Optimal Guidance of the Isotropic Rocket in the Presence of Wind

We address the minimum-time guidance problem for the so-called isotropic rocket in the presence of wind under an explicit constraint on the acceleration norm. We consider the guidance problem to a prescribed terminal position and a circular target set with a free terminal velocity in both cases. We employ standard techniques from optimal control theory to characterize the structure of the optimal guidance law as well as the corresponding minimum time-to-go function. It turns out that the complete characterization of the solution to the optimal control problem reduces to the solution of a system of nonlinear equations in triangular form. Numerical simulations, that illustrate the theoretical developments, are presented.