65 research outputs found
Wasserstein Distributionally Robust Control of Partially Observable Linear Systems: Tractable Approximation and Performance Guarantee
Wasserstein distributionally robust control (WDRC) is an effective method for
addressing inaccurate distribution information about disturbances in stochastic
systems. It provides various salient features, such as an out-of-sample
performance guarantee, while most of existing methods use full-state
observations. In this paper, we develop a computationally tractable WDRC method
for discrete-time partially observable linear-quadratic (LQ) control problems.
The key idea is to reformulate the WDRC problem as a novel minimax control
problem with an approximate Wasserstein penalty. We derive a closed-form
expression of the optimal solution to the approximate problem using a
nontrivial Riccati equation. We further show the guaranteed cost property of
the resulting controller and identify a provable bound for the optimality gap.
Finally, we evaluate the performance of our method through numerical
experiments using both Gaussian and non-Gaussian disturbances
Structured ambiguity sets for distributionally robust optimization
Distributionally robust optimization (DRO) incorporates robustness against
uncertainty in the specification of probabilistic models. This paper focuses on
mitigating the curse of dimensionality in data-driven DRO problems with optimal
transport ambiguity sets. By exploiting independence across lower-dimensional
components of the uncertainty, we construct structured ambiguity sets that
exhibit a faster shrinkage as the number of collected samples increases. This
narrows down the plausible models of the data-generating distribution and
mitigates the conservativeness that the decisions of DRO problems over such
ambiguity sets may face. We establish statistical guarantees for these
structured ambiguity sets and provide dual reformulations of their associated
DRO problems for a wide range of objective functions. The benefits of the
approach are demonstrated in a numerical example
Data-driven Distributionally Robust Optimal Stochastic Control Using the Wasserstein Metric
Optimal control of a stochastic dynamical system usually requires a good
dynamical model with probability distributions, which is difficult to obtain
due to limited measurements and/or complicated dynamics. To solve it, this work
proposes a data-driven distributionally robust control framework with the
Wasserstein metric via a constrained two-player zero-sum Markov game, where the
adversarial player selects the probability distribution from a Wasserstein ball
centered at an empirical distribution. Then, the game is approached by its
penalized version, an optimal stabilizing solution of which is derived
explicitly in a linear structure under the Riccati-type iterations. Moreover,
we design a model-free Q-learning algorithm with global convergence to learn
the optimal controller. Finally, we verify the effectiveness of the proposed
learning algorithm and demonstrate its robustness to the probability
distribution errors via numerical examples
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