Asymptotic pole assignment by learning

This paper solves the exact pole assignment problem for the single-input stochastic systems with unknown coefficients under the controllability assumption which is necessary and sufficient for the arbitrary pole assignment for systems with known coefficients. The system noise is required to be mutually independent with zero mean and bounded second moment, and the state at a fixed time is assumed to be repeatedly observable for different feedback gains. This paper applies the iterative learning approach which is essentially based on stochastic approximation. The feedback gains are given without invoking the certainty-equivalency principle.