]$; (b) $\|e_{i1}\|$ of each agent when $t\in[1.4,1.5]$; (c) $\|e_{i2}\|$ of each agent when $t\in[0,1]$; (d) $\|e_{i2}\|$ of each agent when $t\in[1.4,1.5]$; (e) $\|e_{i3}\|$ of each agent when $t\in[0,1]$; (f) $\|e_{i3}\|$ of each agent when $t\in[1.4,1.5]$.

• Figure 4

(Color online) Formation error $z_i(t)$ $(i=1,2,\ldots,8)$ under the self-triggered strategy with intermittent communication. (a) $z_{i1}$ of each agent when $t\in[0,1]$; (b) $z_{i1}$ of each agent when $t\in[1.4,1.5]$; (c) $z_{i2}$ of each agent when $t\in[0,1]$; (d) $z_{i2}$ of each agent when $t\in[1.4,1.5]$; (e) $z_{i3}$ of each agent when $t\in[0,1]$; (f) $z_{i3}$ of each agent when $t\in[1.4,1.5]$.

• Figure 5

(Color online) Measurement error $e_i(t)$ $(i=1,2,\ldots,8)$ under the self-triggered strategy with intermittent communication. (a) $\|e_{i1}\|$ of each agent when $t\in[0,1]$; (b) $\|e_{i1}\|$ of each agent when $t\in[1.4,1.5]$; (c) $\|e_{i2}\|$ of each agent when $t\in[0,1]$; (d) $\|e_{i2}\|$ of each agent when $t\in[1.4,1.5]$; (e) $\|e_{i3}\|$ of each agent when $t\in[0,1]$; (f) $\|e_{i3}\|$ of each agent when $t\in[1.4,1.5]$.

• Table 1

Table 1The event-triggering times under the distributed event-triggered strategy

 Agent 1 2 3 4 5 6 7 8 Triggering times under condition (14) 71 83 86 72 142 118 72 87 Triggering times under condition (15) 0 43 3 2 39 6 0 77 Total 71 126 89 74 181 124 72 164
• Table 2

Table 2The event-triggering times under the self-triggered strategy

 Agent 1 2 3 4 5 6 7 8 Triggering times under condition (59) 407 551 439 348 410 572 176 227 Triggering times under condition (62) 5 0 8 2 11 4 7 0 Total 412 551 447 350 421 576 183 227

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