Minimal time control with multiple saturation limits

General rules are proved for minimal time control of a linear system with the constraints that both the manipulated variablem(t)and its derivativeṁ(t)are amplitude limited: 1)ṁ(t)is always at its extreme value unlessm(t)is at its extreme value, 2) for normal systems the minimal time path is unique and consequently optimum switching boundaries can be defined, and 3) the choice ofṁ(t)maximizes a Hamiltonian with a modified adjoint function. The above rules are applied to third-order control systems with decidedly favorable results.