Output Feedback Adaptive Controllers with Swapping Identifiers for Two Unstable PDEs with Infinite Relative Degree

We develop output feedback adaptive controllers for two benchmark parabolic PDEs motivated by a model of thermal instability in solid propellant rockets. Both benchmark plants are unstable, have infinite relative degree, and are controlled from a boundary. One plant has an unknown parameter in the PDE and the other in the boundary condition. Adaptive control of these plants is studied in a companion paper [13] using a Lyapunov method which yields an update law that requires the use of parameter projection and a restriction to low values of adaptation gain. In this paper we show how the swapping identifier design, the most common method used in adaptive control of finite dimensional systems, can be employed for PDEs. This approach does not require parameter projection or restriction on the size of the adaptation gain. The results are illustrated by simulation.