Efficient Implementation of Collocation Methods for Optimization using OpenModelica and ADOL-C

Abstract

Efficient calculation of the solutions of nonlinear op-timal control problems (NOCPs) is becoming more and more important for today's control engineers. The systems to be controlled are typically described using differential-algebraic equations (DAEs), which can be conveniently formulated in Modelica. In addition, the corresponding optimization problem can be expressed using Optimica. Solution algorithms based on collocation methods are highly suitable for discretizing the underlying dy-namic model formulation. Thereafter, the correspond-ing discretized optimization problem can be solved, e.g. by the interior-point optimizer Ipopt. The perfor-mance of the optimizer heavily depends on the avail-ability of derivative information for the underlying op-timization problem. Typically, the gradient of the ob-jective function, the Jacobian of the DAEs as well as the Hessian matrix of the corresponding Lagrangian formulation need to be determined. If only some or none of these derivatives are provided, usually numer-ical approximations are used by the optimizer inter-nally. OpenModelica supports the Optimica language and is capable of automatically generating the discretized op-timization problem using collocation methods as well as the whole symbolic machinery available. In ad-dition, all necessary derivative information is deter-mined using the automatic differentiation capabilities of ADOL-C, which has now been integrated into the OpenModelica environment.