Department of Electrical & Systems Engineering

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  • Publication
    Joint Metering and Conflict Resolution in Air Traffic Control
    (2010-11-28) Le Ny, Jerome; Pappas, George J
    This 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.
  • Publication
    Real-time Heart Model for Implantable Cardiac Device Validation and Verification
    (2010-01-20) Jiang, Zhihao; Pajic, Miroslav; Connolly, Allison T; Dixit, Sanjay; Mangharam, Rahul
    Designing bug-free medical device software is dif- ficult, especially in complex implantable devices that may be used in unanticipated contexts. Safety recalls of pacemakers and implantable cardioverter defibrillators due to firmware problems between 1990 and 2000 affected over 200,000 devices, comprising 41% of the devices recalled and are increasing in frequency. There is currently no formal methodology or open experimental platform to validate and verify the correct operation of medical device software. To this effect, a real-time Virtual Heart Model (VHM) has been developed to model the electrophysiological operation of the functioning (i.e. during normal sinus rhythm) and malfunctioning (i.e. during arrhythmia) heart. We present a methodology to extract timing properties of the heart to construct a timed-automata model. The platform exposes functional and formal interfaces for validation and verification of implantable cardiac devices. We demonstrate the VHM is capable of generating clinically-relevant response to intrinsic (i.e. premature stimuli) and external (i.e. artificial pacemaker) signals for a variety of common arrhythmias. By connecting the VHM with a pacemaker model, we are able to pace and synchronize the heart during the onset of irregular heart rhythms. The VHM has also been implemented on a hardware platform for closed-loop experimentation with existing and virtual medical devices. The VHM allows for exploratory electrophysiology studies for physicians to evaluate their diagnosis and determine the appropriate device therapy. This integrated functional and formal device design approach will potentially help expedite medical device certification for safer operation.
  • Publication
    Technical Report on: Comparative Design, Scaling, and Control of Appendages for Inertial Reorientation
    (2016-09-01) Libby, Thomas; Johnson, Aaron; Full, R J; Koditschek, Daniel E.; Chang-Siu, Evan
  • Publication
    Towards a method for obstacle porosity classification
    (2014-01-01) Roberts, Sonia F
  • Publication
    Functionality-rich Versus Minimalist Platforms: A Two-sided Market Analysis
    (2011-07-24) Sen, Soumya; Guérin, Roch A; Hosanagar, Kartik
    Should a new ``platform'' target a functionality-rich but complex andexpensive design or instead opt for a bare-bone but cheaper one? This is afundamental question with profound implications for the eventual success ofany platform. A general answer is, however, elusive as it involves a complextrade-off between benefits and costs. The intent of this paper is tointroduce an approach based on standard tools from the fields of marketing andeconomics, which can offer some insight into this difficult question. Wedemonstrate its applicability by developing and solving a generic model thatincorporates key interactions between platform stakeholders. The solutionconfirms that the ``optimal'' number of features a platform should offerstrongly depends on variations in cost factors. More interestingly, it revealsa high sensitivity to small relative changes in those costs. The paper'scontribution and motivation are in establishing the potential of such across-disciplinary approach for providing qualitative and quantitativeinsights into the complex question of platform design.
  • Publication
    Always Acyclic Distributed Path Computation
    (2008-05-20) Guérin, Roch A; Ray, Saikat; Kwong, Kin-Wah (Eric); Sofia, Rute
    Distributed routing algorithms may give rise to transient loops during path recomputation, which can pose significant stability problems in high-speed networks. We present a new algorithm, Distributed Path Computation with Intermediate Variables (DIV), which can be combined with any distributed routing algorithm to guarantee that the directed graph induced by the routing decisions remains acyclic at all times. The key contribution of DIV, besides its ability to operate with any routing algorithm, is an update mechanism using simple message exchanges between neighboring nodes that guarantees loop-freedom at all times. DIV provably outperforms existing loop-prevention algorithms in several key metrics such as frequency of synchronous updates and the ability to maintain paths during transitions. Simulation results quantifying these gains in the context of shortest path routing are presented. In addition, DIV's universal applicability is illustrated by studying its use with a routing that operates according to a non-shortest path objective. Specifically, the routing seeks robustness against failures by maximizing the number of next-hops available at each node for each destination.
  • Publication
    DTIME: Discrete Topological Imaging for Multipath Environments
    (2010-08-01) Ghrist, Robert; Owen, H.; Robinson, Michael
    This report is presented to summarize work completed under a DARPA seedling project for the imaging of urban environments, using radio multipath measurements and topology extraction algorithms. This report provides an overview of the mathematical theory behind the work, as well as a description of the simulation and results that accompanies the theory.
  • Publication
    Feedback Control of the National Airspace System
    (2010-06-17) LE NY, Jerome; Balakrishnan, Hamsa
    This 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.
  • Publication
    Adaptive Robot Deployment Algorithms
    (2010-03-25) LE NY, Jerome; Pappas, George J
    In 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.
  • Publication
    Discovering Reduced-Order Dynamical Models From Data
    (2022-04-27) Qian, William; Chaudhari, Pratik A
    This work explores theoretical and computational principles for data-driven discovery of reduced-order models of physical phenomena. We begin by describing the theoretical underpinnings of multi-parameter models through the lens of information geometry. We then explore the behavior of paradigmatic models in statistical physics, including the diffusion equation and the Ising model. In particular, we explore how coarse-graining a system affects the local and global geometry of a “model manifold” which is the set of all models that could be fit using data from the system. We emphasize connections of this idea to ideas in machine learning. Finally, we employ coarse-graining techniques to discover partial differential equations from data. We extend the approach to modeling ensembles of microscopic observables, and attempt to learn the macroscopic dynamics underlying such systems. We conclude each analysis with a computational exploration of how the geometry of learned model manifolds changes as the observed data undergoes different levels of coarse-graining.