IDENTIFICATION OF PARAMETERS IN PARTIAL DIFFERENTIAL EQUATIONS

The identification of parameters in partial differential equations from experimental output data is investigated. It is assumed that a physical process can be represented by a system of nonlinear hyperbolic or parabolic partial differential equations of known form but containing unknown parameters. The parameters may enter in the equations themselves or the boundary conditions. A steep descent algorithm is derived based on minimizing the difference between the experimentally observed output and that predicted by the model. The question of observability of distributed systems is considered. The determination of the reaction velocity constant for a first-order decomposition in an isothermal, laminar-flow tubular reactor is treated in detail. © 1969.