The time optimal control with constraints of the rectangular type for linear time-varying odes

摘要

In this paper, we study a time optimal control problem of some linear time-varying ordinary differential equations, where the control constraint set is of the rectangular type. We derive a necessary and sufficient condition and provide an algorithm for the optimal time, as well as the optimal control for this problem. The basis consists of an equivalence theorem between the time optimal control problem and an associated norm optimal control problem, and the variational characterization of the latter problem.