Direct data-driven control of linear parameter-varying systems

In many control applications, nonlinear plants can be modeled as linear parameter-varying (LPV) systems. This system class models the dynamic behavior as a linear dynamic relationship between input and output signals, which is dependent on some measurable signals, e.g., some parameters describing the operating conditions. When a measured data set from a plant is available, LPV model identification can provide low complexity linear models that can embed the underlying nonlinear dynamic behavior of the plant. For such models, powerful control synthesis tools are available, but the way the modeling error and the conservativeness of the embedding affect the control performance is still largely unknown. Therefore, it appears to be attractive to directly synthesize a LPV controller from data without modeling the plant. In this talk, a direct data-driven synthesis approach is introduced within a stochastic framework to provide a practically applicable solution to the above problem. Both the cases where the controller structure to be used is a-priori fixed (e.g. gain-scheduled PID) and where a suitable structure has to be selected from data are discussed in detail. In particular, the latter problem is addressed from a machine learning point of view. It is finally shown that, although such a change of perspective shows great potential against standard model-based design, it also poses some new challenges from a system theoretic perspective.