  We develop a novel data-driven robust model predictive control (DDRMPC)
approach for automatic control of irrigation systems. The fundamental idea is
to integrate both mechanistic models, which describe dynamics in soil moisture
variations, and data-driven models, which characterize uncertainty in forecast
errors of evapotranspiration and precipitation, into a holistic systems control
framework. To better capture the support of uncertainty distribution, we take a
new learning-based approach by constructing uncertainty sets from historical
data. For evapotranspiration forecast error, the support vector
clustering-based uncertainty set is adopted, which can be conveniently built
from historical data. As for precipitation forecast errors, we analyze the
dependence of their distribution on forecast values, and further design a
tailored uncertainty set based on the properties of this type of uncertainty.
In this way, the overall uncertainty distribution can be elaborately described,
which finally contributes to rational and efficient control decisions. To
assure the quality of data-driven uncertainty sets, a training-calibration
scheme is used to provide theoretical performance guarantees. A generalized
affine decision rule is adopted to obtain tractable approximations of optimal
control problems, thereby ensuring the practicability of DDRMPC. Case studies
using real data show that, DDRMPC can reliably maintain soil moisture above the
safety level and avoid crop devastation. The proposed DDRMPC approach leads to
a 40% reduction of total water consumption compared to the fine-tuned open-loop
control strategy. In comparison with the carefully tuned rule-based control and
certainty equivalent model predictive control, the proposed DDRMPC approach can
significantly reduce the total water consumption and improve the control
performance.
