33,143 research outputs found
Boundary conditions control for a Shallow-Water model
A variational data assimilation technique was used to estimate optimal
discretization of interpolation operators and derivatives in the nodes adjacent
to the rigid boundary. Assimilation of artificially generated observational
data in the shallow-water model in a square box and assimilation of real
observations in the model of the Black sea are discussed. It is shown in both
experiments that controlling the discretization of operators near a rigid
boundary can bring the model solution closer to observations as in the
assimilation window and beyond the window. This type of control allows also to
improve climatic variability of the model.Comment: arXiv admin note: substantial text overlap with arXiv:1112.4293,
arXiv:1112.3503, arXiv:0905.470
A residual based snapshot location strategy for POD in distributed optimal control of linear parabolic equations
In this paper we study the approximation of a distributed optimal control
problem for linear para\-bolic PDEs with model order reduction based on Proper
Orthogonal Decomposition (POD-MOR). POD-MOR is a Galerkin approach where the
basis functions are obtained upon information contained in time snapshots of
the parabolic PDE related to given input data. In the present work we show that
for POD-MOR in optimal control of parabolic equations it is important to have
knowledge about the controlled system at the right time instances. For the
determination of the time instances (snapshot locations) we propose an
a-posteriori error control concept which is based on a reformulation of the
optimality system of the underlying optimal control problem as a second order
in time and fourth order in space elliptic system which is approximated by a
space-time finite element method. Finally, we present numerical tests to
illustrate our approach and to show the effectiveness of the method in
comparison to existing approaches
Combination of direct methods and homotopy in numerical optimal control: application to the optimization of chemotherapy in cancer
We consider a state-constrained optimal control problem of a system of two
non-local partial-differential equations, which is an extension of the one
introduced in a previous work in mathematical oncology. The aim is to minimize
the tumor size through chemotherapy while avoiding the emergence of resistance
to the drugs. The numerical approach to solve the problem was the combination
of direct methods and continuation on discretization parameters, which happen
to be insufficient for the more complicated model, where diffusion is added to
account for mutations. In the present paper, we propose an approach relying on
changing the problem so that it can theoretically be solved thanks to a
Pontryagin Maximum Principle in infinite dimension. This provides an excellent
starting point for a much more reliable and efficient algorithm combining
direct methods and continuations. The global idea is new and can be thought of
as an alternative to other numerical optimal control techniques
Quantum Annealing Applied to De-Conflicting Optimal Trajectories for Air Traffic Management
We present the mapping of a class of simplified air traffic management (ATM)
problems (strategic conflict resolution) to quadratic unconstrained boolean
optimization (QUBO) problems. The mapping is performed through an original
representation of the conflict-resolution problem in terms of a conflict graph,
where nodes of the graph represent flights and edges represent a potential
conflict between flights. The representation allows a natural decomposition of
a real world instance related to wind-optimal trajectories over the Atlantic
ocean into smaller subproblems, that can be discretized and are amenable to be
programmed in quantum annealers. In the study, we tested the new programming
techniques and we benchmark the hardness of the instances using both classical
solvers and the D-Wave 2X and D-Wave 2000Q quantum chip. The preliminary
results show that for reasonable modeling choices the most challenging
subproblems which are programmable in the current devices are solved to
optimality with 99% of probability within a second of annealing time.Comment: Paper accepted for publication on: IEEE Transactions on Intelligent
Transportation System
Optimal boundary conditions at the staircase-shaped coastlines
A 4D-Var data assimilation technique is applied to the rectangular-box
configuration of the NEMO in order to identify the optimal parametrization of
boundary conditions at lateral boundaries. The case of the staircase-shaped
coastlines is studied by rotating the model grid around the center of the box.
It is shown that, in some cases, the formulation of the boundary conditions at
the exact boundary leads to appearance of exponentially growing modes while
optimal boundary conditions allow to correct the errors induced by the
staircase-like appriximation of the coastline.Comment: Submitted to Ocean Dynamics. (27/02/2014
Time-optimal Coordination of Mobile Robots along Specified Paths
In this paper, we address the problem of time-optimal coordination of mobile
robots under kinodynamic constraints along specified paths. We propose a novel
approach based on time discretization that leads to a mixed-integer linear
programming (MILP) formulation. This problem can be solved using
general-purpose MILP solvers in a reasonable time, resulting in a
resolution-optimal solution. Moreover, unlike previous work found in the
literature, our formulation allows an exact linear modeling (up to the
discretization resolution) of second-order dynamic constraints. Extensive
simulations are performed to demonstrate the effectiveness of our approach.Comment: Published in 2016 IEEE/RSJ International Conference on Intelligent
Robots and Systems (IROS
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