Data-Driven Stabilization of Nonlinear Polynomial Systems With Noisy Data

In a recent article, we have shown how to learn controllers for unknown linear systems using finite-length noisy data by solving matrix inequalities. this extend approach deal with nonlinear polynomial formulating stability certificates in the form of data-dependent sum squares programs, whose solution directly provides stabilizing controller and Lyapunov function. We then derive variations result that lead more advantageous designs. The results also reveal connections problem designing starting from least-square estimate system.