Output tracking for ODE system via unstable heat actuator dynamics with mismatched disturbance

In this article, we address the performance output tracking for finite-dimensional systems with infinite-dimensional actuator dynamics and mismatched disturbance. The major difficulties are that the actuator dynamics is covered by an unstable heat equation and it has non-collocated configuration between control input and disturbance. To overcome these difficulties, the trajectory planning technique is first introduced to carry the disturbance to control channel, and then backstepping strategy is applied to cope with the source term of instability in the heat equation. Following, by virtue of system similarity, the recently developed dynamic compensation approach for linear system is utilised to guarantee the performance output tracks reference signal exponentially and closed-loop states are uniformly bounded. Finally, some numerical results are given to support the effectiveness of the theoretical statements.