Sparse Data-Driven Identification of Nonlinear Controllers
Keywords: Data-driven Control, Regularization, System Identification, Nonlinear Systems
AbstractThis work presents the use of l1-regularization on the nonlinear formulation of the Virtual Reference Feedback Tuning. When the controller has a substantial quantity of parameters to be estimated, which tends to be the case in black-box nonlinear identification, the least-squares method yields estimates with inadequate statistical properties. To handle that, the use of l1-regularization on the controller estimation is addressed, reducing the variance and the bias, as well as thresholding the unneeded parameters. In this paper, three different regularization methods are described and their algorithms are presented. For the purpose of illustrating the main properties of these methods, two numerical examples are presented.