MILP modelling for the time optimal control problem in the case of multiple targets

Optimal guidance for a dynamical system from a given point to a set of targets is discussed. Detecting for the best target is done in such a way that the capture time is minimized and desirability of targets is maximized. By extending measure theoretical approach for the classical optimal control problem to this case, the nearly optimal control is constructed from the solution of a mixed integer linear programming problem. To find the lower bound of the optimal time a search algorithm is proposed. Numerical examples are also given.