arXiv subjects

Murti Salapaka

Publications and source records attributed to Murti Salapaka.

16 recordsLinked to original sources

arXiv2024

Topology Learning of unknown Networked Linear Dynamical System excited by Cyclostationary inputs

Topology learning of networked dynamical systems is an important problem with implications to optimal control, decision-making over networks, cybersecurity and safety. The majority of prior work in consistent topology estimation relies on dynamical systems excited by temporally uncorrelated processes. In this article, we present a novel algorithm for guaranteed topology learning of networks that are excited by temporally (colored) cyclostationary processes, which encompasses a wide range of temporal correlation including wide-sense stationarity. Furthermore, unlike prior work, the framework applies to linear dynamic system with complex valued dependencies, and leverages group lasso regularization for effective learning of the network structure. In the second part of the article, we analyze conditions for consistent topology learning for bidirected tree networks when a subset of the network is unobserved. Here, the full topology along with unobserved nodes are recovered from observed node's time-series alone. Our theoretical contributions are validated on simulated data as well as on real-world climate data.

math.OC↗

arXiv2022

Efficient and passive learning of networked dynamical systems driven by non-white exogenous inputs

We consider a networked linear dynamical system with $p$ agents/nodes. We study the problem of learning the underlying graph of interactions/dependencies from observations of the nodal trajectories over a time-interval $T$. We present a regularized non-casual consistent estimator for this problem and analyze its sample complexity over two regimes: (a) where the interval $T$ consists of $n$ i.i.d. observation windows of length $T/n$ (restart and record), and (b) where $T$ is one continuous observation window (consecutive). Using the theory of $M$-estimators, we show that the estimator recovers the underlying interactions, in either regime, in a time-interval that is logarithmic in the system size $p$. To the best of our knowledge, this is the first work to analyze the sample complexity of learning linear dynamical systems \emph{driven by unobserved not-white wide-sense stationary (WSS) inputs}.

cs.LG↗

arXiv2021

Energetics of Feedback: Application to Memory Erasure

Landauer's erasure principle states that any irreversible erasure protocol of a single bit memory needs work of at least $k_B T ln2.$ Recent proof of concept experiments has demonstrated that the erasure protocols with work close to the Landauer limit can be devised. Under feedback, where the state of the bit can be measured, the work needed for bit erasure can be lower than $k_B T ln2.$ In this article, we analyze the energetics of feedback enabled erasure, while incorporating the imperfections of experimentally realized memory and bit erasure protocols that admit failure probabilities. We delineate the role of uncertainty in measurements and its effects on the work and entropy changes for a feedback-based erasure. We quantitatively demonstrate that the deficit between the Landauer limit and the minimum average work needed in a feedback-based erasure is accounted for by the mutual information between the measurement and the state of the memory, while incorporating the imperfections inherent in any realization. We experimentally demonstrate analysis results on a memory and erasure protocol realized using optical fields.

cs.IT↗

arXiv2020

Topology Learning in Radial Dynamical Systems with Unreliable Data

Many complex engineering systems admit bidirectional and linear couplings between their agents. Blind and passive methods to identify such influence pathways/couplings from data are central to many applications. However, dynamically related data-streams originating at different sources are prone to corruption caused by asynchronous time-stamps of different streams, packet drops and noise. Such imperfect information may be present in the entire observation period, and hence not detected by change-detection algorithms that require an initial clean observation period. Prior work has shown that spurious links are inferred in the graph structure due to the corrupted data-streams, which prevents consistent learning. In this article, we provide a novel approach to detect the location of corrupt agents as well as present an algorithm to learn the structure of radial dynamical systems despite corrupted data streams. In particular, we show that our approach provably learns the true radial structure if the unknown corrupted nodes are at least three hops away from each other. Our theoretical results are further validated in test dynamical network.

eess.SY↗

arXiv2020

Tractable learning in under-excited power grids

Estimating the structure of physical flow networks such as power grids is critical to secure delivery of energy. This paper discusses statistical structure estimation in power grids in the "under-excited" regime, where a subset of internal nodes do not have external injection. Prior estimation algorithms based on nodal potentials or voltages fail in the under-excited regime. We propose a novel topology learning algorithm for learning underexcited general (non-radial) networks based on physics-informed conservation laws. We prove the asymptotic correctness of our algorithm for grids with non-adjacent under-excited internal nodes. More importantly, we theoretically analyze our algorithm's efficacy under noisy measurements, and determine bounds on maximum noise under which asymptotically correct recovery is guaranteed. Our approach is validated through simulations with non-linear voltage samples generated on test grids with real injection data

eess.SY↗

arXiv2020

Graphical Models in Meshed Distribution Grids: Topology estimation, change detection and limitations

