Data-Driven Feedback Domination Control of a Class of Nonlinear Systems

This letter investigates the data-driven control (DDC) problem for a class of nonlinear systems satisfying the linear growth condition. The studied system has completely unknown model parameters and mismatched nonlinearity and input. A static linear state-feedback domination controller is proposed to make the closed-loop system globally exponentially stable, which is obtained by offline solving the data-based mixed integer programs (MIPs). Compared to the existing DDC methods, our approach can handle high-order nonlinear systems with nontriangular structures. In contrast to adaptive control methods that require introducing adaptive parameters or Nussbaum functions for handling unknown parameters in the control path, resulting in a dynamic nonlinear controller, our proposed approach only requires offline computation to achieve the desired control objectives using a static linear controller. Two numerical examples are given to illustrate the effectiveness of the proposed method.