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A multiresolution-based technique is proposed for the finite-dimensionalization of the controller parameter adaptation laws in adaptive control of distributed parameter systems (DPS) with spatially-varying coefficients. This technique permits efficient incorporation of the prior knowledge of the specific plant parameter characteristics, such as nonsmoothness, into controller implementation through the choice of parameter approximation basis, yielding a high fidelity parameter representation by a small number of basis coefficients. For this purpose, a new tool - the multiresolution Lyapunov functional is introduced. Using the latter, the existence of the wavelet-based finite-dimensional parameter adaptation law providing the desired tracking accuracy, while retaining the well-posedness of the closed-loop system with the infinite-dimensional plant is proven. The benefits of the technique in both real-time and off-line performance enhancement of the control law, such as reduction of computational demand and increase in the output convergence rate unaccompanied by the corresponding increase in the control effort are demonstrated, as well.

A recently introduced class of the well-posed error systems and the corresponding robust model reference adaptive control (MRAC) laws for systems represented by parabolic or hyperbolic partial differential equations (PDEs) with spatially varying parameters is extended to encompass the disturbance rejection capability. The disturbance is modeled as a space-time-varying signal generated by a parabolic PDE with known parameters or as a spatially-varying time-invariant signal.