Finite-dimensional adaptive observers applied to distributed parameter systems

The application of adaptive observers to distributed parameter systems is considered. The effects of the infinite-dimensional unmodeled dynamics (residuals) on the observer state and parameter estimates are analyzed. For the purpose of the analysis, the state and parameter estimates of the nth-order observer are interpreted as estimates of an nth-order reduced-order model (ROM) of the infinite-dimensional plant. These estimates can then be compared to the states and parameters of a true ROM and bounds for the errors can be derived. It is proven that if the input provides definite excitation and the residual energy is bounded over a finite time interval, the estimation errors are ultimately bounded, with no assumption regarding stability of the plant or boundedness of the plant input