Output-Feedback Control for Stochastic Systems with Low Sensitivity

Abstract

The chapter treats the problem of controlling stochastic linear systems with quadratic criteria, including sensitivity variables, when noisy measurements are available. It is proved that the low-sensitivity control strategy with risk aversion can be realized by the cascade of (1) the conditional mean estimate of the current state using a Kalman-like estimator and (2) optimally feedback, which is effectively supported by the mathematical statistics of performance uncertainty as if the conditional mean state estimate was the true state of the system. In other words, the certainty equivalence principle still holds for this statistical optimal control problem.