211 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
Optimal Universal Controllers for Roll Stabilization
Roll stabilization is an important problem of ship motion control. This
problem becomes especially difficult if the same set of actuators (e.g. a
single rudder) has to be used for roll stabilization and heading control of the
vessel, so that the roll stabilizing system interferes with the ship autopilot.
Finding the "trade-off" between the concurrent goals of accurate vessel
steering and roll stabilization usually reduces to an optimization problem,
which has to be solved in presence of an unknown wave disturbance. Standard
approaches to this problem (loop-shaping, LQG, -control etc.)
require to know the spectral density of the disturbance, considered to be a
\colored noise". In this paper, we propose a novel approach to optimal roll
stabilization, approximating the disturbance by a polyharmonic signal with
known frequencies yet uncertain amplitudes and phase shifts. Linear quadratic
optimization problems in presence of polyharmonic disturbances can be solved by
means of the theory of universal controllers developed by V.A. Yakubovich. An
optimal universal controller delivers the optimal solution for any uncertain
amplitudes and phases. Using Marine Systems Simulator (MSS) Toolbox that
provides a realistic vessel's model, we compare our design method with
classical approaches to optimal roll stabilization. Among three controllers
providing the same quality of yaw steering, OUC stabilizes the roll motion most
efficiently
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