Kernel Methods and Gaussian Processes for System Identification and Control: A Road Map on Regularized Kernel-Based Learning for Control

The commonly adopted route to control a dynamic system and make it follow the desired behavior consists of two steps. First, a model of the system is learned from input-output data, a task known as system identification in the engineering literature. Here, an important point is not only to derive a nominal model of the plant but also confidence bounds around it. The information coming from the first step is then exploited to design a controller that should guarantee a certain performance also under the uncertainty affecting the model. This classical way to control dynamic systems has recently been the subject of new intense research, thanks to an interesting cross-fertilization with the field of machine learning. New system identification and control techniques have been developed with links to function estimation and mathematical foundations in reproducing kernel Hilbert spaces (RKHSs) and Gaussian processes (GPs). This has become known as the Gaussian regression (kernel-based) approach to system identification and control. It is the purpose of this article to give an overview of this development (see 'Summary').