Data-driven explicit predictive control with limited resources: an exploration-based strategy

Retrieving optimal control actions in a receding horizon fashion at run time might be a challenging task, especially when the sampling time of the system to be controlled is small and the optimization problem is large. Although explicit solutions have been proposed to tackle this challenge, the complexity of the explicit control law scales poorly with the dimension of the problem. In the attempt to cope with these limitations within the challenging data-driven setup, we propose to construct a limited-complexity approximation of the explicit predictive law by iteratively exploring the state/reference space while leveraging structural priors on the input parameterization. The same approximation can be exploited to compute the control action also when the closed-loop system visits unexplored regions. The performance of the proposed strategy is assessed on a simple numerical example.