Distributed fault-tolerant control for a class of uncertain cascaded ODE-PDE multi-agent systems

In this paper, a distributed fault-tolerant control is proposed for a class of uncertain cascaded ordinary differential equation (ODE)-partial differential equation (PDE) multi-agents. For the cascaded system under consideration, the output of ODEs serves as the input signal of PDEs such that a distributed control involving states of the ODE as well as the PDE system is expected to be designed for consensus tracking. Based on the designed distributed control, where the actuator is assumed to be healthy, a distributed fault-tolerant control is designed to guarantee the performance of the system, and it is further improved to deal with actuator failures. To enhance the robustness of the cascaded system, the system uncertainties and the external disturbances of both followers and leader are compensated using adaptive laws and an adaptive distributed observer, based on which the stabilization of the cascaded ODE-PDE multi-agent system can be achieved with partially known agents’ information. Simulation results are carried out to prove the effectiveness of the proposed method.