Indirect adaptive pole-placement control of MIMO stochastic systems: self-tuning results

We consider indirect adaptive pole-placement control (APPC) of linear multivariable stochastic systems. We propose a nonminimal but otherwise uniquely identifiable overlapping parameterization instead of the minimal representation used in current literature. Requiring less restrictive prior information than observability (and controllability) indices, this parameterization is more appropriate for multivariable ARMAX model representations. It is shown that by using the stochastic gradient (SG) identification method, and with sufficient external excitation. The parameter estimates are strongly consistent for all intial conditions. Moreover, under more restrictive assumptions and minor modification, the MIMO adaptive pole-placement controller is globally, asymptotically self-tuning even in the absence of external excitation. These represent the most complete study of stochastic multivariable APPC systems so far