New estimator and duality of control for multiplicative noise systems with applications to packet dropping and multiple input delay systems

In this paper, we propose a new linear estimator for multiplicative-noise systems by defining an innovation sequence under a new criteria index. With the proposed estimation approach, we present a novel derivation for the stochastic LQ controller and show that the stochastic LQ control is fitly dual to the predictor defined in this paper, and from which we convert a more complicated problem of stochastic control for multiplicative noise systems with multiple input delays into a smoothing and filtering estimate problem. As the applications of the proposed new estimator, we also propose a novel estimator with measurement packet dropping.