Finite/Fixed-Time Adaptive Control with Composite Learning and μ-modification

This study focuses on achieving finite-time and fixed-time convergence for both control errors and estimation errors for adaptive control of uncertain systems. A linear regression equation is constructed to analyze the effects of parametric uncertainties and to quantitatively collect historical excitation information. The parameter estimation error is orthogonally decomposed into the excited and unexcited components. Based on composite learning and μ-modification techniques, a finite/fixed-time adaptive control scheme is presented that sufficiently utilizes the collected excitation information. Notably, it is demonstrated that under non-persistent partial excitation, the control error and the excited estimation error component converge to zero within a finite/fixed time, while the unexcited component remains bounded. Simulation outcomes are provided to demonstrate and confirm the efficacy of the theoretical conclusions.