Robust Adaptive Finite Time Parameter Estimation with Relaxed Persistence of Excitation

In this paper, a novel robust adaptive finite time parameter estimation method is proposed to solve the parameter estimation problem for a class of linearly parameterized nonlinear systems. The main feature of the proposed methods is that concurrent learning technique is incorporated into the existing parameter estimation method such that the strict PE condition on the regression matrix is relaxed to a rank condition on the recorded data, which makes the presented method more practical. Furthermore, the convergence rate of the proposed parameter update law is improved significantly due to the consideration of the recorded data in the construction of the filtered regression vector/matrix. The simulation results of the existing general nonlinear system illustrate the aforementioned features. Comparison with existing methods from literatures proves the effectiveness and robustness of the proposed method.