916 research outputs found
Distributionally Robust Optimization: A Review
The concepts of risk-aversion, chance-constrained optimization, and robust
optimization have developed significantly over the last decade. Statistical
learning community has also witnessed a rapid theoretical and applied growth by
relying on these concepts. A modeling framework, called distributionally robust
optimization (DRO), has recently received significant attention in both the
operations research and statistical learning communities. This paper surveys
main concepts and contributions to DRO, and its relationships with robust
optimization, risk-aversion, chance-constrained optimization, and function
regularization
Risk-Averse Model Predictive Operation Control of Islanded Microgrids
In this paper we present a risk-averse model predictive control (MPC) scheme
for the operation of islanded microgrids with very high share of renewable
energy sources. The proposed scheme mitigates the effect of errors in the
determination of the probability distribution of renewable infeed and load.
This allows to use less complex and less accurate forecasting methods and to
formulate low-dimensional scenario-based optimisation problems which are
suitable for control applications. Additionally, the designer may trade
performance for safety by interpolating between the conventional stochastic and
worst-case MPC formulations. The presented risk-averse MPC problem is
formulated as a mixed-integer quadratically-constrained quadratic problem and
its favourable characteristics are demonstrated in a case study. This includes
a sensitivity analysis that illustrates the robustness to load and renewable
power prediction errors
Distributionally Robust Model Predictive Control with Total Variation Distance
This paper studies the problem of distributionally robust model predictive
control (MPC) using total variation distance ambiguity sets. For a
discrete-time linear system with additive disturbances, we provide a
conditional value-at-risk reformulation of the MPC optimization problem that is
distributionally robust in the expected cost and chance constraints. The
distributionally robust chance constraint is over-approximated as a tightened
chance constraint, wherein the tightening for each time step in the MPC can be
computed offline, hence reducing the computational burden. We conclude with
numerical experiments to support our results on the probabilistic guarantees
and computational efficiency
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