Decomposition Solution of Open-Loop ´Cheap´ Control Problem

In this paper the singular perturbation approach is used to obtain an alternate and more efficient method of solving the two point boundary value problem for the linear quadratic optimal open-loop ´cheap´ control. The original two-point boundary value problem is transformed to completely decoupled initial value problems. The solution obtained in this manner clearly exhibits both the singular arc and the fast transients, separately. Considerable reduction in computational requirements is also achieved.