Local linear regression for efficient data-driven control

The problem of data-driven control (DDC) represents an important topic in the area of automation, due to the availability of large amount of data generated by the production processes occurring in industrial plants. The aim of this work is the study of an efficient DDC approach for nonlinear dynamic systems that exploits the data directly coming from the plant. In this framework, the control problem consists in the design of an automatic regulator able to execute a task by using the data collected during the successful operation of the plant, regulated by a reference controller such as a human operator. The proposed synthetic regulator is based on local linear regression models chosen for their simplicity of training and efficiency in incorporating new data generated by the plant. The conditions under which the derived controller converges to the optimal one are analysed in the context of statistical learning theory, which provides an appropriate framework to efficiently address this kind of DDC problem. Simulation results involving a dynamical system are provided to show the properties of the proposed method in an applicative context.