Numerical methods for optimum experimental design in DAE systems

• Published in: Journal of computational and applied mathematics Vol. 120; no. 1; pp. 1 - 25
• Main Authors: Bauer, Irene, Bock, Hans Georg, Körkel, Stefan, Schlöder, Johannes P.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.08.2000
• Subjects: Chemical reaction kinetics; Direct approach; Internal numerical differentiation; Nonlinear DAE models; Optimum experimental design; Parameter estimation; Parameter estimation; Nonlinear DAE models; Optimum experimental design; Direct approach; Internal numerical differentiation; Chemical reaction kinetics
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/S0377-0427(00)00300-9

Subject of this paper is the design of optimal experiments for chemical processes described by nonlinear DAE models. The optimization aims at maximizing the statistical quality of a parameter estimate from experimental data. This leads to optimal control problems with an unusual and intricate objective function which depends implicitly on first derivatives of the solution of the underlying DAE. We treat these problems by the direct approach and solve them using a structured SQP method. The required first and second derivatives of the solution of the DAE are computed very efficiently by a special coupling of the techniques of internal numerical differentiation and automatic differentiation. The performance of our approach is demonstrated for an application to chemical reaction kinetics.