Theory of Aiming Control for Linear Stochastic Systems

Abstract

The problem of aiming control is formulated and solved for linear time-invariant systems perturbed by small additive white noise. Both state feedback and dynamic output feedback laws are considered. In the case of dynamic output feedback, noiseless and noisy measurements are analyzed. In the noiseless measurement case it is shown that the fundamental bounds on the achievable precision of aiming may or may not be finite depending on the nonminimum phase zeros and the invertibility of the system. In the noisy measurement case the achievable precision of aiming is shown to be always bounded. Aiming controller design techniques that result in controllers compatible with the bounds are developed. The approach is based on the asymptotic large deviations theory.