Competitive Interaction Design of Cooperative Systems Against Attacks

This technical note proposes a resilient cooperative control design for networked cooperative systems when subjected to external attacks. The systems considered in this paper can have any information topology described by a leader-follower digraph. A potential attack on such systems consists of unknown bounded signals generated from any linear or nonlinear finite-$L_2$-gain exogenous dynamical system and injected distributively into nodes of the system's network. The purpose of the attack is to destabilize the consensus dynamics by intercepting the system's communication network and corrupting its local state feedback. The proposed resilient control design consists of introducing a virtual system with hidden network such that the overall system consisting of the original consensus system, the virtual system, and the attack dynamics is stable without requiring any information about the locations or nature of the attack. This is accomplished by utilizing the concept of competitive interaction to provide explicit design criteria for the hidden network of the virtual system to interact with the original system. A graph theoretical approach and a Lyapunov direct method are used to analyze the overall system and show that the proposed design ensures stability of the overall system and preserves the consensus of the original system. An example, which includes several scenarios, is used to illustrate the results.