| Abstract: |
A technique is presented for modeling and identifying distributed parameter systems. The technique, which is generally applicable, differs from previous work in three significant respects: (1) The modeling and identification process need not be based on a detailed knowledge of system dynamics. The basis of model construction is an orthogonal vector space which is independent of the system, but can be tailored to the system to the extent dictated by prior knowledge. (2) The art of modeling is transferred from writing a partial differential equation, or a set of ordinary differential equations, to choosing an influence function for the system. A set of differential equations comes out of the modeling process somewhat automatically. However, the coefficients of the equations are directly related to the system influence function, which must be estimated. (3) The basis vectors of the space are derived from Jacobi polynomials. They offer accuracy and computational ease not obtained from other approximating methods. |
