Practical fixed-time composite-learning control for full-state constraint strict-feedback non-linear systems: A dynamic regressor extension and mixing based approach

A practical fixed-time composite learning control scheme, by combining dynamic regressor extension and mixing (DREM) parameter identification algorithm and adaptive dynamic surface control (DSC) technique, is proposed for a class of strict-feedback non-linear systems subjected to linear-in-parameters uncertainties and full-state constraint. To address the problem of state constraint, a non-linear transformation function is introduced to convert the originally constrained non-linear system into an unconstrained one. Meanwhile, the hyperbolic tangent function is employed to avoid singularity issues that often appeared in the traditional fixed-time (FXT) control designs. In order to relax the requirement of persistency of excitation condition, a modified FXT-DREM parameter identification approach with an interval excitation condition is constructed by introducing a three-layer transformation technique derived from the classical DREM algorithm. Then, the modified FXT-DREM parameter identification algorithm is seamlessly integrated into the adaptive DSC framework, resulting in a composite-learning control scheme. By employing Lyapunov stability analysis, the fixed-time convergence of both the parameter estimation error and the trajectory tracking error is proved. Finally, the effectiveness of the proposed design is demonstrated through simulation test.