Batch Least Squares Adaptive Control in the Presence of Unmodelled Dynamics

The stability robustness of an indirect adaptive control algorithm using batch least squares identification is examined. By enforcing a persistence of excitation condition on the reference input, a bound on the parameter estimation errors due to the unmodelled dynamics is developed. Conditions under which the closed loop stability of a pole-placement adaptive control strategy can be expected are then developed from this bound using Kharitonov´s theorem. The stability robustness of the algorithm is tested on two simulation examples, one of which includes very lightly damped unmodelled dynamics.