Effiziente reduzierte Newton-ähnliche Verfahren zur Behandlung hochdimensionaler strukturierter Optimierungsprobleme mit Anwendung bei biologischen und chemischen Prozessen

A new direct multiple shooting method for multistage constrained optimization problems with large-scale differential-algebraic process models is presented. It is advantageous in case of optimization problems with many state variabels but few degrees of freedom, as they arise often in optimal control and parameter identification of spatially discretized partial differential-algebraic equation (PDAE) models. By a piecewise control parameterization and a multiple shooting state parameterization on the same grid we solve the resulting multipoint boundary value problem with specially tailored partially reduced Newton-type methods. The present work provides an extension of the direct multiple shooting approach for DAE models of index one (Bock and Plitt 1984, [20] and Leineweber 1999, [57]; Bock 1987, [16] and Schlöder 1988, [82]) to problems with many states but few degrees of freedom due to e. g. initial conditions on the states or a low number of control and global parameters. Emphasis is put on reducing the number of directional derivatives in the Newton-type methods to speed up computation of the Newton iterates. It is shown that the number of directional derivatives is independent of the state dimension. This can be achieved by projection onto the reduced space of control and global parameters. Intertwining of algorithmic differentiation for the model equations and Internal Numerical Differentiation can be used to efficiently set up the reduced QPs of the Newton-type optimization algorithms. It is shown that the new methods are well suited for offline optimization and also for online purposes in the context of Nonlinear Model Predictive Control. The performance of the new methods is demonstrated by multistage optimal control applications from the literature and applications from (bio-)chemical engineering: 1. Parameter estimation of the in-vitro drug release of a gum implant modelled by an instationary reaction-diffusion 1D-PDE. 2. Optimal setpoint control of a continuous distillation column modelled by a large-scale stiff DAE (maintaining purity requirements). 3. Parameter estimation and optimal control of capacity maximization of a catalytic tube reactor modelled by an instationary convection-diffusion 2D-PDE (cooperation with Bayer, Leverkusen). The first application is scaled in the space discretization mesh. Different IND approaches, model implementations and reduced space approaches are compared. The second application serves as a benchmark problem in the offline and online context. A comparison to a state-of-the-art real-time optimization algorithm (Diehl 2002, [28]) is presented. The last application shows the suitability of the new methods for industrial large-scale PDAE constrained optimization. It is shown that the optimal capacity can be increased by 12 % together with a 50 % reduction of the amount of catalyst.