  Stochastic model predictive control (SMPC) has been a promising solution to
complex control problems under uncertain disturbances. However, traditional
SMPC approaches either require exact knowledge of probabilistic distributions,
or rely on massive scenarios that are generated to represent uncertainties. In
this paper, a novel scenario-based SMPC approach is proposed by actively
learning a data-driven uncertainty set from available data with machine
learning techniques. A systematical procedure is then proposed to further
calibrate the uncertainty set, which gives appropriate probabilistic guarantee.
The resulting data-driven uncertainty set is more compact than traditional
norm-based sets, and can help reducing conservatism of control actions.
Meanwhile, the proposed method requires less data samples than traditional
scenario-based SMPC approaches, thereby enhancing the practicability of SMPC.
Finally the optimal control problem is cast as a single-stage robust
optimization problem, which can be solved efficiently by deriving the robust
counterpart problem. The feasibility and stability issue is also discussed in
detail. The efficacy of the proposed approach is demonstrated through a
two-mass-spring system and a building energy control problem under uncertain
disturbances.
