Data-driven adaptive control for uncertain nonlinear systems

For a class of nonlinear systems with uncertain parameters, this paper proposes a novel data-driven adaptive control method. This method utilizes a designed parameter estimator to steer the closed-loop system to the predefined ideal system on the manifold. It achieves finite-time convergence of the system through a terminal sliding mode controller. Based on the data-driven concept, the parameter regression matrix is expanded to acquire the unknown parameters of the system indirectly. By introducing a perturbation matrix, the issue that the expanded parameter regression matrix needs to satisfy certain excitation conditions to be full-rank is overcome, and an algebraic equation-based parameter estimator is constructed to achieve an arbitrary small convergence of the parameter estimation error. A global non-singular fast terminal sliding mode controller is designed for the system on the manifold, achieving finite-time convergence of the system. The stability of the closed-loop system is verified through Lyapunov-based stability analysis. As an application, the effectiveness and superiority of the proposed method are validated through numerical simulations of Euler-Lagrange systems with unknown inertia parameters.