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Murti V. Salapaka

Publications and source records attributed to Murti V. Salapaka.

At least 19 recordsLinked to original sources
arXiv2026

Large-Signal Stability Analysis of Optimization-Based Secondary Control for Distributed Energy Resources

This article develops a large-signal stability analysis for a sampled-data optimization-based secondary controller for distributed energy resources (DERs) in power systems. The induced closed loop combines nonlinear inverter power-flow dynamics, filtered active and reactive power measurements, constrained optimization updates, and interpolation-based actuation between sampling instants. We study this optimization-in-the-loop nonlinear sampled-data system beyond local linearization. The analysis provides computable bounds on the voltage, filtered reactive power, and the secondary control input. We further characterize steady-state operating points and establish how the optimizer objectives and constraints connect voltage regulation with equal per-unitized reactive power sharing. Finally, input-to-state stability of the frequency dynamics is established with respect to DER voltages and control inputs. These results provide a rigorous mathematical foundation for sampled-data optimization-based secondary control of DERs.

eess.SY↗
arXiv2026

Storage and Transport Capacity Design for a Self-Reliable Two-Node Stochastic Resource System

We study a two-node stochastic resource system operating over a finite horizon. Each node experiences uncertain supply and demand and is equipped with finite storage. The objective is to ensure that resource levels remain within prescribed limits with high probability. To this end, we formulate a chance-constrained capacity-design problem in which resources can be exchanged through a capacity-limited transport link. We characterize the minimum storage required at each node, derive the optimal transport policy, and quantify the trade-off between storage and transport capacities. Our results show the existence of a critical transport-capacity threshold that enables full risk pooling between the nodes. Moreover, this threshold decreases with the operating horizon, implying that full-pooling performance can be achieved with progressively smaller transport capacity over longer horizons.

eess.SY↗
arXiv2025

Uncovering the Influence Flow Model of Transistor Amplifiers, Its Reconstruction and Application

Multistage transistor amplifiers can be effectively modeled as network of dynamic systems where individual amplifier stages interact through couplings that are dynamic in nature. Using circuit analysis techniques, we show that a large class of transistor amplifiers can be modeled as Linear Dynamic Influence Model (LDIM), where the interactions between different amplifier stages are modeled as linear dynamic equations. LDIM modeling of transistor circuits leads to application of data-driven network reconstruction techniques to characterize stage interactions and identify faults and critical circuit parameters efficiently. Employing graphical modeling techniques and Wiener filtering, we demonstrate that the network structure can be reconstructed solely from voltage time-series measurements sampled at specified points in the circuit. The efficacy of these network reconstruction methods in multistage amplifiers is demonstrated through extensive simulations involving multiple amplifier circuits in Cadence, as well as experimental results on physical hardware. The ability to infer network structure directly from measurement data offers designers and users efficient tools to design, analyze, and debug amplifier circuits. To demonstrate the utility of network reconstruction in multistage amplifier circuits, a fault diagnosis method leveraging these techniques is presented.

eess.SY↗
arXiv2024

Guaranteeing Service in Connected Microgrids: Storage Planning and Optimal Power Sharing Policy

The integration of renewable energy sources (RES) into power distribution grids poses challenges to system reliability due to the inherent uncertainty in their power production. To address this issue, battery energy sources (BESs) are being increasingly used as a promising solution to counter the uncertainty associated with RES power production. During the overall system planning stage, the optimal capacity of the BES has to be decided. In the operational phase, policies on when to charge the BESs and when to use them to support loads must be determined so that the BES remains within its operating range, avoiding depletion of charge on one hand and remaining within acceptable margins of maximum charge on the other. In this paper, a stochastic control framework is used to determine battery capacity, for microgrids, which ensures that during the operational phase, BESs' operating range is respected with pre-specified high probability. We provide an explicit analytical expression of the required BESs energy capacity for a single microgrid with RES as the main power source. Leveraging insights from the single microgrid case, the article focuses on the design and planning of BESs for the two-microgrid scenario. In this setting, microgrids are allowed to share power while respecting the capacity constraints imposed by the power lines. We characterize the optimal power transfer policy between the microgrids and the optimal BES capacity for multiple microgrids. This provides the BES savings arising from connecting the microgrids.

eess.SY↗
arXiv2024

A Distributed Malicious Agent Detection Scheme for Resilient Power Apportioning in Microgrids

