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Vijay Gupta

Vijay Gupta appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
Systems and Controlmath.OCeess.SYeess.SPMachine Learningmath.CAMultiagent SystemsApplicationsArtificial IntelligenceComputer Science and Game TheoryCryptography and SecurityDistributed, Parallel, and Cluster Computingecon.GNInformation Theorymath.DSmath.ITmath.NTphysics.soc-phq-fin.EC

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Published work

38 published item(s)

preprint2026arXiv

A Survey of Security Challenges and Solutions for UAS Traffic Management (UTM) and small Unmanned Aerial Systems (sUAS)

The rapid growth of small Unmanned Aerial Systems (sUAS) for civil and commercial missions has intensified concerns about their resilience to cyber-security threats. Operating within the emerging UAS Traffic Management (UTM) framework, these lightweight and highly networked platforms depend on secure communication, navigation, and surveillance (CNS) subsystems that are vulnerable to spoofing, jamming, hijacking, and data manipulation. While prior reviews of UAS security addressed these challenges at a conceptual level, a detailed, system-oriented analysis for resource-constrained sUAS remains lacking. This paper presents a comprehensive survey of cyber-security vulnerabilities and defenses tailored to the sUAS and UTM ecosystem. We organize existing research across the full cyber-physical stack, encompassing CNS, data links, sensing and perception, UTM cloud access, and software integrity layers, and classify attack vectors according to their technical targets and operational impacts. Correspondingly, we review defense mechanisms ranging from classical encryption and authentication to adaptive intrusion detection, lightweight cryptography, and secure firmware management. By mapping threats to mitigation strategies and evaluating their scalability and practical effectiveness, this work establishes a unified taxonomy and identifies open challenges for achieving safe, secure, and scalable sUAS operations within future UTM environments.

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preprint2026arXiv

Quotient-Categorical Representations for Bellman-Compatible Average-Reward Distributional Reinforcement Learning

Average-reward reinforcement learning requires estimating the gain and the bias, which is defined only up to an additive constant. This makes direct distributional analogues ill-posed on the real line. We introduce a quotient-space formulation in which state-indexed bias laws are identified up to a common translation, together with a categorical parameterization that respects this symmetry. On this quotient-categorical space, we define a projected average-reward distributional operator and show that it is well-defined, non-expansive in a coordinate Cramér metric, and admits fixed points. We then study sampled recursions whose mean-field maps are asynchronous relaxations of this operator. In an idealized centered-reward setting, a one-state temporal-difference update enjoys almost sure convergence together with finite-iteration residual bounds under both i.i.d. and Markovian sampling. When the gain is unknown, we augment the recursion with an online gain estimator, and prove non-expansiveness and Markovian convergence of the resulting coupled scheme. Finally, we show that synchronous exact updates are gain-independent at the quotient-law level, isolating a structural contrast between ideal quotient distributions and practical fixed-grid categorical representations.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Communication-Efficient Algorithms for Solving Pressure Poisson Equation for Multiphase Flows using Parallel Computers

Numerical solution of partial differential equations on parallel computers using domain decomposition usually requires synchronization and communication among the processors. These operations often have a significant overhead in terms of time and energy. In this paper, we propose communication-efficient parallel algorithms for solving partial differential equations that alleviate this overhead. First, we describe an asynchronous algorithm that removes the requirement of synchronization and checks for termination in a distributed fashion while maintaining the provision to restart iterations if necessary. Then, we build on the asynchronous algorithm to propose an event-triggered communication algorithm that communicates the boundary values to neighboring processors only at certain iterations, thereby reducing the number of messages while maintaining similar accuracy of solution. We demonstrate our algorithms on a successive over-relaxation solver for the Pressure Poisson equation arising from variable density incompressible multiphase flows in 3-D and show that our algorithms improve time and energy efficiency.