Graphical models are a succinct way to represent the structure in probability distributions. This article analyzes the graphical model of nodal voltages in non-radial power distribution grids. Using algebraic and structural properties of graphical models, algorithms exactly determining topology and detecting line changes for distribution grids are presented along with their theoretical limitations. We show that if distribution grids have cycles/loops of size greater than three, then nodal voltages are sufficient for efficient topology estimation without additional assumptions on system parameters. In contrast, line failure or change detection using nodal voltages does not require any structural assumption. Under noisy measurements, we provide the first non-trivial bounds on the maximum noise that the system can tolerate for asymptotically correct topology recovery. The performance of the designed algorithms is validated with nonlinear AC power flow samples generated by Matpower on test grids, including scenarios with injection correlations and system noise.

eess.SY↗

arXiv2019

Exact Topology Learning in a Network of Cyclostationary Processes

Learning the structure of a network from time series data, in particular cyclostationary data, is of significant interest in many disciplines such as power grids, biology and finance. In this article, an algorithm is presented for reconstruction of the topology of a network of cyclostationary processes. To the best of our knowledge, this is the first work to guarantee exact recovery without any assumptions on the underlying structure. The method is based on a lifting technique by which cyclostationary processes are mapped to vector wide sense stationary processes and further on semi-definite properties of matrix Wiener filters for the said processes.We demonstrate the performance of the proposed algorithm on a Resistor-Capacitor network and present the accuracy of reconstruction for varying sample sizes.

eess.SY↗

arXiv2018

Data-driven identification of a thermal network in multi-zone building

System identification of smart buildings is necessary for their optimal control and application in demand response. The thermal response of a building around an operating point can be modeled using a network of interconnected resistors with capacitors at each node/zone called RC network. The development of the RC network involves two phases: obtaining the network topology, and estimating thermal resistances and capacitance's. In this article, we present a provable method to reconstruct the interaction topology of thermal zones of a building solely from temperature measurements. We demonstrate that our learning algorithm accurately reconstructs the interaction topology for a $5$ zone office building in EnergyPlus with real-world conditions. We show that our learning algorithm is able to recover the network structure in scenarios where prior research prove insufficient.

eess.SY↗

arXiv2018

Realizing Information Erasure in Finite Time

In this article, we focus on erasure of a bit of information in finite time. Landauer's principle states that the average heat dissipation due to erasure of information is k_B T ln 2, which is achievable only in an asymptotic manner. Recent theoretical developments in non-equilibrium thermodynamics and stochastic control, predict a more general bound for finite time erasure dependent on the Wasserstein distances between the initial and final configurations. These predictions suggest improvements to experimental protocol with regards to minimizing average heat dissipation for bit erasure in finite time from a bistable well, under overdamped Langevin dynamics. We present a comparative study of a theoretically optimal protocol with an existing protocol, and highlight the closeness and deviation from optimality

cond-mat.stat-mech↗

arXiv2018

Topology Learning of Radial Dynamical Systems with Latent Nodes

In this article, we present a method to reconstruct the topology of a partially observed radial network of linear dynamical systems with bi-directional interactions. Our approach exploits the structure of the inverse power spectral density matrix and recovers edges involving nodes up to four hops away in the underlying topology. We then present an algorithm with provable guarantees, which eliminates the spurious links obtained and also identifies the location of the unobserved nodes in the inferred topology. The algorithm recovers the exact topology of the network by using only time-series of the states at the observed nodes. The effectiveness of the method developed is demonstrated by applying it on a typical distribution system of the electric grid.

eess.SY↗

arXiv2017

Topology Estimation in Bulk Power Grids: Guarantees on Exact Recovery

The topology of a power grid affects its dynamic operation and settlement in the electricity market. Real-time topology identification can enable faster control action following an emergency scenario like failure of a line. This article discusses a graphical model framework for topology estimation in bulk power grids (both loopy transmission and radial distribution) using measurements of voltage collected from the grid nodes. The graphical model for the probability distribution of nodal voltages in linear power flow models is shown to include additional edges along with the operational edges in the true grid. Our proposed estimation algorithms first learn the graphical model and subsequently extract the operational edges using either thresholding or a neighborhood counting scheme. For grid topologies containing no three-node cycles (two buses do not share a common neighbor), we prove that an exact extraction of the operational topology is theoretically guaranteed. This includes a majority of distribution grids that have radial topologies. For grids that include cycles of length three, we provide sufficient conditions that ensure existence of algorithms for exact reconstruction. In particular, for grids with constant impedance per unit length and uniform injection covariances, this observation leads to conditions on geographical placement of the buses. The performance of algorithms is demonstrated in test case simulations.

