Adaptive pole placement for linear stochastic systems with unknown parameters

The control of single-input single-output stochastic systems with unknown parameters is discussed. We consider first the stochastic pole placement strategy and highlight some of its properties. It is shown that the desired controller can be obtained by solving a linear polynomial equation. In addition, we show that for any stochastic pole placement problem there exists, under suitable conditions, an equivalent problem where the open-loop system is a "least-squares" model. Three approaches to the adaptive control problem are proposed: the identification control (IC), the least-squares identification/control (LSIC) and the control parameter estimation (CPE) methods. A computational example is given.