Feedback regulator for ODE system with unstable heat actuator dynamics subject to non-collocated configuration

Performance output tracking for ODE system with unstable heat equation actuator dynamics is considered. The aim of the present paper is to design a feedback control based on the state of the observer to achieve that the output of the ODE system can track exponentially the reference signal generated by an external system that meanwhile generates interference signals to disturb cascaded ODE–PDE system. The main difficulties come from the fact that the diffuse PDE dynamics is subject to an anti-stable factor and configurations, control and disturbance are not collocated. Besides, the controller designed is based on the state of the observer. Finally, the numerical simulations validate the effectiveness of the theoretical statements.