arXiv subjects

Rajasekhar Anguluri

Publications and source records attributed to Rajasekhar Anguluri.

At least 19 recordsLinked to original sources

arXiv2026

To Erase, or Not to Erase: Robust Training-Free Concept Erasure with Preservation aware Adaptive Ranked Subspace Expansion

Concept erasure techniques (CETs) edit text-to-image diffusion models to erase undesired targets such as NSFW content or copyrighted styles, while preserving model utility on benign concepts. Current CETs face a trade-off between erasure robustness and utility: stronger edits erase the target more reliably but degrade utility on non-target concepts, and vice versa. This stems from how existing methods define what to erase and what to preserve. Many CETs rely on static concept banks specified manually, generated by LLMs, or selected by CLIP image-text similarity. Such banks do not model how prompts steer the model during denoising, leaving it vulnerable to triggers that reintroduce the target while suppressing nearby benign concepts. We present Preservation-aware Adaptive Ranked Subspace Expansion (PARSE), a training-free framework for robust concept erasure in latent diffusion models. Given a target, PARSE queries the diffusion model with classifier-free guidance to dynamically discover target-inducing erase concepts and nearby retain concepts in the model vocabulary. It then edits the cross-attention value space with a preservation-aware projection that removes target directions while leaving retain directions intact. For triggers beyond this vocabulary-indexed space, PARSE iteratively searches for re-emergence triggers by textual inversion and adaptively expands the erased subspace only when a new trigger direction does not conflict with retain semantics. We also introduce the Balanced Erasure Utility Score (BEUS), which combines robustness (ASR under multiple attacks) and utility preservation (FID) via bounded monotone transforms and harmonic mean aggregation. Experiments on NSFW, artistic style, and object erasure, with a large-scale robustness-utility analysis over many CET baselines, show that PARSE erases multiple concepts robustly without sacrificing post-edit utility.

cs.CV↗

arXiv2026

A Constrained Formulation for Simultaneous Line Parameter Estimation and Instrument Transformer Calibration

The process of calibrating instrument transformers (ITs) has been greatly simplified by using phasor measurement unit (PMU) data since this process eliminates the need for (a) additional hardware, and (b) taking ITs offline. However, such simplification comes at the cost of knowing the line parameters, whose estimation using PMU data in turn requires calibrated ITs. To solve this interdependency problem, we propose a novel framework that incorporates power system domain knowledge as constraints to perform simultaneous line parameter estimation and IT calibration. We demonstrate the effectiveness of our approach with simulated and real PMU data as well as for a power system application that uses both PMU data and line parameter information.

eess.SY↗

arXiv2025

Alternating Minimization for Time-Shifted Synergy Extraction in Human Hand Coordination

Identifying motor synergies -- coordinated hand joint patterns activated at task-dependent time shifts -- from kinematic data is central to motor control and robotics. Existing two-stage methods first extract candidate waveforms (via SVD) and then select shifted templates using sparse optimization, requiring at least two datasets and complicating data collection. We introduce an optimization-based framework that jointly learns a small set of synergies and their sparse activation coefficients. The formulation enforces group sparsity for synergy selection and element-wise sparsity for activation timing. We develop an alternating minimization method in which coefficient updates decouple across tasks and synergy updates reduce to regularized least-squares problems. Our approach requires only a single data set, and simulations show accurate velocity reconstruction with compact, interpretable synergies.

cs.RO↗

arXiv2025

State-Derivative Feedback Control for Damping Low-Frequency Oscillations in Bulk Power Systems

Low-frequency oscillations remain a major challenge in bulk power systems with high renewable penetration, long lines, and large loads. Existing damping strategies based on power modulation of high voltage DC (HVDC) or energy storage, are often limited by fixed control architectures, leaving some modes poorly damped. This paper introduces a state-derivative feedback (SDF) damping controller that uses both frequency and its rate of change as feedback signals. Incorporating state derivatives enhances modal damping and accelerates frequency recovery, enabling HVDC and energy storage to effectively stabilize the grid. We evaluate the SDF controller on two- and three-area systems and compare performance with a frequency difference-based damping scheme. Results show that the SDF control reproduces state-feedback performance while providing good damping of both inter- and intra-area oscillations compared to the frequency-difference method, highlighting its potential as a practical solution for stabilizing power-electronics-rich grids.

