Numerical Treatment of Optimal Control Problems with Differential-Algebraic Equations and Applications to Virtual Test-drives

Abstract

In recent years direct methods have been developed for solving optimal control problems with ordinary differential equation (ODE) systems. Because of special problems arising from differential-algebraic equation (DAE) systems (e.g. computation of consistent initial values, higher index) these methods can not be applied to optimal control problems with DAE systems without advanced techniques. Therefore a new direct shooting approach for the numerical solution of optimal control problems with DAE systems even of higher index is presented. The method is used to simulate virtual test-drives of automobiles. Today detailed mathematical models of automobiles are generated automatically using mechanical multi-body simulation software. The resulting equations of motion are described by DAE systems of possibly higher index. By formulation of an optimal control problem subject to these equations of motion and additional constraints for the roadway a virtual test-driver is modeled.