A POSTERIORI ERROR CONTROL OF DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC OBSTACLE PROBLEMS

In this article, we derive an a posteriori error estimator for various discontinuous Galerkin (DG) methods that are proposed in (Wang, Han and Cheng, SIAM J. Numer. Anal., 48: 708-733, 2010) for an elliptic obstacle problem. Using a key property of DG methods, we perform the analysis in a general framework. The error estimator we have obtained for DG methods is comparable with the estimator for the conforming Galerkin (CG) finite element method. In the analysis, we construct a non-linear smoothing function mapping DG finite element space to CG finite element space and use it as a key tool. The error estimator consists of a discrete Lagrange multiplier associated with the obstacle constraint. It is shown for non-over-penalized DG methods that the discrete Lagrange multiplier is uniformly stable on non-uniform meshes. Finally, numerical results demonstrating the performance of the error estimator are presented.

STOKES' SYSTEM IN A DOMAIN WITH OSCILLATING BOUNDARY: HOMOGENIZATION AND ERROR ANALYSIS OF AN INTERIOR OPTIMAL CONTROL PROBLEM

Homogenization and error analysis of an optimal interior control problem in the framework of Stokes' system, on a domain with rapidly oscillating boundary, are the subject matters of this article. We consider a three dimensional domain constituted of a parallelepiped with a large number of rectangular cylinders at the top of it. An interior control is applied in a proper subdomain of the parallelepiped, away from the oscillating volume. We consider two types of functionals, namely a functional involving the L-2-norm of the state variable and another one involving its H-1-norm. The asymptotic analysis of optimality systems for both cases, when the cross sectional area of the rectangular cylinders tends to zero, is done here. Our major contribution is to derive error estimates for the state, the co-state and the associated pressures, in appropriate functional spaces.

A Networked Control Systems Perspective for Wide-Area Monitoring Control of Smart Power Grids

This paper presents a networked control systems (NCS) framework for wide area monitoring control of smart power grids. We consider a scenario in which wide area measurements are transmitted to controllers at remote locations. We model the effects of delays and packet dropouts due to limited communication capabilities in the grid. We also design a robust networked controller to damp wide-area oscillations based on information obtained from Wide Area Monitoring Systems (WAMS), and analyze the improvement in system stability due to networked control. With communication integration being an important feature of the smart grid, detailed consideration of the effects of communication is essential in the control design for future power systems. We believe that this work is an essential step in this direction.

Computational framework to integrate the effect of antigen recognition on disease epidemiology outcome: multi-scale approach

Human Leukocyte Antigen (HLA) plays an important role, in presenting foreign pathogens to our immune system, there by eliciting early immune responses. HLA genes are highly polymorphic, giving rise to diverse antigen presentation capability. An important factor contributing to enormous variations in individual responses to diseases is differences in their HLA profiles. The heterogeneity in allele specific disease responses decides the overall disease epidemiological outcome. Here we propose an agent based computational framework, capable of incorporating allele specific information, to analyze disease epidemiology. This framework assumes a SIR model to estimate average disease transmission and recovery rate. Using epitope prediction tool, it performs sequence based epitope detection for a given the pathogenic genome and derives an allele specific disease susceptibility index depending on the epitope detection efficiency. The allele specific disease transmission rate, that follows, is then fed to the agent based epidemiology model, to analyze the disease outcome. The methodology presented here has a potential use in understanding how a disease spreads and effective measures to control the disease.

PolyGLoT: A Polyhedral Loop Transformation Framework for a Graphical Dataflow Language

Polyhedral techniques for program transformation are now used in several proprietary and open source compilers. However, most of the research on polyhedral compilation has focused on imperative languages such as C, where the computation is specified in terms of statements with zero or more nested loops and other control structures around them. Graphical dataflow languages, where there is no notion of statements or a schedule specifying their relative execution order, have so far not been studied using a powerful transformation or optimization approach. The execution semantics and referential transparency of dataflow languages impose a different set of challenges. In this paper, we attempt to bridge this gap by presenting techniques that can be used to extract polyhedral representation from dataflow programs and to synthesize them from their equivalent polyhedral representation. We then describe PolyGLoT, a framework for automatic transformation of dataflow programs which we built using our techniques and other popular research tools such as Clan and Pluto. For the purpose of experimental evaluation, we used our tools to compile LabVIEW, one of the most widely used dataflow programming languages. Results show that dataflow programs transformed using our framework are able to outperform those compiled otherwise by up to a factor of seventeen, with a mean speed-up of 2.30x while running on an 8-core Intel system.

