13,873 research outputs found
Robust Model Predictive Control via Scenario Optimization
This paper discusses a novel probabilistic approach for the design of robust
model predictive control (MPC) laws for discrete-time linear systems affected
by parametric uncertainty and additive disturbances. The proposed technique is
based on the iterated solution, at each step, of a finite-horizon optimal
control problem (FHOCP) that takes into account a suitable number of randomly
extracted scenarios of uncertainty and disturbances, followed by a specific
command selection rule implemented in a receding horizon fashion. The scenario
FHOCP is always convex, also when the uncertain parameters and disturbance
belong to non-convex sets, and irrespective of how the model uncertainty
influences the system's matrices. Moreover, the computational complexity of the
proposed approach does not depend on the uncertainty/disturbance dimensions,
and scales quadratically with the control horizon. The main result in this
paper is related to the analysis of the closed loop system under
receding-horizon implementation of the scenario FHOCP, and essentially states
that the devised control law guarantees constraint satisfaction at each step
with some a-priori assigned probability p, while the system's state reaches the
target set either asymptotically, or in finite time with probability at least
p. The proposed method may be a valid alternative when other existing
techniques, either deterministic or stochastic, are not directly usable due to
excessive conservatism or to numerical intractability caused by lack of
convexity of the robust or chance-constrained optimization problem.Comment: This manuscript is a preprint of a paper accepted for publication in
the IEEE Transactions on Automatic Control, with DOI:
10.1109/TAC.2012.2203054, and is subject to IEEE copyright. The copy of
record will be available at http://ieeexplore.ieee.or
Stochastic Optimal Power Flow Based on Data-Driven Distributionally Robust Optimization
We propose a data-driven method to solve a stochastic optimal power flow
(OPF) problem based on limited information about forecast error distributions.
The objective is to determine power schedules for controllable devices in a
power network to balance operation cost and conditional value-at-risk (CVaR) of
device and network constraint violations. These decisions include scheduled
power output adjustments and reserve policies, which specify planned reactions
to forecast errors in order to accommodate fluctuating renewable energy
sources. Instead of assuming the uncertainties across the networks follow
prescribed probability distributions, we assume the distributions are only
observable through a finite training dataset. By utilizing the Wasserstein
metric to quantify differences between the empirical data-based distribution
and the real data-generating distribution, we formulate a distributionally
robust optimization OPF problem to search for power schedules and reserve
policies that are robust to sampling errors inherent in the dataset. A simple
numerical example illustrates inherent tradeoffs between operation cost and
risk of constraint violation, and we show how our proposed method offers a
data-driven framework to balance these objectives
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