arXiv subjects

Murti V. Salapaka

Publications and source records attributed to Murti V. Salapaka.

At least 37 records · Page 2Linked to original sources

arXiv2020

Convex Decreasing Algorithms: Distributed Synthesis and Finite-time Termination in Higher Dimension

We introduce a general mathematical framework for distributed algorithms, and a monotonicity property frequently satisfied in application. These properties are leveraged to provide finite-time guarantees for converging algorithms, suited for use in the absence of a central authority. A central application is to consensus algorithms in higher dimension. These pursuits motivate a new peer to peer convex hull algorithm which we demonstrate to be an instantiation of the described theory. To address the diversity of convex sets and the potential computation and communication costs of knowing such sets in high dimension, a lightweight norm based stopping criteria is developed. More explicitly, we give a distributed algorithm that terminates in finite time when applied to consensus problems in higher dimensions and guarantees the convergence of the consensus algorithm in norm, within any given tolerance. Applications to consensus least squared estimation and distributed function determination are developed. The practical utility of the algorithm is illustrated through MATLAB simulations.

eess.SY↗

arXiv2020

Distributed Power Apportioning with Early Dispatch for Ancillary Services in Renewable Grids

This article develops a distributed framework for coordinating distributed energy resources (DERs) in a power network to provide secondary frequency response (SFR) as an ancillary service to the bulk power system. A distributed finite-time protocol-based solution is adopted that allows each DER in the network to determine power reference commands. The distributed protocol respects information exchange constraints posed by a communication network layer while being robust to delays in the communications channels. The proposed framework enables coordinated response and control of the aggregated DERs by apportioning the share of generation that each DER needs to provide towards meeting any specified global SFR command while allowing for adjustments due to variability in generation and demand in order to prioritize renewable energy sources in the network. A novel early dispatch mechanism with brown start is synthesized to achieve initial DER response to changing SFR commands that is faster than state-of-the-art distributed approaches. The proposed power apportioning protocol is validated using an end-to-end power hardware-in-the-loop configuration at a distribution system scale with 40+ physical hardware DERs, underlying 7-MW power system model, a 250-DER communication topology with physical and simulated distributed controller nodes, varied communication protocols, and an underlying real-world power system model. Experimental results demonstrate the efficacy of the proposed method toward distributed coordination of hundreds of DERs for providing fast response at SFR timescales.

eess.SY↗

arXiv2020

On Mitigating the Uncertainty in Renewable Generation in Distribution Microgrids

In this article, we focus on the problem of mitigating the risk of not being able to meet the power demand, due to the inherent uncertainty of renewable energy generation sources in microgrids. We consider three different demand scenarios, namely meeting short-time horizon power demand, a sustained energy demand and a scenario where the power demand at a prescribed future time has to be met with almost sure guarantee with power generation being stochastic and following dynamics governed by geometric Brownian motion. For each of these scenarios we provide solutions to meet the electrical demand. We present results of numerical experiments to demonstrate the applicability of our schemes.

eess.SY↗

arXiv2020

Causal Structure Identification from Corrupt Data-Streams

Complex networked systems can be modeled and represented as graphs, with nodes representing the agents and the links describing the dynamic coupling between them. The fundamental objective of network identification for dynamic systems is to identify causal influence pathways. However, dynamically related data-streams that originate from different sources are prone to corruption caused by asynchronous time stamps, packet drops, and noise. In this article, we show that identifying causal structure using corrupt measurements results in the inference of spurious links. A necessary and sufficient condition that delineates the effects of corruption on a set of nodes is obtained. Our theory applies to nonlinear systems, and systems with feedback loops. Our results are obtained by the analysis of conditional directed information in dynamic Bayesian networks. We provide consistency results for the conditional directed information estimator that we use by showing almost-sure convergence.

