1,431 research outputs found
Distributionally Robust Chance Constrained Data-enabled Predictive Control
We study the problem of finite-time constrained optimal control of unknown
stochastic linear time-invariant systems, which is the key ingredient of a
predictive control algorithm -- albeit typically having access to a model. We
propose a novel distributionally robust data-enabled predictive control (DeePC)
algorithm which uses noise-corrupted input/output data to predict future
trajectories and compute optimal control inputs while satisfying output chance
constraints. The algorithm is based on (i) a non-parametric representation of
the subspace spanning the system behaviour, where past trajectories are sorted
in Page or Hankel matrices; and (ii) a distributionally robust optimization
formulation which gives rise to strong probabilistic performance guarantees. We
show that for certain objective functions, DeePC exhibits strong out-of-sample
performance, and at the same time respects constraints with high probability.
The algorithm provides an end-to-end approach to control design for unknown
stochastic linear time-invariant systems. We illustrate the closed-loop
performance of the DeePC in an aerial robotics case study
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
Data-Driven Chance Constrained Optimization under Wasserstein Ambiguity Sets
We present a data-driven approach for distributionally robust chance
constrained optimization problems (DRCCPs). We consider the case where the
decision maker has access to a finite number of samples or realizations of the
uncertainty. The chance constraint is then required to hold for all
distributions that are close to the empirical distribution constructed from the
samples (where the distance between two distributions is defined via the
Wasserstein metric). We first reformulate DRCCPs under data-driven Wasserstein
ambiguity sets and a general class of constraint functions. When the
feasibility set of the chance constraint program is replaced by its convex
inner approximation, we present a convex reformulation of the program and show
its tractability when the constraint function is affine in both the decision
variable and the uncertainty. For constraint functions concave in the
uncertainty, we show that a cutting-surface algorithm converges to an
approximate solution of the convex inner approximation of DRCCPs. Finally, for
constraint functions convex in the uncertainty, we compare the feasibility set
with other sample-based approaches for chance constrained programs.Comment: A shorter version is submitted to the American Control Conference,
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