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preprint2022arXiv

Cooperative Actor-Critic via TD Error Aggregation

In decentralized cooperative multi-agent reinforcement learning, agents can aggregate information from one another to learn policies that maximize a team-average objective function. Despite the willingness to cooperate with others, the individual agents may find direct sharing of information about their local state, reward, and value function undesirable due to privacy issues. In this work, we introduce a decentralized actor-critic algorithm with TD error aggregation that does not violate privacy issues and assumes that communication channels are subject to time delays and packet dropouts. The cost we pay for making such weak assumptions is an increased communication burden for every agent as measured by the dimension of the transmitted data. Interestingly, the communication burden is only quadratic in the graph size, which renders the algorithm applicable in large networks. We provide a convergence analysis under diminishing step size to verify that the agents maximize the team-average objective function.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Model-free Learning for Risk-constrained Linear Quadratic Regulator with Structured Feedback in Networked Systems

We develop a model-free learning algorithm for the infinite-horizon linear quadratic regulator (LQR) problem. Specifically, (risk) constraints and structured feedback are considered, in order to reduce the state deviation while allowing for a sparse communication graph in practice. By reformulating the dual problem as a nonconvex-concave minimax problem, we adopt the gradient descent max-oracle (GDmax), and for modelfree setting, the stochastic (S)GDmax using zero-order policy gradient. By bounding the Lipschitz and smoothness constants of the LQR cost using specifically defined sublevel sets, we can design the stepsize and related parameters to establish convergence to a stationary point (at a high probability). Numerical tests in a networked microgrid control problem have validated the convergence of our proposed SGDmax algorithm while demonstrating the effectiveness of risk constraints. The SGDmax algorithm has attained a satisfactory optimality gap compared to the classical LQR control, especially for the full feedback case.

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preprint2022arXiv

On the Sample Complexity of Decentralized Linear Quadratic Regulator with Partially Nested Information Structure

We study the problem of control policy design for decentralized state-feedback linear quadratic control with a partially nested information structure, when the system model is unknown. We propose a model-based learning solution, which consists of two steps. First, we estimate the unknown system model from a single system trajectory of finite length, using least squares estimation. Next, based on the estimated system model, we design a control policy that satisfies the desired information structure. We show that the suboptimality gap between our control policy and the optimal decentralized control policy (designed using accurate knowledge of the system model) scales linearly with the estimation error of the system model. Using this result, we provide an end-to-end sample complexity result for learning decentralized controllers for a linear quadratic control problem with a partially nested information structure.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Robustness against Adversarial Attacks in Neural Networks using Incremental Dissipativity

Adversarial examples can easily degrade the classification performance in neural networks. Empirical methods for promoting robustness to such examples have been proposed, but often lack both analytical insights and formal guarantees. Recently, some robustness certificates have appeared in the literature based on system theoretic notions. This work proposes an incremental dissipativity-based robustness certificate for neural networks in the form of a linear matrix inequality for each layer. We also propose an equivalent spectral norm bound for this certificate which is scalable to neural networks with multiple layers. We demonstrate the improved performance against adversarial attacks on a feed-forward neural network trained on MNIST and an Alexnet trained using CIFAR-10.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Data-Driven Contract Design for Multi-Agent Systems with Collusion Detection

In applications such as participatory sensing and crowd sensing, self-interested agents exert costly effort towards achieving an objective for the system operator. We study such a setup where a principal incentivizes multiple agents of different types who can collude with each other to derive rent. The principal cannot observe the efforts exerted directly, but only the outcome of the task, which is a noisy function of the effort. The type of each agent influences the effort cost and task output. For a duopoly in which agents are coupled in their payments, we show that if the principal and the agents interact finitely many times, the agents can derive rent by colluding even if the principal knows the types of the agents. However, if the principal and the agents interact infinitely often, the principal can disincentivize agent collusion through a suitable data-driven contract.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Data-Driven Incident Detection in Power Distribution Systems

