Research will be conducted on the modeling and least squares parameter identification of nonlinear differential and differential-delay systems using projected equation error methods. The projections are designed to obviate the necessity of dealing with unknown initial or boundary conditions for time limited input-output data. Special emphasis is given to a projection method based on Fourier-type modulating functions which facilitates utilizing well known Fast Fourier Transform techniques at each stage of the least squares identification. Topics include delineating and extending the class of nonlinear systems that are amenable to the projection methods, structure determination procedures for the various classes of models, methods for handling modeling errors, determining optimal inputs for the projected equation error identification, and incorporating controller parameter update rules for adaptation in certain nonlinear control systems.
