A numerical approach to model reduction for optimal control of multiscale ODE
FacultiesFakultät für Mathematik und Wirtschaftswissenschaften
The topic of this thesis is model (order) reduction in the context of numerical optimal control. Complex mathematical models based on ordinary differential equations can often be reduced in order to decrease computational complexity and enable their use in control algorithms. A feature that can be exploited for the purpose of model reduction is time scale separation, which means that the system dynamics are comprised of fast and slow processes. Fast states relax to a slow invariant manifold in the state space, which is parametrized by the slow states. This manifold is approximated numerically and the fast species can be eliminated from the full model and thus also from the optimal control problem. To this end multivariate interpolation based on radial basis functions is used and compared with an online approach that solves the model reduction problem ad hoc. Singular perturbation theory is employed to illustrate the theoretical background and illustrate how reduced models influence the solution of the optimal control problem. It is shown via numerical experiments that the application of the model reduction techniques can lead to significant savings in computation time without compromising the quality of the optimal control solution.
Subject HeadingsOptimale Kontrolle [GND]
Multiscale modeling [LCSH]
Nonlinear programming [LCSH]