eess.SY↗

arXiv2025

Laplacian Flows in Complex-valued Directed Networks: Analysis, Design, and Consensus

In the interdisciplinary field of network science, a complex-valued network, with edges assigned complex weights, provides a more nuanced representation of relationships by capturing both the magnitude and phase of interactions. Additionally, an important application of this setting arises in distribution power grids. Motivated by the richer framework, we study the necessary and sufficient conditions for achieving consensus in both strongly and weakly connected digraphs. The paper establishes that complex-valued Laplacian flows converge to consensus subject to an additional constraint termed as real dominance which relies on the phase angles of the edge weights. Our approach builds on the complex Perron-Frobenius properties to study the spectral properties of the Laplacian and its relation to graphical conditions. Finally, we propose modified flows that guarantee consensus even if the original network does not converge to consensus. Additionally, we explore diffusion in complex-valued networks as a dual process of consensus and simulate our results on synthetic and real-world networks.

eess.SY↗

arXiv2025

A Practical Approach Towards Inertia Estimation Using Ambient Synchrophasor Data

Real-time tracking of inertia is important because it reflects the power system's ability to withstand contingencies and maintain frequency security. This paper proposes a practical approach to estimate inertia using ambient phasor measurement unit (PMU) data and a partitioned form of the swing equation. The approach accounts for (bounded) uncertainties in network parameters and PMU measurements, enabling precise estimation of inertia and damping constants, as well as mechanical power inputs. Instead of assuming constant mechanical power input throughout, the approach leverages knowledge of power system operations to determine intervals when it is actually constant to maintain estimation consistency. Simulation results on the IEEE 14-bus system and IEEE 39 bus system integrated with renewable energy sources affirm the method's accuracy and applicability.

eess.SY↗

arXiv2025

Mode Participation and Inter-Area-Observability Blocking Controllers for Power Networks

In recent papers [1] and [2], the second author developed full-state feedback controllers for networked systems to block the observability and controllability of certain remote nodes. In this paper, we build on these control schemes to an interconnected power system with the aims of blocking (i) mode participation factors and (ii) inter-area mode observability in tie-line power flow measurements. Since participation factors depend on both controllable and observable eigenvectors, the control techniques from the cited works must be carefully tailored to this setting. Our research is motivated by cyber-security concerns in power systems, where an adversary aims to deceive the operator by tampering the system's modal content. We present extensive numerical results on a 3-machine, 9-bus system and a 16-machine, 68-bus system.

math.OC↗

arXiv2025

Structure Learning via ADMM in Networks obeying Conservation Laws

Learning the edge connectivity structure of networked systems from limited data is a fundamental challenge in many critical infrastructure domains, including power, traffic, and finance. Such systems obey steady-state conservation laws: x = L*y, where x and y represent injected flows (inputs) and potentials (outputs), respectively. The sparsity pattern of the pxp Laplacian L* encodes the underlying edge structure. In a stochastic setting, the goal is to infer this sparsity pattern from zero-mean i.i.d. samples of y. Recent work by \cite{rayas2022learning} has established statistical consistency results for this learning problem by considering an $\ell_1$-regularized maximum likelihood estimator. However, their approach did not develop a scalable algorithm but relies on solving a convex program via the CVX package. To address this gap, we propose an alternating direction method of multipliers (ADMM), which is transparent and fast. A key contribution is to demonstrate the role of an algebraic matrix Riccati equation in the primal update step of ADMM. Numerical experiments on a host of synthetic and benchmark networks, including power and water systems, show the efficiency of our method.

