Variable structure model reference adaptive control of parabolic distributed parameter systems

The objective of this note is to extend results of variable structure model reference adaptive control (VS-MRAC) for finite dimensional systems to a class of parabolic distributed parameter systems. Using a priori bounds on the plant's unknown parameters, a switching law along with a control law is proposed which guarantees exponential convergence of the model reference state error to zero. In a similar fashion as in the finite dimensional case, the presence of unmodelled dynamics yields exponential convergence of the state error to a residual set. Numerical studies of a 1D parabolic system are included to provide insight into the applicability of VS-MRAC to distributed parameter systems.