In a power distribution network with energy storage systems (ESS) and advanced controls, traditional monitoring and protection schemes are not well suited for detecting anomalies such as malfunction of controllable devices. In this work, we propose a data-driven technique for the detection of incidents relevant to the operation of ESS in distribution grids. This approach leverages the causal relationship observed among sensor data streams, and does not require prior knowledge of the system model or parameters. Our methodology includes a data augmentation step which allows for the detection of incidents even when sensing is scarce. The effectiveness of our technique is illustrated through case studies which consider active power dispatch and reactive power control of ESS.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Distributed Resource Allocation over Time-varying Balanced Digraphs with Discrete-time Communication

This work is concerned with the problem of distributed resource allocation in continuous-time setting but with discrete-time communication over infinitely jointly connected and balanced digraphs. We provide a passivity-based perspective for the continuous-time algorithm, based on which an intermittent communication scheme is developed. Particularly, a periodic communication scheme is first derived through analyzing the passivity degradation over output sampling of the distributed dynamics at each node. Then, an asynchronous distributed event-triggered scheme is further developed. The sampled-based event-triggered communication scheme is exempt from Zeno behavior as the minimum inter-event time is lower bounded by the sampling period. The parameters in the proposed algorithm rely only on local information of each individual nodes, which can be designed in a truly distributed fashion

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

On Stability and Convergence of Distributed Filters

Recent years have bore witness to the proliferation of distributed filtering techniques, where a collection of agents communicating over an ad-hoc network aim to collaboratively estimate and track the state of a system. These techniques form the enabling technology of modern multi-agent systems and have gained great importance in the engineering community. Although most distributed filtering techniques come with a set of stability and convergence criteria, the conditions imposed are found to be unnecessarily restrictive. The paradigm of stability and convergence in distributed filtering is revised in this manuscript. Accordingly, a general distributed filter is constructed and its estimation error dynamics is formulated. The conducted analysis demonstrates that conditions for achieving stable filtering operations are the same as those required in the centralized filtering setting. Finally, the concepts are demonstrated in a Kalman filtering framework and validated using simulation examples.

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preprint2021arXiv

Optimal Stationary State Estimation Over Multiple Markovian Packet Drop Channels

In this paper, we investigate the state estimation problem over multiple Markovian packet drop channels. In this problem setup, a remote estimator receives measurement data transmitted from multiple sensors over individual channels. By the method of Markovian jump linear systems, an optimal stationary estimator that minimizes the error variance in the steady state is obtained, based on the mean-square (MS) stabilizing solution to the coupled algebraic Riccati equations. An explicit necessary and sufficient condition is derived for the existence of the MS stabilizing solution, which coincides with that of the standard Kalman filter. More importantly, we provide a sufficient condition under which the MS detectability with multiple Markovian packet drop channels can be decoupled, and propose a locally optimal stationary estimator but computationally more tractable. Analytic sufficient and necessary MS detectability conditions are presented for the decoupled subsystems subsequently. Finally, numerical simulations are conducted to illustrate the results on the MS stabilizing solution, the MS detectability, and the performance of the optimal and locally optimal stationary estimators.

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preprint2021arXiv

Renewable Power Trades and Network Congestion Externalities

Integrating renewable energy production into the electricity grid is an important policy goal to address climate change. However, such an integration faces economic and technological challenges. As power generation by renewable sources increases, power transmission patterns over the electric grid change. Due to physical laws, these new transmission patterns lead to non-intuitive grid congestion externalities. We derive the conditions under which negative network externalities due to power trades occur. Calibration using a stylized framework and data from Europe shows that each additional unit of power traded between northern and western Europe reduces transmission capacity for the southern and eastern regions by 27% per unit traded. Such externalities suggest that new investments in the electric grid infrastructure cannot be made piecemeal. In our example, power infrastructure investment in northern and western Europe needs an accompanying investment in southern and eastern Europe as well. An economic challenge is regions facing externalities do not always have the financial ability to invest in infrastructure. Power transit fares can help finance power infrastructure investment in regions facing network congestion externalities. The resulting investment in the overall electricity grid facilitates integration of renewable energy production.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Distributed Mixed Voltage Angle and Frequency Droop Control of Microgrid Interconnections with Loss of Distribution-PMU Measurements

