Locally optimal adaptive control without persistent excitation (Q674948)

This paper presents an adaptive controller that does not require a persistence of excitation condition for its parameter estimation. It is shown that a least-square adaptive control law can be obtained by making the controller parameters to be a suitable function of the current estimate. The resulting control law is found to be a locally optimal control that minimizes the conditional expectation of a one-step increment of a cost function that is quadratic in the regression output. The key to the approach is to show that without the persistence of excitation condition the least-squares estimates converge to a manifold whose equation depends on the type of control law applied. It is proven that there exists a unique control law that is invariable in the manifold.