State Space Approach to the Problem of Adaptive Pole Assignment

摘要

An algorithm for adaptive pole-placement for the class of single-input/single-output systems of order n is proposed. The asymptotic properties of the algorithm do not depend on persistently exciting signals. Excitation is used only initially to avoid pole-zero cancellation of the parameter estimates. The main result is that the asymptotic behavior of the system equals the behavior obtained on the basis of the true system. Identification of the system-parameters however, does not necessarily take place. The reason that such a result can be obtained without identification of the true system is the following: suppose a wrong estimate of the system of the system is used to generate the controls, and that the incorrectness of the estimate is not revealed by the resulting closed-loop behavior of the system, then the inputs are exactly equal to the ones which would be applied if the system was known.