Optimal control analysis of the dynamic growth behavior of microorganisms

Understanding the growth behavior of microorganisms using modeling and optimization techniques is an active area of research in the fields of biochemical engineering and systems biology. In this paper, we propose a general modeling framework, based on Monad model, to model the growth of microorganisms. Utilizing the general framework, we formulate an optimal control problem with the objective of maximizing a long-term cellular goal and solve it analytically under various constraints for the growth of microorganisms in a two substrate batch environment. We investigate the relation between long term and short term cellular goals and show that the objective of maximizing cellular concentration at a fixed final time is equivalent to maximization of instantaneous growth rate. We then establish the mathematical connection between the generalized framework and optimal and cybernetic modeling frameworks and derive generalized governing dynamic equations for optimal and cybernetic models. We finally illustrate the influence of various constraints in the cybernetic modeling framework on the optimal growth behavior of microorganisms by solving several dynamic optimization problems using genetic algorithms. (C) 2014 Published by Elsevier Inc.

Broadcast Control Mechanism for Positional Consensus in Multiagent Systems

In this paper, a strategy for controlling a group of agents to achieve positional consensus is presented. The problem is constrained by the requirement that every agent must be given the same control input through a broadcast communication mechanism. Although the control command is computed using state information in a global framework, the control input is implemented by the agents in a local coordinate frame. We propose a novel linear programming (LP) formulation that is computationally less intensive than earlier proposed methods. Moreover, a random perturbation input in the control command that helps the agents to come close to each other even for a large number of agents, which was not possible with an existing strategy in the literature, is introduced. The method is extended to achieve positional consensus at a prespecified location. The effectiveness of the approach is illustrated through simulation results. A comparison between the LP approach and the existing second-order cone programming-based approach is also presented. The algorithm was successfully implemented on a robotic platform with three robots.

ANRC Hybrid Test Bed Implementation and an End-to-End Performance Characterization of Dynamic Spectrum Access

An abundance of spectrum access and sensing algorithms are available in the dynamic spectrum access (DSA) and cognitive radio (CR) literature. Often, however, the functionality and performance of such algorithms are validated against theoretical calculations using only simulations. Both the theoretical calculations and simulations come with their attendant sets of assumptions. For instance, designers of dynamic spectrum access algorithms often take spectrum sensing and rendezvous mechanisms between transmitter-receiver pairs for granted. Test bed designers, on the other hand, either customize so much of their design that it becomes difficult to replicate using commercial off the shelf (COTS) components or restrict themselves to simulation, emulation /hardware-in-Ioop (HIL), or pure hardware but not all three. Implementation studies on test beds sophisticated enough to combine the three aforementioned aspects, but at the same time can also be put together using COTS hardware and software packages are rare. In this paper we describe i) the implementation of a hybrid test bed using a previously proposed hardware agnostic system architecture ii) the implementation of DSA on this test bed, and iii) the realistic hardware and software-constrained performance of DSA. Snapshot energy detector (ED) and Cumulative Summation (CUSUM), a sequential change detection algorithm, are available for spectrum sensing and a two-way handshake mechanism in a dedicated control channel facilitates transmitter-receiver rendezvous.

Flexible implementation of power system corrective topology control

This paper proposes a novel decision making framework for optimal transmission switching satisfying the AC feasibility, stability and circuit breaker (CB) reliability requirements needed for practical implementation. The proposed framework can be employed as a corrective tool in day to day operation planning scenarios in response to potential contingencies. The switching options are determined using an efficient heuristic algorithm based on DC optimal power flow, and are presented in a multi-branch tree structure. Then, the AC feasibility and stability checks are conducted and the CB condition monitoring data are employed to perform a CB reliability and line availability assessment. Ultimately, the operator will be offered multiple AC feasible and stable switching options with associated benefits. The operator can use this information, other operating conditions not explicitly considered in the optimization, and his/her own experience to implement the best and most reliable switching action(s). The effectiveness of the proposed approach is validated on the IEEE-118 bus test system. (C) 2015 Elsevier B.V. All rights reserved.