Recent advances in distribution-level phasor measurement unit (D-PMU) technology have enabled the use of voltage phase angle measurements for direct load sharing control in distribution-level microgrid interconnections with high penetration of renewable distributed energy resources (DERs). In particular, D-PMU enabled voltage angle droop control has the potential to enhance stability and transient performance in such microgrid interconnections. However, these angle droop control designs are vulnerable to D-PMU angle measurement losses that frequently occur due to the unavailability of a GPS signal for synchronization. In the event of such measurement losses, angle droop controlled microgrid interconnections may suffer from poor performance and potentially lose stability. In this paper, we propose a novel distributed mixed voltage angle and frequency droop control (D-MAFD) framework to improve the reliability of angle droop controlled microgrid interconnections. In this framework, when the D-PMU phase angle measurement is lost at a microgrid, conventional frequency droop control is temporarily used for primary control in place of angle droop control to guarantee stability. We model the microgrid interconnection with this primary control architecture as a nonlinear switched system and design distributed secondary controllers to guarantee transient stability of the network. Further, we incorporate performance specifications such as robustness to generation-load mismatch and network topology changes in the distributed control design. We demonstrate the performance of this control framework by simulation on a test 123-feeder distribution network.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Distributed Synthesis of Local Controllers for Networked Systems with Arbitrary Interconnection Topologies

We consider the problem of designing distributed controllers to guarantee dissipativity of a networked system comprised of dynamically coupled subsystems. We require that the control synthesis is carried out locally at the subsystem-level, without explicit knowledge of the dynamics of other subsystems in the network. We solve this problem in two steps. First, we provide distributed subsystem-level dissipativity analysis conditions whose feasibility is sufficient to guarantee dissipativity of the networked system. We then use these conditions to synthesize controllers locally at the subsystem-level, using only the knowledge of the dynamics of that subsystem, and limited information about the dissipativity of the subsystems to which it is dynamically coupled. We show that the subsystem-level controllers synthesized in this manner are sufficient to guarantee dissipativity of the networked dynamical system. We also provide an approach to make this synthesis compositional, that is, when a new subsystem is added to an existing network, only the dynamics of the new subsystem, and information about the dissipativity of the subsystems in the existing network to which it is coupled are used to design a controller for the new subsystem, while guaranteeing dissipativity of the networked system including the new subsystem. Finally, we demonstrate the application of this synthesis in enabling plug-and-play operations of generators in a microgrid by extending our results to networked switched systems.

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preprint2020arXiv

Incentive Design in a Distributed Problem with Strategic Agents

In this paper, we consider a general distributed system with multiple agents who select and then implement actions in the system. The system has an operator with a centralized objective. The agents, on the other hand, are selfinterested and strategic in the sense that each agent optimizes its own individual objective. The operator aims to mitigate this misalignment by designing an incentive scheme for the agents. The problem is difficult due to the cost functions of the agents being coupled, the objective of the operator not being social welfare, and the operator having no direct control over actions being implemented by the agents. This problem has been studied in many fields, particularly in mechanism design and cost allocation. However, mechanism design typically assumes that the operator has knowledge of the cost functions of the agents and the actions being implemented by the operator. On the other hand, cost allocation classically assumes that agents do not anticipate the effect of their actions on the incentive that they obtain. We remove these assumptions and present an incentive rule for this setup by bridging the gap between mechanism design and classical cost allocation. We analyze whether the proposed design satisfies various desirable properties such as social optimality, budget balance, participation constraint, and so on. We also analyze which of these properties can be satisfied if the assumptions of cost functions of the agents being private and the agents being anticipatory are relaxed.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Mixed Voltage Angle and Frequency Droop Control for Transient Stability of Interconnected Microgrids with Loss of PMU Measurements

