Best estimated inverse versus inverse of the best estimator

The construction of a feed-forward controller frequently requires the estimation of an inverse function. Two possible methods to achieve this are: (i) learning the best estimated inverse (BEI), a method that is sometimes referred to as direct inverse learning and (ii) learning the inverse of the best estimator (IBE), a method that is sometimes referred to as indirect inverse learning. We analyze a general control problem, in the presence of noise, and show analytically that these two methods are asymptotically significantly different, even for simple linear nonredundant systems. We further demonstrate that the IBE method is typically superior for control purposes. (C) 2001 Elsevier Science Ltd. All ri-hts reserved.