Multilevel approaches to the combined problem of system optimization and parameter identification

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Abstract
This report considers the interdependence of the two problems of system optimization and parameter estimation when the system is described by mathematical models containing uncertain parameters and whose structure is also uncertain or deliberately simplified in order to facilitate the solution of the optimization problem. Two computational procedures, produced by previous investigators, are described which combine the two problems into a single joint problem formulated as a two-level structure. The first procedure combines the two problems using a parametric formulation and the second technique replaces the identification problem by an inequality constraint. Following previous work in this field it is claimed that these two procedures have advantages over the two-step approach often employed in practice where the two problems are each considered separately and solved recursively. In addition, methods for decomposing the combined problem into two subproblems representing modified optimization and identification problems using multilevel optimization techniques are reviewed. The alternative techniques are exemplified by considering their application to optimization problems defined by a quadratic performance criterion and a linear mathematical model, and also to the maximization of profit from a chemical reactor described by a non-linear mathematical model which has been deliberately simplified in order to reduce computational requirements.

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