Sigmoid-like Event-Triggered Security Cruise Control under Stochastic False Data Injection Attacks
Abstract
:1. Introduction
- A novel Sigmoid-like ETS is proposed to cope with the co-design of the control and communication of CCSs. Compared with the traditional static ETSs [23], adaptive ETSs [21,22] and dynamic ETSs [6,11], the proposed Sigmoid-like ETS will guarantee the upper bound of event-triggered thresholds while making full use of the state perception;
- The security control of CCSs under stochastic FDI attacks is well characterized with the proposed Sigmoid-like ETS. Rather than detecting the FDI attacks in a complicated way [18,19,24], the studied event-triggered security control of CCSs is of ${H}_{\infty}$ performance even on the condition that the FDI attack detection fails.
2. Preliminaries
2.1. Sigmoid-like ETS
- The $\tilde{\delta}\left({t}_{k}h\right)$ is a monotonic decreasing function along with $\left|\right|{x}_{c}\left({t}_{k}h\right){\left|\right|}^{2}$;
- It is obvious that $\tilde{\delta}\left({t}_{k}h\right)\in (0,\frac{{\varphi}_{\u03f5}}{1+\u03f5}]$ is held.
2.2. Stochastic FDI Attacks
2.3. Control Objectives
3. Main Results
Algorithm 1: Find the controller gain $\mathcal{K}$, event-triggered parameter $\frac{{\varphi}_{\u03f5}}{1+\u03f5}$ and weighting matrix $\Lambda $ |
1: Set the positive scalars $\u03f5$, $\overline{\eta}$ and the initial event-triggered parameter ${\varphi}_{\u03f5}$. Give the increasing step $\Delta >0$ and an optimization target $topt<0$; |
2: While $topt<0$; |
3: ${\varphi}_{\u03f5}={\varphi}_{\u03f5}+\Delta $; |
4: Solve LMIs (18), if there is a feasible solution X, $\tilde{\mathcal{H}}$, $\tilde{\mathcal{R}}$ and $\tilde{\Lambda}$ satisfying LMIs (18), go to the next step. Otherwise, return $Step$ 1; |
5: Return ${\varphi}_{\u03f5}-\Delta $ and calculate $\mathcal{K}$, $\Lambda $. |
4. Simulation Examples
4.1. Parameters Setting
- System parameters:Set the vehicle to cruise with different velocities: 5 m/s, 10 m/s, 15 m/s. In the system (3), the disturbance is ${w}_{\eta}\left(t\right)=0.01{e}^{-t}$, $t\in [0,30]$ s, and the other parameters are ${\eta}_{d}=0.5$ s, $\sigma =0.16$ s, $\overline{\eta}=0.2$ s, $\rho =0.63$, $\gamma =200$, the initial state ${x}_{c}\left(0\right)=[-0.5;0;1]$;
- FDI attack parameters:The probability of FDI attack is $\theta $ with $\Vert f\left({x}_{c}\left({t}_{k}h\right)\right){\Vert}_{2}$⩽$\Vert {S}_{EC}{x}_{c}\left({t}_{k}h\right){\Vert}_{2}$ and $f\left({x}_{c}\left({t}_{k}h\right)\right)$ = $[-tanh\left(0.2{x}_{1}\left({t}_{k}h\right)\right)$; $-tanh\left(0.1{x}_{2}\left({t}_{k}h\right)\right)$; $-tanh\left(0.2{x}_{3}\left({t}_{k}h\right)\right)]$, where the weighting matrix ${S}_{EC}$ = diag{$0.2$ $0.1$$0.2$};
- Event-triggered parameters:The event-triggered related parameter $\u03f5=1$, $\tilde{\delta}\left(0\right)=0$, $a=0.01$ (a is in Sigmoid-like function).
4.2. Discussions of Simulation Results
- Case I: FDI-free case
- Case II: FDI attack case
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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$\mathit{\theta}$ | N | $\tilde{\mathit{N}}$ | T | $\tilde{\mathit{T}}$ |
---|---|---|---|---|
0.2 | 75 | 114 | 0.3824 | 0.2599 |
0.3 | 72 | 111 | 0.3321 | 0.2508 |
0.4 | 63 | 118 | 0.4563 | 0.2536 |
0.5 | 61 | 158 | 0.4633 | 0.1271 |
0.6 | 69 | 418 | 0.4046 | 0.0710 |
0.7 | 71 | 2357 | 0.4189 | 0.0126 |
0.8 | - | - | - | - |
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Zhang, P.; Sun, H.; Peng, C.; Tan, C. Sigmoid-like Event-Triggered Security Cruise Control under Stochastic False Data Injection Attacks. Processes 2022, 10, 1326. https://doi.org/10.3390/pr10071326
Zhang P, Sun H, Peng C, Tan C. Sigmoid-like Event-Triggered Security Cruise Control under Stochastic False Data Injection Attacks. Processes. 2022; 10(7):1326. https://doi.org/10.3390/pr10071326
Chicago/Turabian StyleZhang, Pengfei, Hongtao Sun, Chen Peng, and Cheng Tan. 2022. "Sigmoid-like Event-Triggered Security Cruise Control under Stochastic False Data Injection Attacks" Processes 10, no. 7: 1326. https://doi.org/10.3390/pr10071326