math.OC↗

arXiv2024

Learning Networks from Wide-Sense Stationary Stochastic Processes

Complex networked systems driven by latent inputs are common in fields like neuroscience, finance, and engineering. A key inference problem here is to learn edge connectivity from node outputs (potentials). We focus on systems governed by steady-state linear conservation laws: $X_t = {L^{\ast}}Y_{t}$, where $X_t, Y_t \in \mathbb{R}^p$ denote inputs and potentials, respectively, and the sparsity pattern of the $p \times p$ Laplacian $L^{\ast}$ encodes the edge structure. Assuming $X_t$ to be a wide-sense stationary stochastic process with a known spectral density matrix, we learn the support of $L^{\ast}$ from temporally correlated samples of $Y_t$ via an $\ell_1$-regularized Whittle's maximum likelihood estimator (MLE). The regularization is particularly useful for learning large-scale networks in the high-dimensional setting where the network size $p$ significantly exceeds the number of samples $n$. We show that the MLE problem is strictly convex, admitting a unique solution. Under a novel mutual incoherence condition and certain sufficient conditions on $(n, p, d)$, we show that the ML estimate recovers the sparsity pattern of $L^\ast$ with high probability, where $d$ is the maximum degree of the graph underlying $L^{\ast}$. We provide recovery guarantees for $L^\ast$ in element-wise maximum, Frobenius, and operator norms. Finally, we complement our theoretical results with several simulation studies on synthetic and benchmark datasets, including engineered systems (power and water networks), and real-world datasets from neural systems (such as the human brain).

stat.ML↗

arXiv2024

Are the flows of complex-valued Laplacians and their pseudoinverses related?

Laplacian flows model the rate of change of each node's state as being proportional to the difference between its value and that of its neighbors. Typically, these flows capture diffusion or synchronization dynamics and are well-studied. Expanding on these classical flows, we introduce a pseudoinverse Laplacian flow system, substituting the Laplacian with its pseudoinverse within complex-valued networks. Interestingly, for undirected graphs and unsigned weight-balanced digraphs, Laplacian and the pseudoinverse Laplacian flows exhibit an interdependence in terms of consensus. To show this relation, we first present the conditions for achieving consensus in the pseudoinverse Laplacian flow system using the property of real eventually exponentially positivity. Thereafter, we show that the pseudoinverse Laplacian flow system converges to consensus if and only if the Laplacian flow system achieves consensus in the above-mentioned networks. However, these are only the sufficient conditions for digraphs. Further, we illustrate the efficacy of the proposed approach through examples, focusing primarily on power networks.

eess.SY↗

arXiv2024

Real Eventual Exponential Positivity of Complex-valued Laplacians: Applications to Consensus in Multi-agent Systems

In this paper, we explore the property of eventual exponential positivity (EEP) in complex matrices. We show that this property holds for the real part of the matrix exponential for a certain class of complex matrices. Next, we present the relation between the spectral properties of the Laplacian matrix of an unsigned digraph with complex edge-weights and the property of real EEP. Finally, we show that the Laplacian flow system of a network is stable when the negated Laplacian admits real EEP. Numerical examples are presented to demonstrate the results.

eess.SY↗

arXiv2024

Resilient Infrastructure Network: Sparse Edge Change Identification via L1-Regularized Least Squares

Adversarial actions and a rapid climate change are disrupting operations of infrastructure networks (e.g., energy, water, and transportation systems). Unaddressed disruptions lead to system-wide shutdowns, emphasizing the need for quick and robust identification methods. One significant disruption arises from edge changes (addition or deletion) in networks. We present an $\ell_1$-norm regularized least-squares framework to identify multiple but sparse edge changes using noisy data. We focus only on networks that obey equilibrium equations, as commonly observed in the above sectors. The presence or lack of edges in these networks is captured by the sparsity pattern of the weighted, symmetric Laplacian matrix, while noisy data are node injections and potentials. Our proposed framework systematically leverages the inherent structure within the Laplacian matrix, effectively avoiding overparameterization. We demonstrate the robustness and efficacy of the proposed approach through a series of representative examples, with a primary emphasis on power networks.

cs.SI↗

arXiv2024

Localizing Single and Multiple Oscillatory Sources: A Frequency Divider Approach

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.

stat.AP↗

arXiv2024

Model Predictive Control for Joint Ramping and Regulation-Type Service from Distributed Energy Resource Aggregations

