Learning a nonlinear controller from data: theory and computation

In this paper, we consider the problem of learning a nonlinear controller directly from experimental data. We assume that an existing, unknown controller, able to stabilize the plant, is available, and that input-output measurements can be collected during closed loop operation. A theoretical analysis shows that the error between the input issued by the existing controller and the input given by the learned one shall have low variability in order to achieve closed loop stability. This result is exploited to derive a $\ell_{1}$-norm regularized learning algorithm that achieves the stability condition as the number of data points tends to infinity. The approach is completely based on convex optimization.