Dynamic Regressor Extension and Mixing-based Re-design of Adaptive Observer for Affine Systems

The dynamic regressor extension and mixing procedure is employed to redesign a conventional adaptive observer algorithm for affine systems. A reduced-order observer is designed without the construction of the state transition matrix. The dynamics of the regressor are redesigned to incorporate feedback from its extension, transforming the regressor dynamics into a perturbed damped nonlinear oscillator form. This introduces some flexibility in reducing the degradation of parameter convergence due to the lack of the transition matrix and in enhancing the excitation property of the extension matrix.