Optimal Rejection of Stochastic and Deterministic Disturbances

The problem of optimal ;}(zrejection of noisy disturbances while asymptotically rejecting constant or sinusoidal disturbances is considered. The internal model principle is used to ensure that the expected value of the output approaches zero asymptotically hi the presence of persistent detenninistic disturbances. Necessary conditions are gi.venfor dynamic output feedback controllers that minimize an (}{zdisturbance rejection cost plus an upper bound on the integral square output cost for transient perfonnance. The necessary conditions provide expressions for the gradients of the cost with respect to each of the control gains. These expressions are then used in a quasi-Newton gradient search algorithm to find the optimal feedback gains.