Probing and caution in adaptive control systems

Adaptive controllers are being designed on the basis of certainty equivalence, neglecting the interaction between the estimators and controllers. This enforced separation leads to simple designs such as self-tuning regulators and the controllers based on model reference approaches. In some cases it may lead to non-optimal solutions due to system non-linearities or those non-linearities created by using state dependent parameter estimates. Under these circumstances the control exhibits a dual effect. The control affects not only the state, but also the uncertainty associated with the state. Due to this nonneutral behavior the estimation accuracy becomes a function of the control generated. Further, this uncertainty affects the control design. Hence, adaptive control systems are neither neutral nor separable. Linear systems with quadratic cost functions and Gaussian disturbances are neutral, separable and certainty equivalent. [1] In a stochastic framework the Gaussian noise requirement may be relaxed under certain other assumptions. [2,3] However, some non-linear systems also satisfy the above three properties. At present the necessary conditions are not known.