Systematic Synthesis of a Class of Smooth Parameter Projection Operators for Stable Adaptive Systems

Abstract

In this letter, a systematic synthesis of a new class of smooth parameter projection operators is presented. To elaborate such an approach, the adaptive control problem for a nth-order, single-input, linearly parametrizable, nonlinear system in the controllable canonical structure is considered. The stability of the closed-loop adaptive system, with the augmentation of such a class of smooth projection operators, is analyzed by a Lyapunov-like analysis. With this systematic construction, two novel smooth projection operators are devised as examples. A simulation study is performed to validate the proposed strategy and compare its performance against a non-smooth, parameter projection solution.