On adaptive control in the presence of impulsive measurement noise

The paper presents a new approach to design of adaptive control systems in the case where the plant output is corrupted with noise impulses/outliers. It is shown that the task of simultaneous parameter estimation and noise pulse elimination can be stated as a nonlinear filtering problem in the state space and solved using the theory of extended Kalman filters. The resulting algorithm can be viewed as a combination of two Kalman filters coupled in a nonlinear fashion: the first filter is designed to track slow parameter variations and the second one performs the on-line reconstruction of those variables comprising the regression vector which were called in question by the outlier detection routine. The method can be used in combination with a wide range of adaptive controllers.