Adaptive guaranteed cost control of systems with uncertain parameters

Guaranteed cost control is a method of synthesizing a closed-loop system in which the controlled plant has large parameter uncertainty. This paper gives the basic theoretical development of guaranteed cost control, and shows how it can be incorporated into an adaptive system. The uncertainty in system parameters is reduced first by either: 1) on-line measurement and evaluation, or 2) prior knowledge on the parametric dependence of a certain easily measured situation parameter. Guaranteed cost control is then used to take up the residual uncertainty. It is shown that the uncertainty in system parameters can be taken care of by an additional term in the Riccati equation. A Fortran program for computing the guaranteed cost matrix and control law is developed and applied to an airframe control problem with large parameter variations.