Online Data-Driven Control of Nonlinear Systems Using Semidefinite Programming

This letter proposes a novel Data-Driven (DD) method for controlling unknown input-affine nonlinear systems. First, we estimate the system dynamics from noisy data offline through Subspace Identification of Nonlinear Dynamics. Then, at each time step during runtime, we exploit this estimation to deduce a feedback-linearization control law that robustly regulates all the systems consistent with the data. Notably, the control law is derived by solving a Semidefinite Programming (SDP) online. Moreover, closed-loop stability is ensured by constraining a Lyapunov function to descend in each time step using a linear-matrix-inequality representation. Unlike related DD control approaches for nonlinear systems based on SDP, our approach does not require any approximation of the nonlinear dynamics, while requiring the knowledge of a library of candidate basis functions. Finally, we validate our theoretical contributions by simulations for stabilization and tracking, outperforming another DD literature-inspired controller.