Optimization-based adaptive control for MIMO nonlinear systems: A data-driven method

This article concentrates on the challenging adaptive tracking problem of multi-input and multi-output (MIMO) nonlinear systems with unknown nonlinear dynamics, for which a novel optimization-based data-driven adaptive control (ODDAC) equipped with an extended dynamic linearization method is developed. Through considering MIMO nonlinear systems in the fully-actuated case and over-actuated case separately, the ODDAC is proposed consisting of a parameter updating algorithm and an adaptive control law. A new design of parameter updating algorithm is presented such that the estimation can be guaranteed to be bounded by a strict contraction process. By leveraging properties of the nonnegative matrix, a grouping-based contraction mapping (GCM) analysis method is proposed for the convergence of tracking error. Notably, the GCM does not require the contraction mapping condition to hold at all time instants. The proposed ODDAC is data-based, avoiding reliance on model information, and its validity is verified through simulations.