Hybrid Computer Solution of Optimal Control Problems by the Maximum Principle

When the maximum principle is applied to optimal control problems, a two-point boundary value problem must by necessity be solved. This paper discusses a solution method for general problems in which the initial and terminal states of the system are given, but in which the time of arrival at the terminal state is unknown. Various difficulties accompanying the conventional methods used in the past are pointed out, and a new method for solving these difficulties is proposed. The hybrid computing system is suitable for carrying out this method, and hybrid computers have been applied to the solution of numerous concrete problems. As a result, it becomes possible to seek a solution completely automatically, and it has been proven that this method is extremely practical.