Combining model reference adaptive controllers and stochastic self-tuning regulators

The similarities between model reference adaptive controllers (MRAC) for minimum phase plants where the control objectives are specified by reference models and stochastic self-tuning regulators (S-STURE) for minimum phase plants where the control objectives are specified by autoregressive moving average (ARMA) stochastic models are investigated.These similarities permit the extension, for these two classes of adaptive systems, of the duality existing in the linear case with known parameters between modal control and minimum variance control. The convergence analysis of these schemes in a combined deterministic and stochastic environment allows one finally to define schemes which behave as a desired MRAC in a deterministic environment and as a desired S-STURE in a stochastic environment. The problem of removing the positive real conditions for convergence in deterministic and stochastic environment is also discussed.