Incomplete feedback control linear systems with random parameters

The problem of incomplete feedback control of stochastic linear systems is considered. The system is modeled by an uncertain parameter, linear, time-invariant integral equation driven by Gaussian white noise and an incomplete observation which is a random, linear transformation of the states. The optimal control is the linear time invariant transformation of the observation which minimizes the expected value of a quadratic performance index. The necessary conditions that the optimal control must satisfy are given. This gradient is then applied to a flight control design problem. This problem concerns finding feedback gains to improve the longitudional handling qualities of a jet transport aircraft with uncertainty in the stability derivatives. The results of this simplified example demonstrate the usefulness of this technique to improve system response when there is uncertainty in the system parameters.