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.