582 research outputs found
Inverse Optimal Planning for Air Traffic Control
We envision a system that concisely describes the rules of air traffic
control, assists human operators and supports dense autonomous air traffic
around commercial airports. We develop a method to learn the rules of air
traffic control from real data as a cost function via maximum entropy inverse
reinforcement learning. This cost function is used as a penalty for a
search-based motion planning method that discretizes both the control and the
state space. We illustrate the methodology by showing that our approach can
learn to imitate the airport arrival routes and separation rules of dense
commercial air traffic. The resulting trajectories are shown to be safe,
feasible, and efficient
Planar tilting maneuver of a spacecraft: singular arcs in the minimum time problem and chattering
In this paper, we study the minimum time planar tilting maneuver of a
spacecraft, from the theoretical as well as from the numerical point of view,
with a particular focus on the chattering phenomenon. We prove that there exist
optimal chattering arcs when a singular junction occurs. Our study is based on
the Pontryagin Maximum Principle and on results by M.I. Zelikin and V.F.
Borisov. We give sufficient conditions on the initial values under which the
optimal solutions do not contain any singular arc, and are bang-bang with a
finite number of switchings. Moreover, we implement sub-optimal strategies by
replacing the chattering control with a fixed number of piecewise constant
controls. Numerical simulations illustrate our results.Comment: 43 pages, 18 figure
On Minimum-time Paths of Bounded Curvature with Position-dependent Constraints
We consider the problem of a particle traveling from an initial configuration
to a final configuration (given by a point in the plane along with a prescribed
velocity vector) in minimum time with non-homogeneous velocity and with
constraints on the minimum turning radius of the particle over multiple regions
of the state space. Necessary conditions for optimality of these paths are
derived to characterize the nature of optimal paths, both when the particle is
inside a region and when it crosses boundaries between neighboring regions.
These conditions are used to characterize families of optimal and nonoptimal
paths. Among the optimality conditions, we derive a "refraction" law at the
boundary of the regions that generalizes the so-called Snell's law of
refraction in optics to the case of paths with bounded curvature. Tools
employed to deduce our results include recent principles of optimality for
hybrid systems. The results are validated numerically.Comment: Expanded version of paper in Automatic
An Algorithmic Framework for Strategic Fair Division
We study the paradigmatic fair division problem of allocating a divisible
good among agents with heterogeneous preferences, commonly known as cake
cutting. Classical cake cutting protocols are susceptible to manipulation. Do
their strategic outcomes still guarantee fairness?
To address this question we adopt a novel algorithmic approach, by designing
a concrete computational framework for fair division---the class of Generalized
Cut and Choose (GCC) protocols}---and reasoning about the game-theoretic
properties of algorithms that operate in this model. The class of GCC protocols
includes the most important discrete cake cutting protocols, and turns out to
be compatible with the study of fair division among strategic agents. In
particular, GCC protocols are guaranteed to have approximate subgame perfect
Nash equilibria, or even exact equilibria if the protocol's tie-breaking rule
is flexible. We further observe that the (approximate) equilibria of
proportional GCC protocols---which guarantee each of the agents a
-fraction of the cake---must be (approximately) proportional. Finally, we
design a protocol in this framework with the property that its Nash equilibrium
allocations coincide with the set of (contiguous) envy-free allocations
On local martingale and its supremum: harmonic functions and beyond
We discuss certain facts involving a continuous local martingale and its
supremum . A complete characterization of -harmonic
functions is proposed. This yields an important family of martingales, the
usefulness of which is demonstrated, by means of examples involving the
Skorokhod embedding problem, bounds on the law of the supremum, or the local
time at 0, of a martingale with a fixed terminal distribution, or yet in some
Brownian penalization problems. In particular we obtain new bounds on the law
of the local time at 0, which involve the excess wealth order
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