Real-Time Solutions for Perturbed Optimal Control Problems by a Mixed Open- and Closed-Loop Strategy

Abstract

Many dynamical processes arising in engineering and natural science can be math ematically modelled by systems of differential equations. Often control functions, by which the process can be influenced, are to be chosen such that a certain objective function is op timized under observation of the differential equations and additional constraints. Today one of the greatest demands on such optimal control problems is to solve them in real-time.

Open-loop strategies have their advantage with respect to optimality whereas the approx imated solutions may not be admissible. Closed-loop strategies guarantee admissibility, but may lead to approximate solutions which are worse in view of optimality. Hence a new mixed strategy is proposed which benefits from the advantages of both methods, without suffering from their disadvantages. Finally an illustrative example from flight mechanics is discussed which shows the efficiency and robustness of the proposed method.