【Paper】2020_Event-triggered bipartite consensus over cooperation-competition networks under DoS atta

2024-05-09 00:39:00

Hu, A., Park, J.H., Cao, J. et al. Event-triggered bipartite consensus over cooperation-competition networks under DoS attacks. Sci. China Technol. Sci. 64, 157–168 (2021).

文章目录

1 Introduction
2 Problem description and preliminaries
- 2.1 Multiagent modeling and signed graph
- 2.2 Event-triggered bipartite consensus
- 2.3 DoS attack
- 2.4 Preliminaries
3. Main
- 3.1 Event-triggered scheme under DoS attacks
4. Numerical simulations

1 Introduction

2 Problem description and preliminaries

2.1 Multiagent modeling and signed graph

x˙i(t)=ui(t)(1)\dot{x}_i(t) = u_i(t) \tag{1}x˙i(t)=ui(t)(1)

2.2 Event-triggered bipartite consensus

连续时间的一致性控制协议：
ui(t)=∑j∈Ni∣aij∣(sgn(aij)xj(t)−xi(t))(2)u_i(t) = \sum_{j \in N_i} |a_{ij}| (\text{sgn}(a_{ij}) ~ x_j(t) - x_i(t)) \tag{2}ui(t)=j∈Ni∑∣aij∣(sgn(aij) xj(t)−xi(t))(2)

基于事件触发机制下，连续时间的一致性控制协议：
ui(t)=∑j∈Ni∣aij∣(sgn(aij)x^j(t)−x^i(t))(3)u_i(t) = \sum_{j \in N_i} |a_{ij}| (\text{sgn}(a_{ij}) ~ \red{\hat{x}_j(t)} - \red{\hat{x}_i(t)} ) \tag{3}ui(t)=j∈Ni∑∣aij∣(sgn(aij) x^j(t)−x^i(t))(3)

事件触发的状态值
x^i(t)=xi(tki)\hat{x}_i(t) = x_i(\red{t_k^i})x^i(t)=xi(tki)
x^j(t)=xj(tk′j)\hat{x}_j(t) = x_j(\red{t_{k'}^j})x^j(t)=xj(tk′j)

事件触发时刻用 tpit_p^itpi 表示
tki=max⁡tpi{tpi≤t,p=1,2,⋯}t_k^i = \max_{t_p^i} \{ t_p^i \le t, p = 1,2,\cdots \}tki=maxtpi{tpi≤t,p=1,2,⋯}
tk′j=max⁡tpj{tpj≤t,p=1,2,⋯}t_{k'}^j = \max_{t_p^j} \{ t_p^j \le t, p = 1,2,\cdots \}tk′j=maxtpj{tpj≤t,p=1,2,⋯}

2.3 DoS attack

TqT_qTq 表示攻击开始时间
τq\tau_qτq 表示攻击持续时间
[Tq,Tq+τq][T_q, T_q + \tau_q][Tq,Tq+τq] 时间段内无信息交换

Δa(t0,t)\Delta^a(t_0,t)Δa(t0,t) 表示在时间段 [t0,t][t_0, t][t0,t] 内不能交换信息的总时间
Δs(t0,t)\Delta^s(t_0,t)Δs(t0,t) 表示在时间段 [t0,t][t_0, t][t0,t] 内能交换信息的总时间

2.4 Preliminaries

3. Main

3.1 Event-triggered scheme under DoS attacks

采样周期 h>0h>0h>0

tp+1i=min⁡μ=1,2,⋯{tpi+μh∣fi(tpi+μh)>0}(8)t^i_{p+1} = \min_{\mu=1,2,\cdots} \{ t_p^i + \mu h ~|~ f_i(t_p^i + \mu h) > 0 \} \tag{8}tp+1i=μ=1,2,⋯min{tpi+μh ∣ fi(tpi+μh)>0}(8)

其中 fi(tpi+μh)f_i(t_p^i + \mu h)fi(tpi+μh) 是一个关于误差的函数。

4. Numerical simulations

程序 Main_2020.m 的结果：

加入事件触发机制 Main_2020_ETC.m：

自己改的 DoS Main_2020_ETC_DoS.m：

在之前工作的基础上，又修改了 DoS 的触发条件，改成了概率触发，对应程序 Main_2020_ETC_DoS2.m

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