Improved Battery Models of an Aggregation of Thermostatically Controlled Loads for Frequency Regulation

Recently it has been shown that an aggregation of Thermostatically Controlled Loads (TCLs) can be utilized to provide fast regulating reserve service for power grids and the behavior of the aggregation can be captured by a stochastic battery with dissipation. In this paper, we address two practical issues associated with the proposed battery model. First, we address clustering of a heterogeneous collection and show that by finding the optimal dissipation parameter for a given collection, one can divide these units into few clusters and improve the overall battery model. Second, we analytically characterize the impact of imposing a no-short-cycling requirement on TCLs as constraints on the ramping rate of the regulation signal. We support our theorems by providing simulation results.Comment: to appear in the 2014 American Control Conference - AC

Concentration of Measure Inequalities for Toeplitz Matrices with Applications

We derive Concentration of Measure (CoM) inequalities for randomized Toeplitz matrices. These inequalities show that the norm of a high-dimensional signal mapped by a Toeplitz matrix to a low-dimensional space concentrates around its mean with a tail probability bound that decays exponentially in the dimension of the range space divided by a quantity which is a function of the signal. For the class of sparse signals, the introduced quantity is bounded by the sparsity level of the signal. However, we observe that this bound is highly pessimistic for most sparse signals and we show that if a random distribution is imposed on the non-zero entries of the signal, the typical value of the quantity is bounded by a term that scales logarithmically in the ambient dimension. As an application of the CoM inequalities, we consider Compressive Binary Detection (CBD).Comment: Initial Submission to the IEEE Transactions on Signal Processing on December 1, 2011. Revised and Resubmitted on July 12, 201

Exact topology identification of large-scale interconnected dynamical systems from compressive observations

Abstract — In this paper, we consider the problem of identifying the exact topology of an interconnected dynamical network from a limited number of measurements of the individual nodes. Within the network graph, we assume that interconnected nodes are coupled by a discrete-time convolution process, and we explain how, given observations of the node outputs, the problem of topology identification can be cast as solving a linear inverse problem. We use the term compressive observations in the case when there is a limited number of measurements available and thus the resulting inverse problem is highly underdetermined. Inspired by the emerging field of Compressive Sensing (CS), we then show that in cases where network interconnections are suitably sparse (i.e., the network contains sufficiently few links), it is possible to perfectly identify the topology from small numbers of node observations, even though this leaves a highly underdetermined set of linear equations. This can dramatically reduce the burden of data acquisition for problems involving network identification. The main technical novelty of our approach is in casting the identification problem as the recovery of a block-sparse signal x ∈ R N from the measurements b = Ax ∈ R M with M < N, where the measurement matrix A is a block-concatenation of Toeplitz matrices. We discuss identification guarantees, introduce the notion of network coherence for the analysis of interconnected networks, and support our discussions with illustrative simulations. I

Concentration of Measure Inequalities for Compressive Toeplitz Matrices with Applications to Detection and System Identification

Abstract — In this paper, we derive concentration of measure inequalities for compressive Toeplitz matrices (having fewer rows than columns) with entries drawn from an independent and identically distributed (i.i.d.) Gaussian random sequence. These inequalities show that the norm of a vector mapped by a Toeplitz matrix to a lower dimensional space concentrates around its mean with a tail probability bound that decays exponentially in the dimension of the range space divided by a factor that is a function of the sample covariance of the vector. Motivated by the emerging field of Compressive Sensing (CS), we apply these inequalities to problems involving the analysis of high-dimensional systems from convolution-based compressive measurements. We discuss applications such as system identification, namely the estimation of the impulse response of a system, in cases where one can assume that the impulse response is high-dimensional, but sparse. We also consider the problem of detecting a change in the dynamic behavior of a system, where the change itself can be modeled by a system with a sparse impulse response. I