Performance of Output Tracking for the Linear Heat Equation with a Heat Source at Intermediate Point by Neumann Boundary Control

This article addresses the output tracking problem for the heat equation featuring a heat source at intermediate point. Initially, we used the reference signal to design an auxiliary system. Secondly, servo system is constructed with an inverse transformation. Then, we used the improved backstepping method in order to obtain the exponential stability of error system with output signal minus reference signal. By using this method, it can true the convergence between the original system and the servo system and the output tracking issue is solved. Finally, we do some simulations to illustrated the proposed scheme.