Matrix decomposition-based singularity-free adaptive control for nonlinear MIMO systems with arbitrary relative degrees

This article designs an adaptive controller based on matrix decomposition for nonlinear multiple-input multiple-output (MIMO) continuous-time (CT) systems with arbitrary relative degrees and uncertainties. Specifically, a novel matrix decomposition-based parametrization structure is constructed, and an adaptive control law with modified tracking error is designed on this basis. In terms of effectiveness, the designed adaptive controller ensures closed-loop stability and asymptotic output tracking while effectively addressing the singularity problem commonly encountered in parameter updating. Compared with common control schemes, the designed adaptive controller is suitable for more general uncertain nonlinear systems with arbitrary relative degrees, and will not encounter any transient performance issues and high-gain issues. Finally, the designed scheme is verified by a hypersonic vehicle model simulation.