Least Squares Based Modification for Adaptive Control

A least squares modification is presented to adaptive control problems where the uncertainty can be linearly parameterized. The modified weight training law uses an estimate of the ideal weights formed online by solving a least squares problem using recorded and current data concurrently. The modified adaptive law guarantees the exponential convergence of adaptive weights to their ideal values subject to a verifiable condition on linear independence of the recorded data. This condition is found to be less restrictive and easier to monitor than a condition on persistency of excitation of the reference signal.