Model reference adaptive control using nonparametric adaptive elements

Most current model reference adaptive control methods rely on parametric adap- tive elements, in which the number of parameters of the adaptive element are fixed a-priori, often through expert judgment. Examples of such adaptive elements are the commonly used Radial Basis Function Neural Networks (RBF-NN) with cen- ters allocated a priori based on the expected operating domain. If the system operates outside of the expected operating domain, such adaptive elements can become non-effective, thus rendering the adaptive controller only semi-global in nature. This paper investigates two classes of nonparametric adaptive elements, that is, adaptive elements whose number of parameters grow in response to data. This includes RBF adaptive elements with centers that are allocated dynamically as the system evolves using a Kernel linear independence test, and Gaussian Processes based adaptive elements which generalize the notion of Gaussian Distribution to function approximation. We show that these nonparametric adaptive elements re- sult in good closed loop performance without requiring any prior knowledge about the domain of the uncertainty. These results indicate that the use of such non- parametric adaptive elements can improve the global stability properties adaptive controllers.