Distributed $\mathcal {H}_{\infty }$ Resilient Bipartite Control of Multiagent Systems With Semi-Markov Switching

When information interaction occurs among agents, the communication network could be attacked or the signal interrupted, culminating in systemic instability and mission failure. Therefore, this article proposes <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> resilient bipartite control method to address the security problem of network information interaction among agents within competitive and cooperative multiagent systems. When the communication networks among agents are subject to a replay attack, the system model integrating multisensor weight fusion with an unknown input leader is established first. Then, a detection fusion algorithm is proposed to simultaneously uncover attacker behavior and identify tampered sensors. Considering the intermittent or interrupted communication resulting from the time variability of topology switching among agents, the switching topology is modeled by a semi-Markov process within a signed graph having positive and negative interaction weights. Subsequently, a distributed observer is designed to estimate the unknown input leader, utilizing the semi-Markov interactions among agents and incorporating an adaptive update mechanism to eliminate the dependency on global topology information. Ulteriorly, by solving convex optimization problems, a distributed resilient bipartite controller relying on the observer state is formulated, and achieves the expected <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> performance while remaining resilient against replay attacks. Finally, the superiority of the proposed method is validated through comparative examples.