Optimal control of an elastic crane - trolley - load system – A prototype for optimal control of coupled ODE - PDE systems –

We consider the optimal control of a crane-trolley-load model, where the crane beam is subject to the PDE of static linear elasticity and the motion of the load is described by the dynamics of a pendulum that is fixed to a trolley which moves along the crane beam. The resulting problem serves as a prototype for optimal control of fully coupled partial and ordinary differential equations. This type of coupled systems arises from many applications involving mechanical multi-body systems. We motivate the control problem, show its analytical well-posedness and solve it numerically by means of a projected gradient method.