We consider the problem of guaranteeing transient stability of a network of interconnected angle droop controlled microgrids, where voltage phase angle measurements from phasor measurement units (PMUs) may be lost, leading to poor performance and instability. In this paper, we propose a novel mixed voltage angle and frequency droop control (MAFD) framework to improve the reliability of such angle droop controlled microgrid interconnections. In this framework, when the phase angle measurement is lost at a microgrid, conventional frequency droop control is temporarily used for primary control in place of angle droop control. We model the network of interconnected microgrids with the MAFD architecture as a nonlinear switched system. We then propose a dissipativity-based distributed secondary control design to guarantee transient stability of this network under arbitrary switching between angle droop and frequency droop controllers. We demonstrate the performance of this control framework by simulation on a test 123-feeder distribution network.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

On the Complexity of Sequential Incentive Design

In many scenarios, a principal dynamically interacts with an agent and offers a sequence of incentives to align the agent's behavior with a desired objective. This paper focuses on the problem of synthesizing an incentive sequence that, once offered, induces the desired agent behavior even when the agent's intrinsic motivation is unknown to the principal. We model the agent's behavior as a Markov decision process, express its intrinsic motivation as a reward function, which belongs to a finite set of possible reward functions, and consider the incentives as additional rewards offered to the agent. We first show that the behavior modification problem (BMP), i.e., the problem of synthesizing an incentive sequence that induces a desired agent behavior at minimum total cost to the principal, is PSPACE-hard. Moreover, we show that by imposing certain restrictions on the incentive sequences available to the principal, one can obtain two NP-complete variants of the BMP. We also provide a sufficient condition on the set of possible reward functions under which the BMP can be solved via linear programming. Finally, we propose two algorithms to compute globally and locally optimal solutions to the NP-complete variants of the BMP.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Weak Control for Human-in-the-loop Systems

In this letter, we propose a control framework for human-in-the-loop systems, in which many human decision makers are involved in the feedback loop composed of a plant and a controller. The novelty of the framework is that the decision makers are weakly controlled; in other words, they receive a set of admissible control actions from the controller and choose one of them in accordance with their private preferences. For example, the decision makers can decide their actions to minimize their own costs or by simply relying on their experience and intuition. A class of controllers which output set-valued signals is proposed, and it is shown that the overall control system is stable independently of the decisions made by the humans. Finally, a learning algorithm is applied to the controller that updates the controller parameters to reduce the achievable minimal costs for the decision makers. Effective use of the algorithm is demonstrated in a numerical experiment.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Analysis of Two-Dimensional Feedback Systems over Networks Using Dissipativity

This paper investigates the closed-loop $\mathcal{L}_2$ stability of two-dimensional (2-D) feedback systems across a digital communication network by introducing the tool of dissipativity. First, sampling of a continuous 2-D system is considered and an analytical characterization of the $QSR$-dissipativity of the sampled system is presented. Next, the input-feedforward output-feedback passivity (IF-OFP), a simplified form of $QSR$-dissipativity, is utilized to study the framework of feedback interconnection of two 2-D systems over networks. Then, the effects of signal quantization in communication links on dissipativity degradation of the 2-D feedback quantized system is analyzed. Additionally, an event-triggered mechanism is developed for 2-D networked control systems while maintaining $\mathcal{L}_2$ stability of the closed-loop system. In the end, an illustrative example is provided.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Distributed Estimation in the Presence of Strategic Data Sources

Distributed estimation that recruits potentially large groups of humans to collect data about a phenomenon of interest has emerged as a paradigm applicable to a broad range of detection and estimation tasks. However, it also presents a number of challenges especially with regard to user participation and data quality, since the data resources may be strategic human agents instead of physical sensors. We consider a static estimation problem in which an estimator collects data from self-interested agents. Since it incurs cost to participate, mechanisms to incentivize the agents to collect and transmit data of desired quality are needed. Agents are strategic in the sense that they can take measurement with different levels of accuracy by expending different levels of effort. They may also misreport their information in order to obtain greater compensation, if possible. With both the measurements from the agents and their accuracy unknown to the estimator, we design incentive mechanisms that encourage desired behavior from strategic agents. Specifically, we solve an optimization problem at the estimator which minimizes the expected total compensation to the agents while guaranteeing a specified quality of the global estimate.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Passivity-Based Analysis of Sampled and Quantized Control Implementations