eess.SY↗

arXiv2020

Network Structure Identification from Corrupt Data Streams

Complex networked systems can be modeled as graphs with nodes representing the agents and links describing the dynamic coupling between them. Previous work on network identification has shown that the network structure of linear time-invariant (LTI) systems can be reconstructed from the joint power spectrum of the data streams. These results assumed that data is perfectly measured. However, real-world data is subject to many corruptions, such as inaccurate time-stamps, noise, and data loss. We show that identifying the structure of linear time-invariant systems using corrupt measurements results in the inference of erroneous links. We provide an exact characterization and prove that such erroneous links are restricted to the neighborhood of the perturbed node. We extend the analysis of LTI systems to the case of Markov random fields with corrupt measurements. We show that data corruption in Markov random fields results in spurious probabilistic relationships in precisely the locations where spurious links arise in LTI systems.

eess.SY↗

arXiv2020

The Differential Entropy of Mixtures: New Bounds and Applications

Mixture distributions are extensively used as a modeling tool in diverse areas from machine learning to communications engineering to physics, and obtaining bounds on the entropy of probability distributions is of fundamental importance in many of these applications. This article provides sharp bounds on the entropy concavity deficit, which is the difference between the entropy of the mixture and the weighted sum of entropies of constituent components. Toward establishing lower and upper bounds on the concavity deficit, results that are of importance in their own right are obtained. In order to obtain nontrivial upper bounds, properties of the skew-divergence are developed and notions of "skew" $f$-divergences are introduced; a reverse Pinsker inequality and a bound on Jensen-Shannon divergence are obtained along the way. Complementary lower bounds are derived with special attention paid to the case that corresponds to independent summation of a continuous and a discrete random variable. Several applications of the bounds are delineated, including to mutual information of additive noise channels, thermodynamics of computation, and functional inequalities.

cs.IT↗

arXiv2020

Robust and Optimal Single-loop Voltage Controller for Grid-forming Voltage Source Inverters

Design and implementation of an optimal and robust single-loop voltage controller is proposed for single-phase grid forming voltage source inverter (VSI). The objective of the proposed controller is to have good reference tracking and disturbance rejection. Uncertain nature of loads can significantly alter system's behavior, especially during heavily loaded conditions, and impose an uncertainty in the dynamic model. This deteriorates the robustness of the controller severely. H-Infinity-based controller design is proposed in this article to address this issue. The required objectives of the optimal controller are formulated after modeling the loads as uncertain element of the control system. Time-domain MATLAB/SIMULINK-based simulation study substantiates the fact that the resulting controller exhibits superior robustness in performance during varying loading, conditions of VSI than that of the conventional multi-loop control architecture.

eess.SY↗

arXiv2020

Isochronous Architecture-Based Voltage-Active Power Droop for Multi-Inverter Systems

Advanced microgrids consisting of distributed energy resources interfaced with multi-inverter systems are becoming more common. Consequently, the effectiveness of voltage and frequency regulation in microgrids using conventional droop-based methodologies is challenged by uncertainty in the sizeand schedule of loads. This article proposes an isochronous architecture of parallel inverters with only voltage-active power droop (VP-D) control for improving active power sharing as well as plug-and-play of multi-inverter based distributed energyresources (DERs). In spite of not employing explicit control for frequency regulation, this architecture allows even sharing of reactive power while maintaining reduced circulating currents between inverters. The performance is achieved even when there are mismatches between commanded reference and power demanded from the actual load in the network. The isochronous architecture is implemented by employing a global positioning system (GPS) to disseminate timing signals that enable the microgrid to maintain nominal system frequency in the entire network. This enables direct control of active power through voltage source inverter (VSI) output voltage regulation, even in the presence of system disturbances. A small signal eigenvalue analysis of a multi-inverter system near the steady-state operating point is presented to evaluate the stability of the multi-inverter system with the proposed VP-D control. Simulation studies and hardware experiments on an 1.2 kVA prototype are conducted. The effectiveness of the proposed architecture towards active and reactive power sharing between inverters with load scenarios are demonstrated. Results of the hardware experiments corroborate the viability of the proposed VP-D control architecture.

eess.SY↗

arXiv2019

Distributed finite-time termination for consensus algorithm in switching topologies

