A Numerical Approach to Multiobjective Optimal Control of Multibody Dynamics

Recently, a couple of approaches have been developed that combine multiobjective optimization with direct discretization methods to approximate trajectories of optimal control problems, resulting in restricted optimization problems of high dimension. The solution set of a multiobjective optimization problem is called the Pareto set which consists of optimal compromise solutions. A common way to approximate the Pareto set is to start with at least one given Pareto point and to evolve the Pareto set using a local continuation method. With our approach, we first roughly approximate the feasible set of the multiobjective optimal control problem by using a global root finding approach. The roughly approximated feasible set provides information to find an appropriate scaling of the single objectives and to find initial guesses for the continuation of the Pareto set. Then, the continuation is performed by a reference point method. To reduce the dimension of the underlying optimal control problem, a local reparametrization in combination with a discrete null space method is used.