We consider the framework of distributed aggregation of Distributed Energy Resources (DERs) in power networks to provide ancillary services to the power grid. Existing aggregation schemes work under the assumption of trust and honest behavior of the DERs and can suffer when that is not the case. In this article, we develop a distributed detection scheme that allows the DERs to detect and isolate the maliciously behaving DERs. We propose a model for the maliciously behaving DERs and show that the proposed distributed scheme leads to the detection of the malicious DERs. Further, augmented with the distributed power apportioning algorithm the proposed scheme provides a framework for resilient distributed power apportioning for ancillary service dispatch in power networks. A controller-hardware-in-the-loop (CHIL) experimental setup is developed to evaluate the performance of the proposed resilient distributed power apportioning scheme on an 8-commercial building distribution network (Central Core) connected to a 55 bus distribution network (External Power Network) based on the University of Minnesota Campus. A diversity of DERs and loads are included in the network to generalize the applicability of the framework. The experimental results corroborate the efficacy of the proposed resilient distributed power apportioning for ancillary service dispatch in power networks.

eess.SY↗
arXiv2024

A Plug and Play Distributed Secondary Controller for Microgrids with Grid-Forming Inverters

A distributed controller for secondary control problems in microgrids with grid-forming (GFM) inverter-based resources (IBRs) is developed. The controller is based on distributed optimization and is synthesized and implemented distributively enabling each GFM IBR to utilize decentralized measurements and the neighborhood information in the communication network. We present a convergence analysis establishing voltage regulation and reactive power sharing properties. A controller-hardware-in-the-loop experiment is conducted to evaluate the performance of the proposed controller. The experimental results corroborate the efficacy of the proposed distributed controller for secondary control.

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arXiv2024

Distributed Difference of Convex Optimization

In this article, we focus on solving a class of distributed optimization problems involving $n$ agents with the local objective function at every agent $i$ given by the difference of two convex functions $f_i$ and $g_i$ (difference-of-convex (DC) form), where $f_i$ and $g_i$ are potentially nonsmooth. The agents communicate via a directed graph containing $n$ nodes. We create smooth approximations of the functions $f_i$ and $g_i$ and develop a distributed algorithm utilizing the gradients of the smooth surrogates and a finite-time approximate consensus protocol. We term this algorithm as DDC-Consensus. The developed DDC-Consensus algorithm allows for non-symmetric directed graph topologies and can be synthesized distributively. We establish that the DDC-Consensus algorithm converges to a stationary point of the nonconvex distributed optimization problem. The performance of the DDC-Consensus algorithm is evaluated via a simulation study to solve a nonconvex DC-regularized distributed least squares problem. The numerical results corroborate the efficacy of the proposed algorithm.

math.OC↗
arXiv2024

Information Theoretically Optimal Sample Complexity of Learning Dynamical Directed Acyclic Graphs

In this article, the optimal sample complexity of learning the underlying interactions or dependencies of a Linear Dynamical System (LDS) over a Directed Acyclic Graph (DAG) is studied. We call such a DAG underlying an LDS as dynamical DAG (DDAG). In particular, we consider a DDAG where the nodal dynamics are driven by unobserved exogenous noise sources that are wide-sense stationary (WSS) in time but are mutually uncorrelated, and have the same {power spectral density (PSD)}. Inspired by the static DAG setting, a metric and an algorithm based on the PSD matrix of the observed time series are proposed to reconstruct the DDAG. It is shown that the optimal sample complexity (or length of state trajectory) needed to learn the DDAG is $n=Θ(q\log(p/q))$, where $p$ is the number of nodes and $q$ is the maximum number of parents per node. To prove the sample complexity upper bound, a concentration bound for the PSD estimation is derived, under two different sampling strategies. A matching min-max lower bound using generalized Fano's inequality also is provided, thus showing the order optimality of the proposed algorithm.

stat.ML↗
arXiv2023

Hindering loads prompt clustered configurations that enhance stability during cargo transport by multiple Kinesin-1

Transport of intracellular cargo is often mediated by teams of molecular motors that function in a chaotic environment under varying conditions. We show that the motors have unique steady state behavior which enables transport modalities that are robust. Under reduced ATP concentrations, multi-motor configurations are preferred over single motors. Higher load force drives motors to cluster, but very high loads compel them to separate in a manner that promotes immediate cargo movement once the load subsides. These inferences, backed by analytical guarantees, provide unique insights into the coordination strategies adopted by molecular motors to transport intracellular cargo.

q-bio.SC↗
arXiv2023

Transactive Framework for Dynamic Energy Storage Allocation for Critical Load Management

