Robust Adaptive Finite-Time Parameter Estimation for Nonlinearly Parameterized Nonlinear Systems

The paper proposes a novel adaptive parameter estimation (APE) framework for nonlinearly parameterized nonlinear systems based on the parameter estimation error. The basic idea is to reformulate nonlinearly parameterized systems by using Taylor series expansion, and then tailor a recently proposed APE approach. An expression of the parameter estimation error is derived by introducing auxiliary filtered variables, which are then used to design the adaptive laws to achieve exponential and even finite-time convergence under the standard persistent excitation (PE) condition. Moreover, the robustness of the proposed APE against bounded disturbances is also studied. Two simulation examples demonstrate the effectiveness of the proposed estimation algorithms.