Adaptive control of PDEs with uncertain and spatially variable parameters

This tutorial paper presents comprehensive new techniques for adaptive control of PDE systems. It overviews three design methods - the Lyapunov design, the passive design, and the swapping design and discusses tradeoffs between them. The basic ideas for each design are introduced through benchmark plants with constant unknown coefficients. This is then expanded to PDEs with spatially varying coefficients and with boundary sensing only, employing adaptive PDE observers. These adaptive controllers are applicable even to PDE systems with an infinite relative degree, infinitely many unknown parameters, and open loop unstable.