Abstract
The gradient method for computing the optimal control is usually formulated for a problem in which the final instant is fixed and the final state vector is free. Although the minimum time control problem is the most familiar optimal control problem, it does not belong to the above class of optimal control problems. The usual technique for solving the minimum time control problem is the following. Assume the control time sufficiently shorter than the true (but unknown) minimum control time, and construct the problem to minimize the norm of the final state vector. Then, find the time when the minimum norm just vanishes as the control time is increased little by little. This technique requires some information about the true minimum control time, and moreover is not suitable to deal with the bounded state variable problem. The authors discovered that it is not required to solve the infinite series of optimal control problems, as is done in the ε-method, and that the currently assumed control time is easily determined as shorter or longer than the true minimum control time by solving an optimization problem once with a certain proper value for ε. The true minimum control time is obtained by the interval contraction method. Moreover, a characteristic of the proposed method is that a problem with some kind of bounded state variable as well as a bounded control variable can be dealt with quite easily.
