6,958 research outputs found
Finite Alphabet Control of Logistic Networks with Discrete Uncertainty
We consider logistic networks in which the control and disturbance inputs
take values in finite sets. We derive a necessary and sufficient condition for
the existence of robustly control invariant (hyperbox) sets. We show that a
stronger version of this condition is sufficient to guarantee robust global
attractivity, and we construct a counterexample demonstrating that it is not
necessary. Being constructive, our proofs of sufficiency allow us to extract
the corresponding robust control laws and to establish the invariance of
certain sets. Finally, we highlight parallels between our results and existing
results in the literature, and we conclude our study with two simple
illustrative examples
Event-Driven Network Model for Space Mission Optimization with High-Thrust and Low-Thrust Spacecraft
Numerous high-thrust and low-thrust space propulsion technologies have been
developed in the recent years with the goal of expanding space exploration
capabilities; however, designing and optimizing a multi-mission campaign with
both high-thrust and low-thrust propulsion options are challenging due to the
coupling between logistics mission design and trajectory evaluation.
Specifically, this computational burden arises because the deliverable mass
fraction (i.e., final-to-initial mass ratio) and time of flight for low-thrust
trajectories can can vary with the payload mass; thus, these trajectory metrics
cannot be evaluated separately from the campaign-level mission design. To
tackle this challenge, this paper develops a novel event-driven space logistics
network optimization approach using mixed-integer linear programming for space
campaign design. An example case of optimally designing a cislunar propellant
supply chain to support multiple lunar surface access missions is used to
demonstrate this new space logistics framework. The results are compared with
an existing stochastic combinatorial formulation developed for incorporating
low-thrust propulsion into space logistics design; our new approach provides
superior results in terms of cost as well as utilization of the vehicle fleet.
The event-driven space logistics network optimization method developed in this
paper can trade off cost, time, and technology in an automated manner to
optimally design space mission campaigns.Comment: 38 pages; 11 figures; Journal of Spacecraft and Rockets (Accepted);
previous version presented at the AAS/AIAA Astrodynamics Specialist
Conference, 201
Navigating Central Path with Electrical Flows: from Flows to Matchings, and Back
We present an -time algorithm for
the maximum s-t flow and the minimum s-t cut problems in directed graphs with
unit capacities. This is the first improvement over the sparse-graph case of
the long-standing time bound due to Even and
Tarjan [EvenT75]. By well-known reductions, this also establishes an
-time algorithm for the maximum-cardinality bipartite
matching problem. That, in turn, gives an improvement over the celebrated
celebrated time bound of Hopcroft and Karp [HK73] whenever the
input graph is sufficiently sparse
Strongly polynomial algorithm for a class of minimum-cost flow problems with separable convex objectives
A well-studied nonlinear extension of the minimum-cost flow problem is to
minimize the objective over feasible flows ,
where on every arc of the network, is a convex function. We give
a strongly polynomial algorithm for the case when all 's are convex
quadratic functions, settling an open problem raised e.g. by Hochbaum [1994].
We also give strongly polynomial algorithms for computing market equilibria in
Fisher markets with linear utilities and with spending constraint utilities,
that can be formulated in this framework (see Shmyrev [2009], Devanur et al.
[2011]). For the latter class this resolves an open question raised by Vazirani
[2010]. The running time is for quadratic costs,
for Fisher's markets with linear utilities and
for spending constraint utilities.
All these algorithms are presented in a common framework that addresses the
general problem setting. Whereas it is impossible to give a strongly polynomial
algorithm for the general problem even in an approximate sense (see Hochbaum
[1994]), we show that assuming the existence of certain black-box oracles, one
can give an algorithm using a strongly polynomial number of arithmetic
operations and oracle calls only. The particular algorithms can be derived by
implementing these oracles in the respective settings
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