This paper considers the use of low-order models for the determination of an approximate optimal control of a high-order system. For a number of such models of a given system, derived using different methods, the approximate optimal control input is calculated. The result of the application of these inputs to the system is compared with the actual optimum. It is shown that optimum low-order models provide a near-optimal control, which may serve as a good first approximation to the optimum. Together with a suitable scheme for on-line identification these models may be used effectively for adaptive control.