Showing papers by "Eric Chu published in 2012"
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TL;DR: A decentralized method for solving a network of devices, each with its own dynamic constraints and objective, connected by lossy capacitated lines, which is fast enough that even a serial implementation can solve substantial problems in reasonable time frames.
Abstract: We consider a network of devices, such as generators, fixed loads, deferrable loads, and storage devices, each with its own dynamic constraints and objective, connected by lossy capacitated lines. The problem is to minimize the total network objective subject to the device and line constraints, over a given time horizon. This is a large optimization problem, with variables for consumption or generation in each time period for each device. In this paper we develop a decentralized method for solving this problem. The method is iterative: At each step, each device exchanges simple messages with its neighbors in the network and then solves its own optimization problem, minimizing its own objective function, augmented by a term determined by the messages it has received. We show that this message passing method converges to a solution when the device objective and constraints are convex. The method is completely decentralized, and needs no global coordination other than synchronizing iterations; the problems to be solved by each device can typically be solved extremely efficiently and in parallel. The method is fast enough that even a serial implementation can solve substantial problems in reasonable time frames. We report results for several numerical experiments, demonstrating the method’s speed and scaling, including the solution of a problem instance with over 30 million variables in 52 minutes for a serial implementation; with decentralized computing, the solve time would be less than one second.
63 citations
01 Dec 2012
TL;DR: Using an insight into the constrained solution structure for the growing horizon, a very accurate iterative update of the arrival cost in the MHE solution is developed.
Abstract: This paper considers moving horizon estimation (MHE) approach to solution of staged quadratic programming (QP) problems Using an insight into the constrained solution structure for the growing horizon, we develop a very accurate iterative update of the arrival cost in the MHE solution The update uses a quadratic approximation of the arrival cost and information about the previously active or inactive constraints In the absence of constraints, the update is the familiar Kalman filter in information form In the presence of the constraints, the update requires solving a sequence of linear systems with varying size The proposed MHE update provides very good performance in numerical examples This includes problems with l 1 regularization where optimal estimation allows us to perform online segmentation of streaming data
10 citations
TL;DR: It is shown that eigenvalues are not generically excluded from the unit circle, thus occurring quite often, except for the complex transpose case when P n is complex and M* ≡ M T.
Abstract: We consider the occurrence of unimodular eigenvalues for palindromic eigenvalue problems associated with the matrix polynomial where A i *= A n − i with M * ≡ M T, M H or . From the properties of palindromic eigenvalues and their characteristic polynomials, we show that eigenvalues are not generically excluded from the unit circle, thus occurring quite often, except for the complex transpose case when P n is complex and M * ≡ M T. This behaviour is observed in numerical simulations and has important implications on several applications such as the vibration of fast trains, surface acoustic wave filters, stability of time-delay systems and crack modelling.
2 citations