Increased penetration of Distributed Energy Resources (DER) and Renewable Energy Systems (RES) transforming the conventional distribution grid into a transactive framework supervised by a distribution system operator (DSO). Although the emerging transactive energy management techniques improve the grid reliability, the inherent uncertainty of RES poses a challenge in meeting the power demand of the critical infrastructure in the microgrid unless sufficient battery energy storage is maintained. However, maintaining expensive battery storage increases the operating cost of the DSO. In this article, we propose a cost-effective dynamic resource allocation strategy to optimize the battery reserve requirement while ensuring the critical demand is met with a provable guarantee. Our proposed scheme enables the DSO to optimize the RES and battery reserve allocation to eliminate the risk of over or underproduction. We present numerical simulations under three different scenarios of multiple microgrids with uncertain renewable generation. The simulation results demonstrate the efficacy of the proposed transactive stochastic control algorithm.

eess.SY↗
arXiv2023

Causal Structure Recovery of Linear Dynamical Systems: An FFT based Approach

Learning causal effects from data is a fundamental and well-studied problem across science, especially when the cause-effect relationship is static in nature. However, causal effect is less explored when there are dynamical dependencies, i.e., when dependencies exist between entities across time. Identifying dynamic causal effects from time-series observations is computationally expensive when compared to the static scenario. We demonstrate that the computational complexity of recovering the causation structure for the vector auto-regressive (VAR) model is $O(Tn^3N^2)$, where $n$ is the number of nodes, $T$ is the number of samples, and $N$ is the largest time-lag in the dependency between entities. We report a method, with a reduced complexity of $O(Tn^3 \log N)$, to recover the causation structure to obtain frequency-domain (FD) representations of time-series. Since FFT accumulates all the time dependencies on every frequency, causal inference can be performed efficiently by considering the state variables as random variables at any given frequency. We additionally show that, for systems with interactions that are LTI, do-calculus machinery can be realized in the FD resulting in versions of the classical single-door (with cycles), front and backdoor criteria. We demonstrate, for a large class of problems, graph reconstruction using multivariate Wiener projections results in a significant computational advantage with $O(n)$ complexity over reconstruction algorithms such as the PC algorithm which has $O(n^q)$ complexity, where $q$ is the maximum neighborhood size. This advantage accrues due to some remarkable properties of the phase response of the frequency-dependent Wiener coefficients which is not present in any time-domain approach.

cs.LG↗
arXiv2023

Topology Identification under Spatially Correlated Noise

This article addresses the problem of reconstructing the topology of a network of agents interacting via linear dynamics, while being excited by exogenous stochastic sources that are possibly correlated across the agents, from time-series measurements alone. It is shown, under the assumption that the correlations are affine in nature, such network of nodal interactions is equivalent to a network with added agents, represented by nodes that are latent, where no corresponding time-series measurements are available; however, here all exogenous excitements are spatially (that is, across agents) uncorrelated. Generalizing affine correlations, it is shown that, under polynomial correlations, the latent nodes in the expanded networks can be excited by clusters of noise sources, where the clusters are uncorrelated with each other. The clusters can be replaced with a single noise source if the latent nodes are allowed to have non-linear interactions. Finally, using the sparse plus low-rank matrix decomposition of the imaginary part of the inverse power spectral density matrix (IPSDM) of the time-series data, the topology of the network is reconstructed. Under non conservative assumptions, the correlation graph is retrieved.

eess.SY↗
arXiv2022

Distributed Average Consensus Over Noisy Communication Links in Directed Graphs

Motivated by the needs of resiliency, scalability, and plug-and-play operation, distributed decision-making is becoming increasingly prevalent. The problem of achieving consensus in a multi-agent system is at the core of distributed decision-making. In this article, we study the problem of achieving average consensus over a directed multi-agent network when the communication links are corrupted with noise. We propose an algorithm where each agent updates its estimates based on the local mixing of information and adds its weighted noise-free initial information to its updates during every iteration. We demonstrate that with appropriately designed weights the agents achieve consensus under additive communication noise. We establish that when the communication links are noiseless the proposed algorithm moves towards consensus at a geometric rate. Under communication noise, we prove that the agent estimates reach a consensus value almost surely. We present numerical experiments to corroborate the efficacy of the proposed algorithm under different noise realizations and various algorithm parameters.

cs.DC↗
arXiv2022

DC-DistADMM: ADMM Algorithm for Constrained Distributed Optimization over Directed Graphs

