Multivariable adaptive model algorithmic control

In this paper the multivariable adaptive control problem is addressed using the Model Algorithmic Control (MAC) method in conjunction with the canonical variate identification method. Under some simplifying assumptions multivariable MAC is shown to be equivalent to a classical controller in a unit feedback configuration. Robustness of the MAC controller against unmodelled dynamics is assessed by perturbation analysis. The canonical variate identification method is described in terms of choosing a state of a given order based upon past information to optimally predict the future. The computation is a noniterative algebraic stochastic realization algorithm that involves primarily a singular value decomposition which is numerically very stable and accurate. The canonical variate method is shown to give an optimal choice of instrumental variables, and simulation results show it to be approximately maximum likelihood.