Ag. Sparks et Ds. Bernstein, OPTIMAL TRADEOFF BETWEEN H-2 PERFORMANCE AND TRACKING ACCURACY IN SERVOCOMPENSATOR SYNTHESIS, Journal of guidance, control, and dynamics, 18(6), 1995, pp. 1239-1243
The problem of optimal H-2 disturbance rejection while tracking uncert
ain constant or sinusoidal reference commands is considered. The inter
nal model principle is used to ensure that the tracking error approach
es zero asymptotically. Necessary conditions are given for controllers
that minimize an H-2 disturbance rejection cost plus a worst-case int
egral square tracking error for transient tracking performance. The ne
cessary conditions provide expressions for the gradients of the cost w
ith respect to each of the control gains. These expressions are then u
sed in a quasi-Newton gradient search algorithm to determine the optim
al feedback gains. Numerical examples demonstrate the tradeoff between
the two competing objectives in the cost function.