18th International Conference on Innovative Computing, Information and Control (ICICIC2024)
Onsite (Qinhuangdao, China) and Online, September 10-13, 2024

PS-29: ICICIC2024-SS17-02
Leader-Follower Consensus of Multiple Euler-Lagrange Systems with Sensor and Actuator Attacks
1,23

4Rui Gao *, Jiangshuai Huang , Yao Wen , Hong Cheng and Zeqiang Li
15College of Cyber Security and Information Law, Chongqing University of Posts and Telecommunications, Chongqing 400065, P. R. China
2
College of Automation, Chongqing University, Chongqing 400044, P. R. China
3
College of Automation, Chongqing University of Post and Telecommunication, Chongqing 400065, P. R. China
4
College of Electrical Engineering, Sichuan University, Chengdu 610065, P. R. China
5
College of Faculty of Science and Technology, University of Macau, Macau SAR, P. R. China*Corresponding author: gaorui@cqupt.edu.cnIntroduction

Mathematical FormulasThis paper investigates the leader-follower
consensus control of multiple uncertain Euler-Lagrange
systems under sensor and actuator attacks. To handle theadverse effects from the attacks due to vulnerability of thecommunication network, a fully distributed adaptive
leader-follower consensus control strategy is proposed totackle the time-varying uncertainties of the cyber attacks.
The main difficulty lies in the negative interaction, which
results from time-varying gains of the attackers and theLaplacian graph of multi-agent systems and has beensuccessfully solved.

 xi ,1 = xi ,2(1)Fi ( xi , pi , t ) + Gi ( xi ,1 , pi ) ui + WIT ( t ) ξi ( xi )  xi ,2 =Research Questions
The existing control protocols are hard to generalize
due to its specificity and could not be used in consensus
control of multiple nonlinear systems such as EulerLagrange systems when there exist sensors and actuator
attacks. Hence, it is more tricky and worthy to be deeper
investigated to solve the problem of the vicious attacks andthe uncertainties synchronously for Euler-Lagrangesystems.

yr ( t=)v∑ f rT,l wr ,l + c=r f rT wr + c=r f rT wr(2)

i =10 ≤ z − z ⋅ sg ( z ) ≤ σV2 ≤ − ρ vV2 + Cv + λ N i ( χ i ) − 1 χ i(3)(4)

FigureFigure 1. Communication graphs subject to attacks

Methodologies
The leader-follower consensus issue of multiple
uncertain Euler-Lagrange systems subjected to cyberattacks is considered. In fact, we assume that the signals
from controller to actuator and sensor to controllertransmission channel would be both attacked. Therefore,
the transmitted control signal of each agent containing its
own signals and the signals derived from the neighbors,
are perturbed through cyber-attacks, which results inadverse impact on the closed-loop system stability of each
entity and consensus of the multiple Euler-Lagrangesystems.

Figure 2. Positions of all agents

Figure 3. Tracking errors of all the agents

Conclusion
In this paper, the proposed control algorithm iscapable of dealing with the leader-follower consensus
problem for multiple uncertain Euler-Lagrange systems
when there exist venomous attacks in sensor and actuator.
The developed fully distributed consensus control protocol
ensures that all the closed-loop signals are uniformly
ultimately bounded against the damage to system
performance from adversaries attacks. The theoretical
proof and numerical simulation are both performed to verify
the proposed control strategy. Our future work will include
but not limited to designing new control strategy to tackle
different attacks with more universal models.

Figure 4. Input signals of the agentsIn the communication topology, the leader and the four
followers subjected to attacks are shown in Figure 1. Figure
2 shows the positions of the four manipulators. Figure 3
illustrates the tracking errors. Figure 4 shows the control
input signals of the agents. It can also be observed that allof the signals for multiagent systems are bounded andoutput of the ith agent can track the given reference with anarbitrarily small error even though there exist cyber attacks.