An Indirect Method for Regular State-Constrained Optimal Control Problems in Flow Fields

This article concerns an indirect method to solve state-constrained optimal control problems. The dynamics of the controlled system is given by ordinary differential equations encompassing the effect of a steady flow field in which the moving object is immersed. The proposed method is based on the maximum principle in Gamkrelidze's form. At the core of the approach is a regularity hypothesis which entails the continuity of the measure Lagrange multiplier associated with the state constraint. This property plays key role in shaping a properly modified shooting method to solve the two-point boundary value problem resulting from the maximum principle. Illustrative applications to time optimal control problems are considered and results of numerical experiments are provided.