42,299 research outputs found
Decomposition and Mean-Field Approach to Mixed Integer Optimal Compensation Problems
Mixed integer optimal compensation deals with optimization problems with integer- and real-valued control variables to compensate disturbances in dynamic systems. The mixed integer nature of controls could lead to intractability in problems of large dimensions. To address this challenge, we introduce a decomposition method which turns the original n-dimensional optimization problem into n independent scalar problems of lot sizing form. Each of these problems can be viewed as a two-player zero-sum game, which introduces some element of conservatism. Each scalar problem is then reformulated as a shortest path one and solved through linear programming over a receding horizon, a step that mirrors a standard procedure in mixed integer programming. We apply the decomposition method to a mean-field coupled multi-agent system problem, where each agent seeks to compensate a combination of an exogenous signal and the local state average. We discuss a large population mean-field type of approximation and extend our study to opinion dynamics in social networks as a special case of interest
Real-Time Predictive Modeling and Robust Avoidance of Pedestrians with Uncertain, Changing Intentions
To plan safe trajectories in urban environments, autonomous vehicles must be
able to quickly assess the future intentions of dynamic agents. Pedestrians are
particularly challenging to model, as their motion patterns are often uncertain
and/or unknown a priori. This paper presents a novel changepoint detection and
clustering algorithm that, when coupled with offline unsupervised learning of a
Gaussian process mixture model (DPGP), enables quick detection of changes in
intent and online learning of motion patterns not seen in prior training data.
The resulting long-term movement predictions demonstrate improved accuracy
relative to offline learning alone, in terms of both intent and trajectory
prediction. By embedding these predictions within a chance-constrained motion
planner, trajectories which are probabilistically safe to pedestrian motions
can be identified in real-time. Hardware experiments demonstrate that this
approach can accurately predict pedestrian motion patterns from onboard
sensor/perception data and facilitate robust navigation within a dynamic
environment.Comment: Submitted to 2014 International Workshop on the Algorithmic
Foundations of Robotic
The shape of disorder broadened Landau subbands in graphene
Density of states (DOS) of graphene under a high uniform magnetic field and
white-noise random potential is numerically calculated. The disorder broadened
zero-energy Landau band has a Gaussian shape whose width is proportional to the
random potential variance and the square root of magnetic field. Wegner-type
calculation is used to justify the results
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