Secure consensus for positive multi-agent systems with bumpless transfer control under Denial-of-Service attacks

This article investigates the secure consensus control problem of positive multi-agent systems under multiple-mode Denial-of-Service (DoS) attacks. A bumpless transfer (BT) control based secure mode strategy is proposed to improve the switching transient performance due to the system being actively switched to secure mode when attack is detected. Considering possible time delays for agents dealing with the issues of DoS attacks, an asynchronous switching model is established between system models and communication topology. With the stability theory of positive systems, sufficient and necessary conditions are established to guarantee the positivity of multi-agent systems under the secure mode strategy. Because the switching law caused by external attacks is unknown in advance, the BT control is specifically implemented through the controller gain interpolation technique. By multiple Lyapunov functions (MLFs) approach, secure consensus is achieved with a trade-off among controller performance, attack parameters, and switching delays. Numerical examples are presented to demonstrate the effectiveness of the obtained results.