An indirect adaptive pole-placement control for MIMO discrete-time stochastic systems

In this paper, an indirect adaptive pole-placement control scheme for multi-input multi-output (MIMO) discrete-time stochastic systems is developed. This control scheme combines a recursive least squares (RLS) estimation algorithm with pole-placement control design to produce a control law with self-tuning capability. A parametric model with a priori prediction outputs is adopted for modelling the controlled system. Then, a RLS estimation algorithm which applies the a posteriori prediction errors is employed to identify the parameters of the model. It is shown that the implementation of the estimation algorithm including a time-varying inverse logarithm step size mechanism has an almost sure convergence. Further, an equivalent stochastic closed-loop system is used here for constructing near supermartingales, allowing that the proposed control scheme facilitates the establishment of the adaptive pole-placement control and prevents the closed-loop control system from occurring unstable pole-zero cancellation. An analysis is provided that this control scheme guarantees parameter estimation convergence and system stability in the mean squares sense almost surely. Simulation studies are also presented to validate the theoretical findings. Copyright (c) 2005 John Wiley & Sons, Ltd.