Abstract
This paper presents a method to determine the time-optimal control of a linear system with a certain state inequality constraint. The method is fully concerned with the maximum principle. In this method we consider two trajectories, at least in principle, simultaneously. One of them starts from the initial state of the system and is computed in the forward direction of time, and the other starts from the target state and is computed backward. These trajectories are iteratively corrected so that they meet together, in an optimal fashion, on the boundary of the state admissible region. The optimality is tested on the basis of the geometric properties of the state attainability set that is particularly defined. In this method one does not have to explicitly consider the discontinuity of the adjoint variable at the junction time, and, further, the junction points are easily located. The computational procedure is given in detail and a numerical example is also shown.
