Parallel Multiple-Shooting and Collocation Optimization with OpenModelica

Nonlinear model predictive control (NMPC) has become increasingly important for today’s control engineers during the last decade. In order to apply NMPC a nonlinear optimal control problem (NOCP) must be solved which in general needs high computational effort. State-of-the-art solution algorithms are based on multiple shooting or collocation algorithms, which are required to solve the underlying dynamic model formulation. This paper describes a general discretization scheme applied to the dynamic model description which can be further concretized to reproduce the multiple shooting or collocation approach. Furthermore, this approach can be refined to represent a total collocation method in order to solve the underlying NOCP much more efficiently. Further speedup of optimization has been achieved by parallelizing the calculation of model specific parts (e.g. constraints, Jacobians, etc.) and is presented in the coming sections. The corresponding discretized optimization problem has been solved by the interior optimizer Ipopt. The proposed parallelized algorithms have been tested on different applications. As industrial relevant application an optimal control of a Diesel-Electric power train has been investigated. The modeling and problem description has been done in Optimica and Modelica. The simulation has been performed using OpenModelica. Speedup curves for parallel execution are presented.