Minimum time control for a Newtonian particle in a spatiotemporal flow field

We address the problem of steering a Newtonian particle to a prescribed terminal position and velocity in a spatiotemporal flow field under an explicit constraint on the norm of its acceleration. The cases when either the terminal position or the terminal velocity of the particle is free are also considered. By employing standard techniques from optimal control theory, we characterize the structure of the candidate time-optimal control and subsequently reduce the original optimal control problem to a system of coupled nonlinear algebraic equations. Although the latter system of equations has to be solved numerically, in general, we show that, in some cases, it can be brought into a triangular form, whose solution does not require a significant computational effort. Numerical simulations that illustrate the theoretical developments are presented.