Anguluri Rajasekhar

We consider robust principal component analysis (RPCA) to perform dimensionality reduction for human hand motor control based on kinematic synergies. RPCA decomposes joint angular velocity data into (i) a low-rank matrix capturing coordinated motion patterns and (ii) a sparse matrix isolating sensor artifacts. Next we apply a robust LASSO method to find synergy recruitment weights, yielding a sparse representation of hand grasping tasks. Experiments on 100 grasp trials show that RPCA maintains stable performance up to approximately 20% corruption, while classical PCA degrades quickly. Our results suggest that robustifying standard PCA and LASSO enables reliable synergy extraction even with inexpensive, low-quality sensors, supporting affordable experimentation and improved prosthetic or robotic hand control.

Localizing sources of troublesome oscillations, particularly forced oscillations (FOs), in power systems has received considerable attention over the last few years. This is driven in part by the massive deployment of phasor measurement units (PMUs) that capture these oscillations when they occur; and in part by the increasing incidents of FOs due to malfunctioning components, wind power fluctuations, and/or cyclic loads. Capitalizing on the frequency divider formula of [1], we develop methods to localize single and multiple oscillatory sources using bus frequency measurements. The method to localize a single oscillation source does not require knowledge of network parameters. However, the method for localizing FOs caused by multiple sources requires this knowledge. We explain the reasoning behind this knowledge difference as well as demonstrate the success of our methods for source localization in multiple test systems.

We study the problem of identifying changes in network systems, encompassing changes such as the addition or removal of edges and their various combinations. We focus on the systems that obey conservation laws and balance equations (e.g., Kirchoff’s laws) in which the nodal injections (inputs) are linearly related to potentials (outputs). For finite-dimensional networks, this relationship is given by the weighted Laplacian matrix, where the non-zero entries correspond to the edges. Assuming that inputs are zero-mean random vectors, we present spectral and algebraic methods to identify edge changes from the output covariance data. The spectral method requires the knowledge of input covariance data, whereas the algebraic method does not require this knowledge. Finally, we validate the performance of our proposed method on many numerical examples, including the IEEE 14 bus power system.

Networked systems that occur in various domains, such as electric networks, the brain, and opinion networks, are known to obey conservation laws. For instance, electric networks obey Kirchoff’s laws, and social networks obey opinion consensus. Conservation laws are often modeled as balance equations that relate appropriate injected flows and potentials at the nodes of the networks. A recent line of work considers the problem of estimating the unknown structure of such networked systems from observations of node potentials (and only the knowledge of the statistics of injected flows). Given the dynamic nature of the systems under consideration, an equally important task is estimating the change in the structure of the network from data – the so called differential network analysis problem. That is, given two sets of node potential observations, the goal is to estimate the structural differences between the underlying networks. We formulate this novel differential network analysis problem for systems obeying conservation laws and devise a convex estimator to learn the edge changes directly from node potentials. We derive conditions under which the estimate is unique in the highdimensional regime and devise an efficient ADMM-based approach to perform the estimation. Finally, we demonstrate the performance of our approach on synthetic and benchmark power network data.

This paper studies the problem of locating the sparse set of sources of forcing inputs driving linear systems from noisy measurements when the initial state is unknown. This problem is particularly relevant to detecting forced oscillations in electric power networks. We express measurements as an additive model comprising the initial state and inputs grouped over time, both expanded in terms of the basis functions (i.e., impulse response coefficients). Using this model, with probabilistic guarantees, we recover the locations and simultaneously estimate the initial state and forcing inputs using a variant of the group LASSO (linear absolute shrinkage and selection operator) method. Specifically, we provide upper bounds on: (i) the probability that the group LASSO estimator incorrectly identifies the locations and (ii) the $\ell _{2}$ -norm of the estimation error. Our bounds depend on the number of measurements, inputs, and sensors; the sensor noise variance; and the minimum singular value of the observability and impulse response matrices. Our theoretical analysis is one of the first to provide a complete treatment for the group LASSO estimator for the left invertible linear systems with delay. Finally, we validate the performance of the estimator on synthetic models and the IEEE 68-bus, 16-machine power system.

Networked systems that occur in various domains, such as the power grid, the brain, and opinion networks, are known to obey conservation laws. For instance, electric networks obey Kirchoff's laws, and social networks display opinion consensus. Such conservation laws are often modeled as balance equations that relate appropriate injected flows and potentials at the nodes of the networks. A recent line of work considers the problem of estimating the unknown structure of such networked systems from observations of node potentials (and only the knowledge of the statistics of injected flows). Given the dynamic nature of the systems under consideration, an equally important task is estimating the change in the structure of the network from data -- the so called differential network analysis problem. That is, given two sets of node potential observations, the goal is to estimate the structural differences between the underlying networks. We formulate this novel differential network analysis problem for systems obeying conservation laws and devise a convex estimator to learn the edge changes directly from node potentials. We derive conditions under which the estimate is unique in the high-dimensional regime and devise an efficient ADMM-based approach to perform the estimation. Finally, we demonstrate the performance of our approach on synthetic and benchmark power network data.

We consider the problem of learning the structure underlying a Gaussian graphical model when the variables (or subsets thereof) are corrupted by independent noise. A recent line of work establishes that even for tree-structured graphical models, only partial structure recovery is possible and goes on to devise algorithms to identify the structure up to an (unavoidable) equivalence class of trees. We extend these results beyond trees and consider the model selection problem under noise for non tree-structured graphs, as tree graphs cannot model several real-world scenarios. Although unidentifiable, we show that, like the tree-structured graphs, the ambiguity is limited to an equivalence class. This limited ambiguity can help provide meaningful clustering information (even with noise), which is helpful in computer and social networks, protein-protein interaction networks, and power networks. Furthermore, we devise an algorithm based on a novel ancestral testing method for recovering the equivalence class. We complement these results with finite sample guarantees for the algorithm in the high-dimensional regime.

This letter studies a topology identification problem for an electric distribution grid using sign patterns of the inverse covariance matrix of bus voltage magnitudes and angles, while accounting for hidden buses. Assuming the grid topology is sparse and the number of hidden buses are fewer than those of the observed buses, we express the observed voltages inverse covariance matrix as the sum of three structured matrices: sparse matrix, low-rank matrix with sparse factors , and low-rank matrix . Using the sign patterns of the first two of these matrices, we develop an algorithm to identify the topology of a distribution grid with a minimum cycle length greater than three. To estimate the structured matrices from the empirical inverse covariance matrix, we formulate a novel convex optimization problem with appropriate sparsity and structured norm constraints and solve it using an alternating minimization method. We validate the proposed algorithm’s performance on a modified IEEE 33 bus system.

We consider a security problem for interconnected systems with linear, discrete, time-invariant, stochastic dynamics, where the objective is to detect exogenous attacks by processing measurements at different locations. We consider centralized and decentralized detectors, which differ primarily in their knowledge of the system model. In particular, a decentralized detector has a model of the dynamics of the isolated subsystems, but is unaware of the interconnection signals that are exchanged among subsystems. Instead, a centralized detector has a model of the entire dynamical system. We characterize the performance of the two detectors and show that, depending on the system and attack parameters, each of the detectors can outperform the other. Hence, it may be possible for the decentralized detector to outperform its centralized counterpart, despite having less information about the system dynamics, and this property is due to the nature of the considered attack detection problem (that is, a simple vs. composite hypothesis testing problem). Finally, we numerically validate our findings on a power system model.