In this article, we present a finite time stopping criterion for consensus algorithms in networks with dynamic communication topology. Recent results provide asymptotic convergence to the consensus algorithm. However, the asymptotic convergence of these algorithms pose a challenge in the practical settings where the response from agents is required in finite time. To this end, we propose a Maximum-Minimum protocol which propagates the global maximum and minimum values of agent states (while running consensus algorithm) in the network. We establish that global maximum and minimum values are strictly monotonic even for a dynamic topology and can be utilized to distributively ascertain the closeness to convergence in finite time. We show that each node can have access to the global maximum and minimum by running the proposed Maximum-Minimum protocol and use it as a finite time stopping criterion for the otherwise asymptotic consensus algorithm. The practical utility of the algorithm is illustrated through experiments where each agent is instantiated by a NodeJS socket.io server.

eess.SY↗

arXiv2019

Signal selection for estimation and identification in networks of dynamic systems: a graphical model approach

Network systems have become a ubiquitous modeling tool in many areas of science where nodes in a graph represent distributed processes and edges between nodes represent a form of dynamic coupling. When a network topology is already known (or partially known), two associated goals are (i) to derive estimators for nodes of the network which cannot be directly observed or are impractical to measure; and (ii) to quantitatively identify the dynamic relations between nodes. In this article we address both problems in the challenging scenario where only some outputs of the network are being measured and the inputs are not accessible. The approach makes use of the notion of $d$-separation for the graph associated with the network. In the considered class of networks, it is shown that the proposed technique can determine or guide the choice of optimal sparse estimators. The article also derives identification methods that are applicable to cases where loops are present providing a different perspective on the problem of closed-loop identification. The notion of $d$-separation is a central concept in the area of probabilistic graphical models, thus an additional contribution is to create connections between control theory and machine learning techniques.

nlin.AO↗

arXiv2018

Physics Informed Topology Learning in Networks of Linear Dynamical Systems

Learning influence pathways of a network of dynamically related processes from observations is of considerable importance in many disciplines. In this article, influence networks of agents which interact dynamically via linear dependencies are considered. An algorithm for the reconstruction of the topology of interaction based on multivariate Wiener filtering is analyzed. It is shown that for a vast and important class of interactions, that respect flow conservation, the topology of the interactions can be exactly recovered. The class of problems where reconstruction is guaranteed to be exact includes power distribution networks, dynamic thermal networks and consensus networks. The efficacy of the approach is illustrated through simulation and experiments on consensus networks, IEEE power distribution networks and thermal dynamics of buildings.

eess.SY↗

arXiv2018

Error Bounds on a Mixed Entropy Inequality

Motivated by the entropy computations relevant to the evaluation of decrease in entropy in bit reset operations, the authors investigate the deficit in an entropic inequality involving two independent random variables, one continuous and the other discrete. In the case where the continuous random variable is Gaussian, we derive strong quantitative bounds on the deficit in the inequality. More explicitly it is shown that the decay of the deficit is sub-Gaussian with respect to the reciprocal of the standard deviation of the Gaussian variable. What is more, up to rational terms these results are shown to be sharp.

cs.IT↗

arXiv2018

Designing Memory Bits with Dissipation lower than the Landauer's Bound

A Brownian particle in a symmetric double well potential is used as a representation for a single bit memory, where, the location of the particle in either well denotes one of the two states of a single bit memory. This article analyzes the effect of modifications to a symmetric double well potential on the minimum heat dissipation associated with erasure of the information stored in a single bit memory. Two types of modifications are considered, viz., overlap between the two wells and the asymmetry between the two wells of a bit of memory. Moreover, the analysis presented here, takes into account the uncertainty in the success of the erasure process. We quantify the effect of the proposed modifications on the heat dissipation accompanying erasure of a bit of information with a comparison to the Landauer's bound. In particular, we conclude that the proposed modifications could result in the minimum heat dissipation being lower than the Landauer's bound in quasi-static erasure processes. Furthermore, we quantify the physical aspect ratio for designing a memory bit which could improve memory density.

