Theory and Flight-Test Validation of a Concurrent-Learning Adaptive Controller

Abstract

Theory and results of flight-test validation are presented for a novel adaptive law that concurrently uses current as well as recorded data for improving the performance of model reference adaptive control architectures. This novel adaptive law is termed concurrent learning. This adaptive law restricts theweight updates based on stored data to the null-space of the weight updates based on current data for ensuring that learning on stored data does not affect responsiveness to current data. This adaptive law alleviates the rank-1 condition on weight updates in adaptive control, thereby improving weight convergence properties and improving tracking performance. Lyapunov-like analysis is used to show that the new adaptive law guarantees uniform ultimate boundedness of all system signals in the framework of model reference adaptive control. Flight-test results confirm expected improvements in performance. Nomenclature A = state matrix for a linear system a = sigmoidal function activation potential a = maximum sigmoidal function activation potential B = input matrix for a linear system bW, bV = neural network biases