LE NY, Jerome
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PublicationJoint Metering and Conflict Resolution in Air Traffic Control(2010-11-28) Le Ny, Jerome; Pappas, George J; Le Ny, Jerome; Pappas, George JThis paper describes a novel optimization-based approach to conflict resolution in air traffic control, based on geometric programming. The main advantage of the approach is that Geometric Programs (GPs) can also capture various metering directives issued by the traffic flow management level, in contrast to most recent methods focusing purely on aircraft separation issues. GPs can also account for some of the nonlinearities present in the formulations of conflict resolution problems, while incurring only a small penalty in computation time with respect to the fastest linear programming based approaches. Additional integer variables can be introduced to improve the quality of the obtained solutions and handle combinatorial choices, resulting in Mixed-Integer Geometric Programs (MIGPs). We present GPs and MIGPs to solve a variety of joint metering and separation scenarios, e.g. including miles-in-trail and minutes-in-trail restrictions through airspace fixes and boundaries. Simulation results demonstrate the efficiency of the approach. PublicationClosing the Loop: A Simple Distributed Method for Control over Wireless Networks(2012-01-01) Pajic, Miroslav; Sundaram, Shreyas; LE NY, Jerome; Pappas, George J.; Mangharam, Rahul; Pajic, Miroslav; Sundaram, Shreyas; LE NY, Jerome; Pappas, George J.; Mangharam, RahulWe present a distributed scheme used for control over a network of wireless nodes. As opposed to traditional networked control schemes where the nodes simply route information to and from a dedicated controller (perhaps performing some encoding along the way), our approach, Wireless Control Network (WCN), treats the network itself as the controller. In other words, the computation of the control law is done in a fully distributed way inside the network. We extend the basic WCN strategy, where at each time-step, each node updates its internal state to be a linear combination of the states of the nodes in its neighborhood. This causes the entire network to behave as a linear dynamical system, with sparsity constraints imposed by the network topology. We demonstrate that with observer style updates, the WCN's robustness to link failures is substantially improved. Furthermore, we show how to design a WCN that can maintain stability even in cases of node failures. We also address the problem of WCN synthesis with guaranteed optimal performance of the plant, with respect to standard cost functions. We extend the synthesis procedure to deal with continuous-time plants and demonstrate how the WCN can be used on a practical, industrial application, using a process-in-the-loop setup with real hardware. PublicationThe Wireless Control Network: Synthesis and Robustness(2010-12-15) Pajic, Miroslav; Sundaram, Shreyas; Ny, Jerome Le; Pappas, George J; Mangharam, Rahul; Pajic, Miroslav; Sundaram, Shreyas; Ny, Jerome Le; Pappas, George J; Mangharam, RahulWe consider the problem of stabilizing a plant with a network of resource constrained wireless nodes. Traditional networked control schemes are designed with one of the nodes in the network acting as a dedicated controller, while the other nodes simply route information to and from the controller and the plant. We introduce the concept of a Wireless Control Network (WCN) where the entire network itself acts as the controller. Specifically, at each time-step, each node updates its internal state to be a linear combination of the states of the nodes in its neighborhood. We show that this causes the entire network to behave as a linear dynamical system, with sparsity constraints imposed by the network topology. We then provide a numerical design procedure to determine the appropriate linear combinations to be applied by each node so that the transmissions of the nodes closest to the actuators will stabilize the plant. We also show how our design procedure can be modified to maintain mean square stability under packet drops in the network. PublicationAdaptive Algorithms for Coverage Control and Space Partitioning in Mobile Robotic Networks(2010-10-25) Le Ny, Jerome; Pappas, George J; Le Ny, Jerome; Pappas, George JWe consider deployment problems where a mobile robotic network must optimize its configuration in a distributed way in order to minimize a steady-state cost function that depends on the spatial distribution of certain probabilistic events of interest. Three classes of problems are discussed in detail: coverage control problems, spatial partitioning problems, and dynamic vehicle routing problems. Moreover, we assume that the event distribution is a priori unknown, and can only be progressively inferred from the observation of the location of the actual event occurrences. For each problem we present distributed stochastic gradient algorithms that optimize the performance objective. The stochastic gradient view simplifies and generalizes previously proposed solutions, and is applicable to new complex scenarios, for example adaptive coverage involving heterogeneous agents. Finally, our algorithms often take the form of simple distributed rules that could be implemented on resource-limited platforms. PublicationAdaptive Robot Deployment Algorithms(2010-03-25) LE NY, Jerome; Pappas, George J; LE NY, Jerome; Pappas, George JIn robot deployment problems, the fundamental issue is to optimize a steady state performance measure that depends on the spatial configuration of a group of robots. For static deployment problems, a classical way of designing high- level feedback motion planners is to implement a gradient descent scheme on a suitably chosen objective function. This can lead to computationally expensive deployment algorithms that may not be adaptive to uncertain dynamic environments. We address this challenge by showing that algorithms for a variety of deployment scenarios in stochastic environments and with noisy sensor measurements can be designed as stochastic gradient descent algorithms, and their convergence properties analyzed via the theory of stochastic approximations. This approach yields often surprisingly simple algorithms that can accommodate complicated objective functions, and adapt to slow temporal variations in environmental parameters. To illustrate the richness of the framework, we discuss several applications, including searching for a field extrema, deployment with stochastic connectivity constraints, coverage, and vehicle routing scenarios. PublicationFeedback Control of the National Airspace System(2010-06-17) LE NY, Jerome; Balakrishnan, Hamsa; LE NY, Jerome; Balakrishnan, HamsaThis paper proposes a general modeling framework adapted to the feedback control of traffic flows in Eulerian models of the National Airspace System (NAS). It is shown that the problems of scheduling and routing aircraft flows in the NAS can be posed as the control of a network of queues with load-dependent service rates. We can then focus on developing techniques to ensure that the aircraft queues in each airspace sector, which are an indicator of the air traffic controller workloads, are kept small. This paper uses the proposed framework to develop control laws that help prepare the NAS for fast recovery from a weather event, given a probabilistic forecast of capacities. In particular, the model includes the management of airport arrivals and departures subject to runway capacity constraints, which are highly sensitive to weather disruptions. PublicationGeometric Programming and Mechanism Design for Air Traffic Conflict Resolution(2010-06-01) Le Ny, Jerome; Pappas, George J; Le Ny, Jerome; Pappas, George JWe develop certain extensions of optimization based conflict resolution methods in air traffic control. The problem considered concerns the scheduling of the crossing times of a set of aircraft through a metering fix, while maintaining aircraft separation. First, we show how to solve this combined path planning and scheduling problem using mixed integer geometric programming. Second, the objective function used to determine the aircraft ordering at the fix is not given a priori but needs to be obtained from the airlines, which are strategic profit maximizing agents and could lie about their true cost. In order to realign individual and global objectives, we study the use of the Clarke-Groves mechanism in this context, which aims at extracting the true utility functions from the airlines using side-payments to the FAA.