cond-mat.stat-mech↗

arXiv2017

Learning the Exact Topology of Undirected Consensus Networks

In this article, we present a method to learn the interaction topology of a network of agents undergoing linear consensus updates in a non invasive manner. Our approach is based on multivariate Wiener filtering, which is known to recover spurious edges apart from the true edges in the topology. The main contribution of this work is to show that in the case of undirected consensus networks, all spurious links obtained using Wiener filtering can be identified using frequency response of the Wiener filters. Thus, the exact interaction topology of the agents is unveiled. The method presented requires time series measurements of the state of the agents and does not require any knowledge of link weights. To the best of our knowledge this is the first approach that provably reconstructs the structure of undirected consensus networks with correlated noise. We illustrate the effectiveness of the method developed through numerical simulations as well as experiments on a five node network of Raspberry Pis.

eess.SY↗

arXiv2017

Single Molecule Studies Under Constant Force Using Model Based Robust Control Design

Optical tweezers have enabled important insights into intracellular transport through the investigation of motor proteins, with their ability to manipulate particles at the microscale, affording femto Newton force resolution. Its use to realize a constant force clamp has enabled vital insights into the behavior of motor proteins under different load conditions. However, the varying nature of disturbances and the effect of thermal noise pose key challenges to force regulation. Furthermore, often the main aim of many studies is to determine the motion of the motor and the statistics related to the motion, which can be at odds with the force regulation objective. In this article, we propose a mixed objective H2-Hinfinity optimization framework using a model-based design, that achieves the dual goals of force regulation and real time motion estimation with quantifiable guarantees. Here, we minimize the Hinfinity norm for the force regulation and error in step estimation while maintaining the H2 norm of the noise on step estimate within user specified bounds. We demonstrate the efficacy of the framework through extensive simulations and an experimental implementation using an optical tweezer setup with live samples of the motor protein kinesin; where regulation of forces below 1 pico Newton with errors below 10 percent is obtained while simultaneously providing real time estimates of motor motion.

math.OC↗

arXiv2017

Distributed Apportioning in a Power Network for providing Demand Response Services

Greater penetration of Distributed Energy Resources (DERs) in power networks requires coordination strategies that allow for self-adjustment of contributions in a network of DERs, owing to variability in generation and demand. In this article, a distributed scheme is proposed that enables a DER in a network to arrive at viable power reference commands that satisfies the DERs local constraints on its generation and loads it has to service, while, the aggregated behavior of multiple DERs in the network and their respective loads meet the ancillary services demanded by the grid. The Net-load Management system for a single unit is referred to as the Local Inverter System (LIS) in this article . A distinguishing feature of the proposed consensus based solution is the distributed finite time termination of the algorithm that allows each LIS unit in the network to determine power reference commands in the presence of communication delays in a distributed manner. The proposed scheme allows prioritization of Renewable Energy Sources (RES) in the network and also enables auto-adjustment of contributions from LIS units with lower priority resources (non-RES). The methods are validated using hardware-in-the-loop simulations with Raspberry PI devices as distributed control units, implementing the proposed distributed algorithm and responsible for determining and dispatching realtime power reference commands to simulated power electronics interface emulating LIS units for demand response.

eess.SY↗

arXiv2017

Distributed Finite Time Termination of Ratio Consensus for Averaging in the presence of Delays

Distributed averaging of agent initial conditions is a well-studied problem in context of networked systems where coordination amongst the agents is of paramount importance. The asymptotic nature of convergence of distributed averaging protocols and presence of communication delays, however, makes it challenging to implement in practical settings. It is important that agents develop the ability to detect on their own when average of the initial conditions of the agents is achieved within some pre-specified tolerance and stop further computations to avoid overhead expenses in the presence of delays. This article presents a distributed finite time stopping criterion for distributed averaging using ratio consensus on a fixed interconnection topology. The practical utility of the algorithm has been illustrated through simulations.

math.OC↗

arXiv2017

Learning Exact Topology of a Loopy Power Grid from Ambient Dynamics

Estimation of the operational topology of the power grid is necessary for optimal market settlement and reliable dynamic operation of the grid. This paper presents a novel framework for topology estimation for general power grids (loopy or radial) using time-series measurements of nodal voltage phase angles that arise from the swing dynamics. Our learning framework utilizes multivariate Wiener filtering to unravel the interaction between fluctuations in voltage angles at different nodes and identifies operational edges by considering the phase response of the elements of the multivariate Wiener filter. The performance of our learning framework is demonstrated through simulations on standard IEEE test cases.

math.OC↗