This paper studies the performance of a continuous controller when implemented on digital devices via sampling and quantization, by leveraging passivity analysis. Degradation of passivity indices from a continuous-time control system to its sampled, input and output quantized model is studied using a notion of quasi-passivity. Based on that, the passivity property of a feedback-connected system where the continuous controller is replaced by its sampled and quantized model is studied, and conditions that ensure the state boundedness of the interconnected system are provided. Additionally, the approximate bisimulation-based control implementation where the controller is replaced by its approximate bisimilar symbolic model whose states are also quantized is analyzed. Several examples are provided to illustrate the theoretical results.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

(p,q)-Beta Functions and Applications in Approximation

In the present paper, we consider (p,q)-analogue of the Beta operators and using it, we propose the integral modification of the generalized Bernstein polynomials. We estimate some direct results on local and global approximation. Also, we illustrate some graphs for the convergence of (p,q)-Bernstein-Durrmeyer operators for different values of the parameters p and q using Mathematica package.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Incentivizing Truth-Telling in MPC-based Load Frequency Control

We present a mechanism for socially efficient implementation of model predictive control (MPC) algorithms for load frequency control (LFC) in the presence of self-interested power generators. Specifically, we consider a situation in which the system operator seeks to implement an MPC-based LFC for aggregated social cost minimization, but necessary information such as individual generators' cost functions is privately owned. Without appropriate monetary compensation mechanisms that incentivize truth-telling, self-interested market participants may be inclined to misreport their private parameters in an effort to maximize their own profits, which may result in a loss of social welfare. The main challenge in our framework arises from the fact that every participant's strategy at any time affects the future state of other participants; the consequences of such dynamic coupling has not been fully addressed in the literature on online mechanism design. We propose a class of real-time monetary compensation schemes that incentivize market participants to report their private parameters truthfully at every time step, which enables the system operator to implement MPC-based LFC in a socially optimal manner.

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preprint2016arXiv

Minimizing Risk of Load Shedding and Renewable Energy Curtailment in a Microgrid with Energy Storage

We consider a microgrid with random load realization, stochastic renewable energy production, and an energy storage unit. The grid controller provides the total net load trajectory that the microgrid should present to the main grid and the microgrid must impose load shedding and renewable energy curtailment if necessary to meet that net load trajectory. The microgrid controller seeks to operate the local energy storage unit to minimize the risk of load shedding, and renewable energy curtailment over a finite time horizon. We formulate the problem of optimizing the operation of the storage unit as a finite stage dynamic programming problem. We prove that the multi-stage objective function of the energy storage is strictly convex in the state of charge of the battery at each stage. The uniqueness of the optimal decision is proven under some additional assumptions. The optimal strategy is then obtained. The effectiveness of the energy storage in decreasing load shedding and RE curtailment is illustrated in simulations.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Pricing Energy in the Presence of Renewables

At present, electricity markets largely ignore the fact that renewable power producers impose significant externalities on non-renewable energy producers. This is because consumers are generally guaranteed electricity within certain load parameters. The intermittent nature of production by renewable energy producers implies that they rely on non-renewable producers so that the aggregate power delivered meets the promised quality of service. This implicit insurance provided by the non-renewable power sector to consumers is not currently priced and leads to an often ignored, hidden monetary transfer from non-renewable producers to renewable producers. As the fraction of energy supplied by renewable resources increases, these externalities also increase. In this paper, we quantify these externalities by developing the market clearing price of energy in the presence of renewable energy. We consider a day-ahead electricity market where renewable and non-renewable generators bid by proposing their asking price per unit of energy to an independent system operator (ISO). The ISO's problem is a multi-stage stochastic optimization problem to dispatch energy from each generator to minimize the cost of purchased energy on behalf of the consumers. We incorporate the notion of load variance using the Conditional Value-at-Risk (CVAR) measure in the day-ahead electricity market to ensure that the generators are able to meet the load within a desired confidence level. We analytically derive the market clearing price of energy as a function of CVAR. It is shown that a higher penetration level of the renewable energies may increase the market clearing price of energy.

