Stochastic-time optimal-control systems

CONTROL SYSTEMS which are so designed that the control system outputs become identical with the control system inputs in the minimum amount of time are known as ¿time optimal-control systems.¿ In other words, a time optimal-control system is one which, given the final desired state, moves from the initial state to the final state in the minimum time. The final state may be the origin of the phase space in which the state of a control system is represented by a point. In general, however, the desired final state will be a function of time. Since essential complications enter into the problem when the desired state of a control system is a function of time, only the problem with the origin as the desired state will be considered in this paper.