This article reports an algorithm for multi-agent distributed optimization problems with a common decision variable, local linear equality and inequality constraints and set constraints with convergence rate guarantees. \textcolor{black}{The algorithm accrues all the benefits of the Alternating Direction Method of Multipliers (ADMM) approach}. It also overcomes the limitations of existing methods on convex optimization problems with linear inequality, equality and set constraints by allowing directed communication topologies. Moreover, the algorithm can be synthesized distributively. The developed algorithm has: (i) a $O(1/k)$ rate of convergence, where $k$ is the iteration counter, when individual functions are convex but not-necessarily differentiable, and (ii) a geometric rate of convergence to any arbitrary small neighborhood of the optimal solution, when the objective functions are smooth and restricted strongly convex at the optimal solution. The efficacy of the algorithm is evaluated by a comparison with state-of-the-art constrained optimization algorithms in solving a constrained distributed $\ell_1$-regularized logistic regression problem, and unconstrained optimization algorithms in solving a $\ell_1$-regularized Huber loss minimization problem. Additionally, a comparison of the algorithm's performance with other algorithms in the literature that utilize multiple communication steps is provided.

eess.SY↗
arXiv2021

Topology Learning of Linear Dynamical Systems with Latent Nodes using Matrix Decomposition

In this article, we present a novel approach to reconstruct the topology of networked linear dynamical systems with latent nodes. The network is allowed to have directed loops and bi-directed edges. The main approach relies on the unique decomposition of the inverse of power spectral density matrix (IPSDM) obtained from observed nodes as a sum of sparse and low-rank matrices. We provide conditions and methods for decomposing the IPSDM of the observed nodes into sparse and low-rank components. The sparse component yields the moral graph associated with the observed nodes, and the low-rank component retrieves parents, children and spouses (the Markov Blanket) of the hidden nodes. The article provides necessary and sufficient conditions for the unique decomposition of a given skew symmetric matrix into sum of a sparse skew symmetric and a low-rank skew symmetric matrices. It is shown that for a large class of systems, the unique decomposition of imaginary part of the IPSDM of observed nodes, a skew symmetric matrix, into the sparse and the low-rank components is sufficient to identify the moral graph of the observed nodes as well as the Markov Blanket of latent nodes. For a large class of systems, all spurious links in the moral graph formed by the observed nodes can be identified. Assuming conditions on hidden nodes required for identifiability, links between the hidden and observed nodes can be reconstructed, resulting in the retrieval of the exact topology of the network from the availability of IPSDM. Moreover, for finite number of data samples, we provide concentration bounds on the entry-wise distance between the true IPSDM and the estimated IPSDM.

eess.SY↗
arXiv2021

Gradient-Consensus: Linearly Convergent Distributed Optimization Algorithm over Directed Graphs

In this article, we propose a new approach, optimize then agree for minimizing a sum $ f = \sum_{i=1}^n f_i(x)$ of convex objective functions over a directed graph. The optimize then agree approach decouples the optimization step and the consensus step in a distributed optimization framework. The key motivation for optimize then agree is to guarantee that the disagreement between the estimates of the agents during every iteration of the distributed optimization algorithm remains under any apriori specified tolerance; existing algorithms do not provide such a guarantee which is required in many practical scenarios. In this method, each agent during each iteration maintains an estimate of the optimal solution and, utilizes its locally available gradient information along with a finite-time approximate consensus protocol to move towards the optimal solution (hence the name Gradient-Consensus algorithm). We establish that the proposed algorithm has a global R-linear rate of convergence if the aggregate function $f$ is strongly convex and Lipschitz differentiable. We also show that under the relaxed assumption of $f_i$'s being convex and Lipschitz differentiable, the objective function error residual decreases at a Q-linear rate (in terms of the number of gradient computation steps) until it reaches a small value, which can be managed using the tolerance value specified on the finite-time approximate consensus protocol; no existing method in the literature has such strong convergence guarantees when $f_i$ are not necessarily strongly convex functions. The communication overhead for the improved guarantees on meeting constraints and better convergence of our algorithm is $O(k\log k)$ iterates in comparison to $O(k)$ of the traditional algorithms. Further, we numerically evaluate the performance of the proposed algorithm by solving a distributed logistic regression problem.

eess.SY↗
arXiv2020

Design of H-infinity-based Robust Controller for Single-phase Grid-feeding Voltage Source Inverters

This article proposes the design of H-infinity-based robust current controller for single-phase grid-feeding voltage source inverter with an LCL filter. The main objective of the proposed controller is to have good reference tracking, disturbance rejection and sufficient LCL resonance damping under a large range of variations of grid impedance. Based on the aforementioned performance requirements, frequency dependent weighting functions are designed. Subsequently, the sub-optimal control problem is formulated and solved to determine the stabilizing controller. Computational footprint of the controller is addressed for ease-of-implementability on low-cost controller boards. Finally controller hardware-in-the-loop simulations on OPAL-RT are performed in the validation stage to obtain performance guarantees of the controller. The proposed controller exhibits fast response during transients and superior reference tracking, disturbance rejection at steady-state when compared with proportional- and resonant-based current controllers.

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