Direct numerical solution of a time-optimal state-constrained control problem in a flow

We consider the following time-optimal control problem with state constraints: compute minimal travelling time of a controllable object moving in a prescribed flow field in a bounded domain between two given points. The optimal control problem is solved numerically using two direct methods – interior-point line search filter method and sequential quadratic programming. Five sample flows are considered, and computational properties of the corresponding simulations are measured and discussed.