Boundary tracking control of an unstable cascaded heat system with a non-collocated feedback

Here, we consider the output tracking problem of two cascaded heat equations through boundary interconnection, where one heat equation is unstable and the control input is placed on the boundary of the other heat equation. A feedforward control is designed to realize the output tracking to the desired reference signal. A non-collocated static feedback control is proposed to stabilize the tracking error system. The admissible feedback gain is obtained by applying the Nyquist criterion. Then the closed-loop tracking error system is showed to be exponentially stable. Finally, the tracking performance is illustrated by the numerical simulation.