The recursive reduced-order solution of an open-loop control problem of linear singularly perturbed systems

A reduced-order method with an arbitrary degree of accuracy is obtained for solving the linear-quadratic optimal open-loop control problem. The original two-point boundary value problem is transformed into the pure-slow and pure-fast reduced-order completely decoupled initial value problems. By doing this, the stiffness of the singularly perturbed two-point boundary value problem is converted into the problem of an ill-defined linear system of algebraic equations