Stochastic adaptive control of non-minimum phase systems

The explicit self-tuning control of linear systems with constant but unknown parameters is analysed. The class of single-input/single-output, discrete-time stochastic systems with coloured noise is considered without imposing a minimum-phase condition. A stochastic approximation type of identification algorithm coupled with a general linear control law structure satisfying weak conditions is shown to lead to the required stability properties of the closed-loop system. Similar approaches have been previously proposed for deterministic systems and for stochastic systems with uncorrelated disturbances. The specific example of a pole-shifting algorithm is considered and it is shown that the required asymptotic behaviour is achieved under certain conditions.