Nonparametric adaptive control in native spaces: A DPS framework (Part I)

This two-part work presents a novel theory for model reference adaptive control (MRAC) of deterministic nonlinear ordinary differential equations (ODEs) that contain functional, nonparametric uncertainties that reside in a native space. The approach is unique in that it relies on interpreting the closed-loop control problem for the ODE as a simple type of distributed parameter system (DPS), from which implementable controllers are subsequently derived. A thorough comparative analysis between the proposed framework and classical MRAC is performed. The limiting distributed parameter system, which underlies the proposed adaptive control framework, is derived and discussed in detail in this first part of the paper. The second part of this work will detail numerous finite-dimensional implementations of the proposed native space-based approach.