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preprint2015arXiv

A Switched Dynamical System Framework for Analysis of Massively Parallel Asynchronous Numerical Algorithms

In the near future, massively parallel computing systems will be necessary to solve computation intensive applications. The key bottleneck in massively parallel implementation of numerical algorithms is the synchronization of data across processing elements (PEs) after each iteration, which results in significant idle time. Thus, there is a trend towards relaxing the synchronization and adopting an asynchronous model of computation to reduce idle time. However, it is not clear what is the effect of this relaxation on the stability and accuracy of the numerical algorithm. In this paper we present a new framework to analyze such algorithms. We treat the computation in each PE as a dynamical system and model the asynchrony as stochastic switching. The overall system is then analyzed as a switched dynamical system. However, modeling of massively parallel numerical algorithms as switched dynamical systems results in a very large number of modes, which makes current analysis tools available for such systems computationally intractable. We develop new techniques that circumvent this scalability issue. The framework is presented on a one-dimensional heat equation as a case study and the proposed analysis framework is verified by solving the partial differential equation (PDE) in a $\mathtt{nVIDIA\: Tesla^{\scriptsize{TM}}}$ GPU machine, with asynchronous communication between cores.

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preprint2015arXiv

Approximation by Complex Baskakov-Szasz-Durrmeyer Operators in Compact Disks

In this paper, we deal with the complex Baskakov-Szasz-Durrmeyer mixed operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth in the open disk of radius R. Also, the exact order of approximation is found. The method used allows to construct complex Szasz-type and Baskakov-type approximation operators without involving the values on the positive real axis.

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preprint2015arXiv

Distributed Charging Control of Electric Vehicles Using Online Learning

We propose an algorithm for distributed charging control of electric vehicles (EVs) using online learning and online convex optimization. Many distributed charging control algorithms in the literature implicitly assume fast two-way communication between a distribution company and EV customers. This assumption is impractical at present and raises privacy and security concerns. Our algorithm does not use this assumption; however, at the expense of slower convergence to the optimal solution. The proposed algorithm requires one-way communication, which is implemented through the distribution company publishing the pricing profiles of the previous days. We provide convergence results of the algorithm and illustrate the results through numerical examples.

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preprint2015arXiv

On the trade-off between control performance and communication cost in event-triggered control

We consider a stochastic system where the communication between the controller and the actuator is triggered by a threshold-based rule. The communication is performed across an unreliable link that stochastically erases transmitted packets. To decrease the communication burden, and as a partial protection against dropped packets, the controller sends a sequence of control commands to the actuator in each packet. These commands are stored in a buffer and applied sequentially until the next control packet arrives. In this context, we study dead-beat control laws and compute the expected linear-quadratic loss of the closed-loop system for any given event-threshold. Furthermore, we provide analytical expressions that quantify the trade-off between the communication cost and the control performance of event-triggered control systems. Numerical examples demonstrate the effectiveness of the proposed framework.

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preprint2015arXiv

Passivity Degradation In Discrete Control Implementations: An Approximate Bisimulation Approach

In this paper, we present some preliminary results for compositional analysis of heterogeneous systems containing both discrete state models and continuous systems using consistent notions of dissipativity and passivity. We study the following problem: given a physical plant model and a continuous feedback controller designed using traditional control techniques, how is the closed-loop passivity affected when the continuous controller is replaced by a discrete (i.e., symbolic) implementation within this framework? Specifically, we give quantitative results on performance degradation when the discrete control implementation is approximately bisimilar to the continuous controller, and based on them, we provide conditions that guarantee the boundedness property of the closed-loop system.

