Fuzzy Observer-Based Consensus Tracking Control for Fractional-Order Multi-Agent Systems Under Cyber-Attacks and Its Application to Electronic Circuits

Consensus control of multi-agent systems (MASs) has applications in various domains. As MASs work in networked environments, their security control becomes critically desirable in response to cyber-attacks. In this paper, the observer-based consensus tracking control problem is investigated for a class of Takagi-Sugeno fuzzy fractional-order multi-agent systems (FOMASs) under cyber-attacks. The malicious cyber attacks can impact the security of topologies of the communication networks of both controllers and observers. To estimate unmeasurable system states, a fuzzy observer is built. It is found that the topology of contact for observer states may be different from that of the feedback signals. A novel mathematical model for T-S fuzzy FOMASs with cyber-attacks is proposed. By using algebraic graph theory, Lyapunov functional, and fractional calculus theory, a distributed feed-back controller is developed for each agent, which guarantee the secure performance of tracking consensus error and observer error. Finally, two numerical examples demonstrate the effectiveness of the suggested control scheme, and the controller design for electronic network circuits shows the applicability of the proposed theoretical results. Simulations results for different differential-orders and coupling strength scenarios are given.