Robust Pareto Points with Respect to Crosswind of an Active Suspension System

In this work, the optimization of control parameters for an active suspension system is considered. Here, two objectives – energy and comfort – play an important role. Thus, a multiobjective optimization problem is formulated which can be solved numerically with a set-oriented approach, for example. The result is the set of optimal compromises of the objectives, the so-called Pareto set. In case of the active suspension system, the crosswind has an influence on the system and thus also on the Pareto set. Therefore, crosswind is modelled as an external parameter which leads to a parametric multiobjective optimization problem. In this work we investigate the question which Pareto points are robust with respect to crosswind variations. We use a recently developed algorithm for the computation of robust solutions. Here, a classical variational problem is formulated which describes a parameter-dependent solution path that varies as little as possible in parameter space. Making use of necessary conditions for this variational problem a nonlinear system of equations is formulated and solved numerically. Although one can observe significant variations of the Pareto sets for our application example, two robust Pareto points are computed. Hence, we can show that our approach reveals additional information which might be used in the self-optimization process in the future.