Output-feedback adaptive boundary control of coupled equidiffusive parabolic PDE systems

This paper investigates the output-feedback adaptive boundary control issue of the n-dimensional coupled parabolic PDE system (PPDES) with the same diffusivity parameters and the unknown spatially varying parameters. To further simplify the target system, the coupled PPDES is converted into its observer canonical form via a backstepping transformation. To estimate system states, an observer is constructed, which is expressed as a linear combination of three filters. To deal with unknown parameters, the swapping identifiers are given. Based on the observer and the swapping identifiers, a backstepping controller is designed to stabilize the target system. It is proved that all the system states will converge to zero with the proposed controller. Finally, a numerical example is given to illustrate the effectiveness of the proposed controller.