Hybrid Data-enabled Predictive Control: Incorporating model knowledge into the DeePC

Predictive control can either be data-based (e.g. data-enabled predictive control, or DeePC) or model-based (model predictive control). In this paper we aim to bridge the gap between the two by investigating the case where only a partial model is available, i.e. incorporating model knowledge into DeePC. In our formulation, the partial knowledge takes the form of known state and output equations that are a subset of the complete model equations. We formulate an approach to take advantage of partial model knowledge which we call hybrid data-enabled predictive control (HDeePC). We prove feasible set equivalence and equivalent closed-loop behavior in the noiseless, LTI case. As we show, this has potential advantages over a purely data-based approach in terms of computational expense and robustness to noise in some cases. Furthermore, this allows applications to certain linear time-varying and nonlinear systems. Finally, a number of case studies, including the control of an energy storage system in a microgrid, a triple-mass system, and a larger power system, illustrate the potential of HDeePC.