Construction of the minimal time control for processes with bounded control amplitudes and rates

Minimal time control of linear time-varying processes with bounded control amplitudes and rates is discussed. Based on the maximum principle, necessary conditions are given which include a specific modified adjoint solution. Two additional conditions that are associated with this modified adjoint solution are derived. These conditions are then utilized to develop a systematic method of constructing the extremal control as an explicit time function. The construction scheme consists of a set of decision rules in the form of inequalities. These decision rules are implemented on a digital computer. The computer program basically checks out the decision rules and determines the appropriate set of prestored parameters, which describes each extremal control. To obtain the minimal time control from the extremal controls, a point-by-point search from the grid on a hypercylindrical surface is required. As an illustration, the computer program is applied to the Ranger Block III attitude control system.