Pole assignment for stochastic systems with unknown coefficients

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. Two approaches to solving the problem are proposed: One is the iterative learning approach which can be applied when the state at a fixed time can be repeatedly observed with different feedback gains; the other is the adaptive control approach which works when the trajectories satisfy a nondegeneracy condition. Both methods are essentially based on stochastic approximation, and the feedback gains are recursively given without invoking the certainty-equivalency-principle.