Regulation-triggered batch identifier-based adaptive control for nonlinear systems with unknown control coefficients

This paper focuses on regulation-triggered batch identifier (RTBI)-based adaptive control for nonlinear systems with unknown control coefficients. The linear regression equation (LRE) is constructed to quantitatively collect historical excitation information. The batch identifier is established to update the parameter estimates by sufficiently utilising the collected excitation information, which is activated by the regulation-triggered condition. To address the singularity issue of control input, two distinct adaptive control schemes are proposed, which pertain to the range of parameter estimates and the excitation richness, respectively. It is shown that under non-persistent partial excitation, the impacts of parametric uncertainties can be eliminated after finite times of parameter updating. By introducing backstepping technique, the proposed adaptive control schemes are extended to the high-order systems with multiple unknown control coefficients and unmatched uncertainties. Simulation results are provided to demonstrate the effectiveness of the proposed adaptive control schemes.