Multiscale Concepts for Moving Horizon Optimization

In chemical engineering complex dynamic optimization problems formulated on moving horizons have to be solved on-line. In this work, we present a multiscale approach based on wavelets where a hierarchy of successively, adaptively refined problems are constructed. They are solved in the framework of nested iteration as long as the real-time restrictions are fulfilled. To avoid repeated calculations previously gained information is extensively exploited on all levels of the solver when progressing to the next finer discretization and/or to the moved horizon. Moreover, each discrete problem has to be solved only with an accuracy comparable to the current approximation error. Hence, we suggest the use of an iterative solver also for the arising systems of linear equations. To facilitate fast data transfer the necessary signal processing of measurements and setpoint trajectories is organized in the same framework as the treatment of the optimization problems. Moreover, since the original estimation problem is potentially ill-posed we apply the multiscale approach to determine a suitable regularization without a priori knowledge of the noise level.