1988 年 36 巻 419 号 p. 565-571
An inverse problem of optimal linear quadratic regulators (LQR) is examined for single-input systems, and the selection of the weighting matrices which achieves a specified pole location is discussed in this paper. In particular, the Kessler polynomial is used as a desirable pole location, and the weighting matrices are derived in an analytical form. Although this pole specification results in the use of some negative weights in the performance index, the existence and uniqueness of the solution are guaranteed by Molinari's theorem. At the sacrifice of the circle condition, it is shown that some of deficiencies of the LQR controllers are avoided and several characteristics which classical controllers provide, but which modern methods cannot so far, are retained. An application to roll autopilot systems for missiles is given to illustrate and substantiate the proposed method as well as to make a comparison with the conventional LQR.