Optimal control for linear time-invariant plants with time, fuel, and energy constraints

The structure of optimum control systems and the form of the optimal control signals are discussed for minimum time, minimum fuel, and minimum energy control of linear time-invariant plants. If the control variables are bounded by 1 in magnitude, then the control signals must have the values +1 or -1 for minimum time response; +1, 0, or -1 for minimum fuel operation; +1, -1 or be linearly related to the state of the plant, between these limits, for minimum energy operation.