Predefined-Time Adaptive Parameter Estimation for Nonlinear Systems

This paper examines a strategy for estimating parameters in nonlinear systems with unknown parameters, featuring predefined-time convergence. A new predefined-time stability criterion is proposed, offering a least upper bound on convergence time and enabling accurate calculation of actual convergence time. Additionally, the parameter estimation error is extracted using a specially designed auxiliary matrix. To mitigate the auxiliary matrix’s impact on parameter estimation, an inverse matrix is developed. Consequently, a novel adaptive law with a predefined-time convergence characteristic is formulated to guarantee zero convergence of parameter errors within a predefined-time. Lastly, the efficacy of this method is demonstrated through a numerical simulation of a nonlinear mass-spring system