Identification of parameters in systems of ordinary differential equations using quasilinearization and data perturbation

Abstract

Abstract Given a set of observed data for a particular physical phenomenon, the problem of computing the “best fit” parameters for the mathematical model describing the phenomenon is a common problem in process or reaction mechanism identification. If the mathematical model comprises a set of non‐linear ordinary differential equations, this leads to a non‐linear boundary value problem. A very powerful way of attacking this class of problem uses an adaptation of the Newton‐Raphson‐Kantorovich procedure, called quasilinearization, which regards the non‐linear problem as the limit of a sequence of linear problems. Starting from an initial trial solution, convergence if it does occur, occurs rapidly; further, convergence is assured if the initial guess is “close enough” to the true solution. The difficulty of making a good initial guess, a serious limitation of the method in the past, can in principle be overcome by the algorithm proposed. When a given vector may not be within the domain of convergence of the original problem, it must be within the domain of convergence of some other derived problem. The latter may then be perturbed towards the original problem in a finite number of steps. In the case of process identification, new data points are derived; these are subsequently adjusted until they coincide with the original data. The algorithm has been successfully applied to several examples from recent chemical engineering literature.