Control Applications

Convergence and Convergence Rate of Stochastic Gradient Search in the Case of Multiple and Non-Isolated Extrema

  • Vladislav B. Tadic
    • Categories Control Applications, Stochastic Programming Tags , , , , ,

    The asymptotic behavior of stochastic gradient algorithms is studied. Relying on some results of differential geometry (Lojasiewicz gradient inequality), the almost sure point-convergence is demonstrated and relatively tight almost sure bounds on the convergence rate are derived. In sharp contrast to all existing result of this kind, the asymptotic results obtained here do not require … Read more

    Real-Time Optimization as a Generalized Equation

  • Mihai Anitescu
  • Victor M. Zavala
    • Categories Complementarity and Variational Inequalities, Control Applications, Nonlinear Optimization Tags , , , ,

    We establish results for the problem of tracking a time-dependent manifold arising in online nonlinear programming by casting this as a generalized equation. We demonstrate that if points along a solution manifold are consistently strongly regular, it is possible to track the manifold approximately by solving a linear complementarity problem (LCP) at each time step. … Read more

    Rank-Sparsity Incoherence for Matrix Decomposition

  • Venkat Chandrasekaran
  • Pablo A. Parrilo
  • Sujay Sanghavi
  • Alan S. Willsky
    • Categories Control Applications, Convex Optimization, Statistics Tags , , , , , , ,

    Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of applications in model and system identification, and is NP-hard in general. In this … Read more

    Convergence Rate of Stochastic Gradient Search in the Case of Multiple and Non-Isolated Minima

  • Vladislav B. Tadic
    • Categories Control Applications, Statistics, Stochastic Programming Tags , , , , , , , ,

    The convergence rate of stochastic gradient search is analyzed in this paper. Using arguments based on differential geometry and Lojasiewicz inequalities, tight bounds on the convergence rate of general stochastic gradient algorithms are derived. As opposed to the existing results, the results presented in this paper allow the objective function to have multiple, non-isolated minima, … Read more

    Optimal Security Response to Attacks on Open Science Grids

  • Mine Altunay
  • Sven Leyffer
  • Jeff Linderoth
  • Zhen Xie
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Control Applications Tags , , , ,

    Cybersecurity is a growing concern, especially in open grids, where attack propagation is easy because of prevalent collaborations among thousands of users and hundreds of institutions. The collaboration rules that typically govern large science experiments as well as social networks of scientists span across the institutional security boundaries. A common concern is that the increased … Read more

    On-Line Economic Optimization of Energy Systems Using Weather Forecast Information

  • Mihai Anitescu
  • Emil M. Constantinescu
  • Victor M. Zavala
  • Theodore Krause
    • Categories Chemical Engineering, Control Applications, Stochastic Programming Tags , , , , ,

    We establish an on-line optimization framework to exploit weather forecast information in the operation of energy systems. We argue that anticipating the weather conditions can lead to more proactive and cost-effective operations. The framework is based on the solution of a stochastic dynamic real-time optimization (D-RTO) problem incorporating forecasts generated from a state-of-the-art weather prediction … Read more

    The Advanced Step NMPC Controller: Optimality, Stability and Robustness

  • Lorenz T. Biegler
  • Victor M. Zavala
    • Categories Control Applications, Nonlinear Optimization, Optimization of Systems modeled by PDEs

    Widespread application of dynamic optimization with fast optimization solvers leads to increased consideration of first-principles models for nonlinear model predictive control (NMPC). However, significant barriers to this optimization-based control strategy are feedback delays and consequent loss of performance and stability due to on-line computation. To overcome these barriers, recently proposed NMPC controllers based on nonlinear … Read more

    A Fast Moving Horizon Estimation Algorithm Based on Nonlinear Programming Sensitivity

  • Lorenz T. Biegler
  • Carl D. Laird
  • Victor M. Zavala
    • Categories Control Applications, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    Moving Horizon Estimation (MHE) is an efficient optimization-based strategy for state estimation. Despite the attractiveness of this method, its application in industrial settings has been rather limited. This has been mainly due to the difficulty to solve, in real-time, the associated dynamic optimization problems. In this work, a fast MHE algorithm able to overcome this … Read more

    On the Optimal On-Line Management of Photovoltaic-Hydrogen Hybrid Energy Systems

  • Mihai Anitescu
  • Victor M. Zavala
  • Theodore Krause
    • Categories Chemical Engineering, Control Applications, Stochastic Programming Tags , , , ,

    We present an on-line management strategy for photovoltaic-hydrogen (PV-H2) hybrid energy systems. The strategy follows a receding-horizon principle and exploits solar radiation forecasts and statistics generated through a Gaussian process model. We demonstrate that incorporating forecast information can dramatically improve the reliability and economic performance of these promising energy production devices. Article Download View On … Read more

    Lipschitz behavior of the robust regularization

  • Adrian Lewis
  • C.H. Jeffrey Pang
    • Categories Control Applications, Nonsmooth Optimization, Robust Optimization Tags , , , , , , , ,

    To minimize or upper-bound the value of a function “robustly”, we might instead minimize or upper-bound the “epsilon-robust regularization”, defined as the map from a point to the maximum value of the function within an epsilon-radius. This regularization may be easy to compute: convex quadratics lead to semidefinite-representable regularizations, for example, and the spectral radius … Read more