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preprint2014arXiv

Anytime Control using Input Sequences with Markovian Processor Availability

We study an anytime control algorithm for situations where the processing resources available for control are time-varying in an a priori unknown fashion. Thus, at times, processing resources are insufficient to calculate control inputs. To address this issue, the algorithm calculates sequences of tentative future control inputs whenever possible, which are then buffered for possible future use. We assume that the processor availability is correlated so that the number of control inputs calculated at any time step is described by a Markov chain. Using a Lyapunov function based approach we derive sufficient conditions for stochastic stability of the closed loop.

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preprint2014arXiv

Moment Estimations of new Szász-Mirakyan-Durrmeyer operators

In [10] Jain introduced the modified form of the Szász-Mirakjan operator, based on certain parameter $0\leβ<1$. Several modifications of the operators are available in the literature. Here we consider actual Durrmeyer variant of the operators due to [10]. It is observed here that the Durrmeyer variant has the nice properties and one need not to take any restriction on $β$ in order to get convergence. We establish moments using the Tricomi's confluent hypergeometric function and Stirling numbers of first kind, also estimate some direct results

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preprint2013arXiv

Sequence-based Anytime Control

We present two related anytime algorithms for control of nonlinear systems when the processing resources available are time-varying. The basic idea is to calculate tentative control input sequences for as many time steps into the future as allowed by the available processing resources at every time step. This serves to compensate for the time steps when the processor is not available to perform any control calculations. Using a stochastic Lyapunov function based approach, we analyze the stability of the resulting closed loop system for the cases when the processor availability can be modeled as an independent and identically distributed sequence and via an underlying Markov chain. Numerical simulations indicate that the increase in performance due to the proposed algorithms can be significant.

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preprint2013arXiv

Stochastic Stability of Event-triggered Anytime Control

We investigate control of a non-linear process when communication and processing capabilities are limited. The sensor communicates with a controller node through an erasure channel which introduces i.i.d. packet dropouts. Processor availability for control is random and, at times, insufficient to calculate plant inputs. To make efficient use of communication and processing resources, the sensor only transmits when the plant state lies outside a bounded target set. Control calculations are triggered by the received data. If a plant state measurement is successfully received and while the processor is available for control, the algorithm recursively calculates a sequence of tentative plant inputs, which are stored in a buffer for potential future use. This safeguards for time-steps when the processor is unavailable for control. We derive sufficient conditions on system parameters for stochastic stability of the closed loop and illustrate performance gains through numerical studies.

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preprint2010arXiv

Convergence Speed of the Consensus Algorithm with Interference and Sparse Long-Range Connectivity

We analyze the effect of interference on the convergence rate of average consensus algorithms, which iteratively compute the measurement average by message passing among nodes. It is usually assumed that these algorithms converge faster with a greater exchange of information (i.e., by increased network connectivity) in every iteration. However, when interference is taken into account, it is no longer clear if the rate of convergence increases with network connectivity. We study this problem for randomly-placed consensus-seeking nodes connected through an interference-limited network. We investigate the following questions: (a) How does the rate of convergence vary with increasing communication range of each node? and (b) How does this result change when each node is allowed to communicate with a few selected far-off nodes? When nodes schedule their transmissions to avoid interference, we show that the convergence speed scales with $r^{2-d}$, where $r$ is the communication range and $d$ is the number of dimensions. This scaling is the result of two competing effects when increasing $r$: Increased schedule length for interference-free transmission vs. the speed gain due to improved connectivity. Hence, although one-dimensional networks can converge faster from a greater communication range despite increased interference, the two effects exactly offset one another in two-dimensions. In higher dimensions, increasing the communication range can actually degrade the rate of convergence. Our results thus underline the importance of factoring in the effect of interference in the design of distributed estimation algorithms.

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