Least-Squares Model-Reference Adaptive Control with Chebyshev Orthogonal Polynomial Approximation

This paper presents a model-reference adaptive control approach for systems with unstructured uncertainty based on two least-squares parameter estimation methods: gradient-based method and recursive leastsquares method. The unstructured uncertainty is approximated by Chebyshev orthogonal polynomial basis functions. The use of orthogonal basis functions improves the function approximation significantly and enables better convergence of parameter estimates. The adaptation of least-squares adaptive control is driven by the plant modeling error which manifestes itself as the tracking error, but not vice versa. A predictor model is introduced to estimate the plant modeling error without the need for differentiation of the state signals which can introduce noise. The least-squares gradient adaptive control achieves superior parameter convergence as compared to the standard model-reference adaptive control. Flight control simulations were conducted with four adaptive controllers: least-squares gradient adaptive control, recursive least-squares adaptive control, standard model-reference adaptive control, and neural-network adaptive control. The results show that the recursive least-squares adaptive control achieves better robustness as measured by a time-delay margin while the least-squares gradient adaptive control achieves better tracking performance than both the standard model-reference adaptive control and neural-network adaptive control.