This research concerns the modeling and least squares parameter identification for a class of nonlinear input-output differential and functional-differential systems using projected equation error methods. Examples for this class will be found in diverse areas such as pharmacokinetics, robotics, lasers, and viscoelastic materials, as well as models for control systems engineering. 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 DFT/FFT techniques at each stage of the least squares identification. Proposed topics include delineating and extending the class of nonlinear systems that are amenable to the projection methods, structure determination procedures for certain classes of models, methods for handling modeling errors, determining optimal inputs for the projected equation error identification, and a multicomponent signal analysis problem. The singular value decomposition and total least squares estimate will aid as important computational tools for the proposed research.