Distributed energy resources (DERs) such as grid-responsive loads and batteries can be harnessed to provide ramping and regulation services across the grid. This paper concerns the problem of optimal allocation of different classes of DERs, where each class is an aggregation of similar DERs, to balance net-demand forecasts. The resulting resource allocation problem is solved using model-predictive control (MPC) that utilizes a rolling sequence of finite time-horizon constrained optimizations. This is based on the concept that we have more accurate estimates of the load forecast in the short term, so each optimization in the rolling sequence of optimization problems uses more accurate short term load forecasts while ensuring satisfaction of capacity and dynamical constraints. Simulations demonstrate that the MPC solution can indeed reduce the ramping required from bulk generation, while mitigating near-real time grid disturbances.

eess.SY↗

arXiv2023

Differential Analysis for Networks Obeying Conservation Laws

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.

eess.SY↗

arXiv2022

Robust Model Selection of Gaussian Graphical Models

In Gaussian graphical model selection, noise-corrupted samples present significant challenges. It is known that even minimal amounts of noise can obscure the underlying structure, leading to fundamental identifiability issues. A recent line of work addressing this "robust model selection" problem narrows its focus to tree-structured graphical models. Even within this specific class of models, exact structure recovery is shown to be impossible. However, several algorithms have been developed that are known to provably recover the underlying tree-structure up to an (unavoidable) equivalence class. In this paper, we extend these results beyond tree-structured graphs. We first characterize the equivalence class up to which general graphs can be recovered in the presence of noise. Despite the inherent ambiguity (which we prove is unavoidable), the structure that can be recovered reveals local clustering information and global connectivity patterns in the underlying model. Such information is useful in a range of real-world problems, including power grids, social networks, protein-protein interactions, and neural structures. We then propose an algorithm which provably recovers the underlying graph up to the identified ambiguity. We further provide finite sample guarantees in the high-dimensional regime for our algorithm and validate our results through numerical simulations.

stat.ML↗

arXiv2022

Parameter Estimation in Ill-conditioned Low-inertia Power Systems

This paper examines model parameter estimation in dynamic power systems whose governing electro-mechanical equations are ill-conditioned or singular. This ill-conditioning is because of converter-interfaced power systems generators' zero or small inertia contribution. Consequently, the overall system inertia decreases, resulting in low-inertia power systems. We show that the standard state-space model based on least squares or subspace estimators fails to exist for these models. We overcome this challenge by considering a least-squares estimator directly on the coupled swing-equation model but not on its transformed first-order state-space form. We specifically focus on estimating inertia (mechanical and virtual) and damping constants, although our method is general enough for estimating other parameters. Our theoretical analysis highlights the role of network topology on the parameter estimates of an individual generator. For generators with greater connectivity, estimation of the associated parameters is more susceptible to variations in other generator states. Furthermore, we numerically show that estimating the parameters by ignoring their ill-conditioning aspects yields highly unreliable results.

eess.SY↗

arXiv2022

Controllability of Coarsely Measured Networked Linear Dynamical Systems (Extended Version)

We consider the controllability of large-scale linear networked dynamical systems when complete knowledge of network structure is unavailable and knowledge is limited to coarse summaries. We provide conditions under which average controllability of the fine-scale system can be well approximated by average controllability of the (synthesized, reduced-order) coarse-scale system. To this end, we require knowledge of some inherent parametric structure of the fine-scale network that makes this type of approximation possible. Therefore, we assume that the underlying fine-scale network is generated by the stochastic block model (SBM) -- often studied in community detection. We then provide an algorithm that directly estimates the average controllability of the fine-scale system using a coarse summary of SBM. Our analysis indicates the necessity of underlying structure (e.g., in-built communities) to be able to quantify accurately the controllability from coarsely characterized networked dynamics. We also compare our method to that of the reduced-order method and highlight the regimes where both can outperform each other. Finally, we provide simulations to confirm our theoretical results for different scalings of network size and density, and the parameter that captures how much community-structure is retained in the coarse summary.

eess.SY↗