Appointed-time and Attack-free Bipartite Synchronization of Generic Linear Multiagent Systems over Directed Switching Networks

This article derives a solution to the appointed-time and attack-free bipartite synchronization problem for generic linear multiagent systems over directed switching networks accommodating cooperative and antagonistic interactions. Herein, appointed-time means that the settling time is independent of any parameters and is preappointed in advance. Attack-free requires that the communication channel is protected, which means that no state and observer information exchange is allowed, and only measured relative output information is available when designing protocols. Firstly, by virtue of Pontryagin’s maximum principle, a distributed appointed-time state-feedback protocol is developed for directed switching networks, which tackles the appointed-time bipartite synchronization problem from a motion-planning approach based on sampling measurements, but takes the risk of facing cyber attacks on information exchange channels. Then, to be free of network attacks, a sampling-based attack-free observer using relative output information is designed to observe bipartite synchronization errors at an appointed time. By combining the appointed-time state-feedback protocol with the sampling-based attack-free observer, an attack-free output-feedback protocol is developed without requiring the state or control input information. The attack-free appointed-time bipartite synchronization problem is thus resolved. Both the state-feedback and attack-free protocols show the ability of disturbance rejection to the nonidentical bounded disturbances. To our knowledge, it is the first time to solve the appointed-time and attack-free bipartite synchronization problem for generic linear multiagents based on state- and output-feedback information, respectively. Finally, simulations verify the effectiveness of the two protocols.