math.OC↗

arXiv2017

Distributed Finite Time Termination of Consensus in the Presence of Delays

Linear consensus iterations guarantee asymptotic convergence, thereby, limiting their applicability in applications where consensus value needs to be used in real time to perform a system level task. It also leads to wastage of power and communication resources. In this article, an algorithm is proposed which enables each node to detect in a distributed manner and in finite number of iterations, when every agent in the network is within a user specified threshold of the consensus value (approximate consensus) and hence terminate further communications and computations associated with consensus iterations. This article develops a distributed algorithm for achieving this approximate consensus in presence of random time-varying bounded communication delays. Moreover, the article instantiates the algorithm developed to distributively determine the average of the initial values held by agents in finite number of iterations. Specifically, this algorithm relies on distributively determining the maximum and minimum of values held by the agents. The approach presented here offers several advantages, including reduced computational complexity, and hence, is suited for hardware implementation. An experimental test bed of Raspberry-Pi agents that communicate wirelessly over neighborhoods is employed as a platform to demonstrate the effectiveness of the developed algorithm.

math.OC↗

arXiv2016

Emergent Transport Properties of Molecular Motor Ensemble Affected by Single Motor Mutations

Intracellular transport is an essential function in eucaryotic cells, facilitated by motor proteins - proteins converting chemical energy into kinetic energy. It is known that motor proteins work in teams enabling unidirectional and bidirectional transport of intracellular cargo over long distances. Disruptions of the underlying transport mechanisms, often caused by mutations that alter single motor characteristics, are known to cause neurodegenerative diseases. For example, phosphorylation of kinesin motor domain at the serine residue is implicated in Huntington's disease, with a recent study of phosphorylated and phosphomimetic serine residues indicating lowered single motor stalling forces. In this article we report the effects of mutations of this nature on transport properties of cargo carried by multiple wild-type and mutant motors. Results indicate that mutants with altered stall forces might determine the average velocity and run-length even when they are outnumbered by wild type motors in the ensemble. It is shown that mutants gain a competitive advantage and lead to an increase in expected run-length when load on the cargo is in the vicinity of the mutant's stalling force or a multiple of its stalling force. A separate contribution of this article is the development of a semi-analytic method to analyze transport of cargo by multiple motors of multiple types. The technique determines transition rates between various relative configurations of motors carrying the cargo using the transition rates between various absolute configurations. This enables exact computation of average velocity and run-length. It can also be used to introduce alterations of various single motor parameters to model a mutation and to deduce effects of such alterations on the transport of a common cargo by multiple motors. Our method is easily implementable and we provide a software package for general use.

q-bio.SC↗

arXiv2010

Maximum-Likelihood Sequence Detector for Dynamic Mode High Density Probe Storage

There is an increasing need for high density data storage devices driven by the increased demand of consumer electronics. In this work, we consider a data storage system that operates by encoding information as topographic profiles on a polymer medium. A cantilever probe with a sharp tip (few nm radius) is used to create and sense the presence of topographic profiles, resulting in a density of few Tb per in.2. The prevalent mode of using the cantilever probe is the static mode that is harsh on the probe and the media. In this article, the high quality factor dynamic mode operation, that is less harsh on the media and the probe, is analyzed. The read operation is modeled as a communication channel which incorporates system memory due to inter-symbol interference and the cantilever state. We demonstrate an appropriate level of abstraction of this complex nanoscale system that obviates the need for an involved physical model. Next, a solution to the maximum likelihood sequence detection problem based on the Viterbi algorithm is devised. Experimental and simulation results demonstrate that the performance of this detector is several orders of magnitude better than the performance of other existing schemes.

cs.IT↗

arXiv2010

Performance evaluation for ML sequence detection in ISI channels with Gauss Markov Noise

Inter-symbol interference (ISI) channels with data dependent Gauss Markov noise have been used to model read channels in magnetic recording and other data storage systems. The Viterbi algorithm can be adapted for performing maximum likelihood sequence detection in such channels. However, the problem of finding an analytical upper bound on the bit error rate of the Viterbi detector in this case has not been fully investigated. Current techniques rely on an exhaustive enumeration of short error events and determine the BER using a union bound. In this work, we consider a subset of the class of ISI channels with data dependent Gauss-Markov noise. We derive an upper bound on the pairwise error probability (PEP) between the transmitted bit sequence and the decoded bit sequence that can be expressed as a product of functions depending on current and previous states in the (incorrect) decoded sequence and the (correct) transmitted sequence. In general, the PEP is asymmetric. The average BER over all possible bit sequences is then determined using a pairwise state diagram. Simulations results which corroborate the analysis of upper bound, demonstrate that analytic bound on BER is tight in high SNR regime. In the high SNR regime, our proposed upper bound obviates the need for computationally expensive simulation.

cs.IT↗

arXiv2008

A Less Conservative Circle Criterion

A weak form of the Circle Criterion for Lur'e systems is stated. The result allows prove global boundedness of all system solutions. Moreover such a result can be employed to enlarge the set of nonlinearities for which the standard Circle Criterion can guarantee absolute stability.

nlin.CD↗