Stability and tunability of an adaptive controller for one-dimensional parabolic PDE with spatially varying coefficients

This paper presents tunability analysis for a proposed model reference adaptive control algorithm for linear, one-dimensional, parabolic partial differential equations. Unknown parameters in the known system structure are either constant or spatially-varying, and distributed actuation and sensing are assumed to be available. The adaptation laws are obtained by the Lyapunov redesign method. It is shown that the concept of persistency of excitation in infinite dimensional adaptive systems should be investigated in relation to time variable, spatial variable, and boundary conditions as well. It is shown that even a constant input signal can be sufficiently rich in infinite dimensional adaptive systems in the sense that it can guarantee the convergence of parameter errors to zero.