An optimal controller arising from minimization of a quadratic performance criterion of indefinite form

The problem of minimizing energy loss in automatic steering of ships is considered. Two ship types are analyzed-a high-speed containership and a large oil tanker. Making use of the sufficiency conditions for existence of a stable closed-loop system, it is shown that there is no theoretical difficulty in using an exact performance criterion for energy losses due to steering with an indefinite form, rather than an approximate criterion which fits the positive semidefiniteness condition of standard linear regulator (LR) theory.