Matrix decomposition-based parametrization and singularity-free adaptive control of MIMO nonlinear systems

This paper proposes a new matrix decomposition-based adaptive control scheme for multi-input and multi-output (MIMO) continuous-time uncertain nonlinear systems with arbitrary vector relative degrees. Novel matrix decomposition-based parametrization structures are constructed for parameter estimation, upon which singularity-free adaptive control laws with modified parameter update laws are formulated to ensure closed-loop stability and output tracking. State feedback and output feedback are addressed, respectively. The proposed adaptive control scheme exhibits the following characteristics when compared with the existing results: (i) it is applicable for control of a broader class of uncertain MIMO nonlinear systems with arbitrary vector relative degrees; (ii) it requires less knowledge of the uncertain control gain matrix, while still ensuring that the adaptive control law is always non-singular during the process of parameter adaptation; and (iii) it guarantees the desired system performance without involving transient or high-gain issues. The proposed adaptive control scheme is verified by a hypersonic vehicle model simulation.