On an inverse problem in optimal control

The problem of optimizing linear-stationary control systems subject to quadratic performance indices and bounded control effort constraints is studied. This problem was first proposed by Letov [1]. His solution, however, has been found to be valid only in some special cases [3]. In this paper, necessary and sufficient conditions for the existence of the optimal control laws of the saturation type are developed. It is shown that the weighting factors in the performance index have to be chosen in a particular manner, and the plants have to satisfy certain conditions to yield an optimal saturation type control law. As the weighting on the control effort in the performance index is decreased, the optimal solution approaches a bang-bang type singular control.