arXiv subjects

Vijay Gupta

Publications and source records attributed to Vijay Gupta.

At least 73 records · Page 4Linked to original sources

arXiv2020

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.

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arXiv2020

Stealthy hacking and secrecy of controlled state estimation systems with random dropouts

We study the maximum information gain that an adversary may obtain through hacking without being detected. Consider a dynamical process observed by a sensor that transmits a local estimate of the system state to a remote estimator according to some reference transmission policy across a packet-dropping wireless channel equipped with acknowledgments (ACK). An adversary overhears the transmissions and proactively hijacks the sensor to reprogram its transmission policy. We define perfect secrecy as keeping the averaged expected error covariance bounded at the legitimate estimator and unbounded at the adversary. By analyzing the stationary distribution of the expected error covariance, we show that perfect secrecy can be attained for unstable systems only if the ACK channel has no packet dropouts. In other situations, we prove that independent of the reference policy and the detection methods, perfect secrecy is not attainable. For this scenario, we formulate a constrained Markov decision process to derive the optimal transmission policy that the adversary should implement at the sensor, and devise a Stackelberg game to derive the optimal reference policy for the legitimate estimator.

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arXiv2020

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.

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arXiv2020

An Insurance Contract Design to Boost Storage Participation in the Electricity Market

Energy storage technologies are key to improving grid flexibility in the presence of increasing amounts of intermittent renewable generation. We propose an insurance contract that suitably compensates energy storage systems for providing flexibility. Such a contract provides a wider range of market opportunities for these systems while also incentivizing higher renewable penetration in the grid. We consider a day-ahead market in which generators, including renewables and storage owners, bid to be scheduled for the next operating day. Due to production uncertainty, renewable generators may be unable to meet their day-ahead production schedule, and thus be subject to a penalty. As a hedge against these penalties, we propose an insurance contract between a renewable producer and a storage owner, in which the storage reserves some energy to be used in case of renewable shortfalls. We show that such a contract incentivizes the renewable player to bid higher, thus increasing renewable participation in the electricity mix. It also provides an extra source of revenue for storage owners that may not be profitable with a purely arbitrage-based strategy in the day-ahead market. Further, we prove this contract is economically beneficial for both players. We validate our analysis through two case studies.

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arXiv2020

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.

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arXiv2020

Optimal Contract Design for Incentive-Based Demand Response

We design an optimal contract between a demand response aggregator (DRA) and a customer for incentive-based demand response. We consider a setting in which the customer is asked to reduce her consumption by the DRA and she is compensated for this reduction. However, since the DRA must supply the customer with as much power as she desires, a strategic customer can temporarily increase her base load to report a larger reduction as a part of the demand response event. The DRA wishes to incentivize the customer both to make the maximal effort in reducing the load and to not falsify the base load. We model the problem of designing the contract by the DRA for the customer as a management contract design problem and present a solution. The optimal contract consists of two parts: a part that depends on (the possibly inflated) load reduction as measured and another that provides a share of the profit that ensues to the DRA through the demand response event to the customer.

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arXiv2020

A Game-Theoretic Approach to a Task Delegation Problem

We study a setting in which a principal selects an agent to execute a collection of tasks according to a specified priority sequence. Agents, however, have their own individual priority sequences according to which they wish to execute the tasks. There is information asymmetry since each priority sequence is private knowledge for the individual agent. We design a mechanism for selecting the agent and incentivizing the selected agent to realize a priority sequence for executing the tasks that achieves socially optimal performance. Our proposed mechanism consists of two parts. First, the principal runs an auction to select an agent to allocate tasks to with minimum declared priority sequence misalignment. Then, the principal rewards the agent according to the realized priority sequence with which the tasks were performed. We show that the proposed mechanism is individually rational and incentive compatible. Further, it is also socially optimal for the case of linear cost of priority sequence modification for the agents.

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arXiv2020

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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arXiv2020

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.

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arXiv2020

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.

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arXiv2019

Weak Control Approach to Consumer-Preferred Energy Management

This paper is devoted to a consumer-preferred community-level energy management system (CEMS), in which a system manager allows consumers their selfish decisions of power-saving while regulating the overall demand-supply imbalance. The key structure of the system is to weakly control consumers: the controller sends the allowable range of the power-saving amount to each consumer, which is modeled by a set-valued control signal. Then, the consumers decide the amount in the range based on their private preference. In this paper, we address the design problem of the controller that generates the set-valued control signals. The controller structure is based on internal model control, which plays the essential role of guaranteeing the consumer-independent stability and the worst-case control performance of the overall CEMS. Finally, a numerical experiment of the consumer-preferred CEMS is performed to demonstrate the design procedure of the controller and to show its effectiveness.

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arXiv2019

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.

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arXiv2019

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.

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arXiv2019

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.

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arXiv2019

Stabilization of Linear Systems Across a Time-Varying AWGN Fading Channel

This technical note investigates the minimum average transmit power required for mean-square stabilization of a discrete-time linear process across a time-varying additive white Gaussian noise (AWGN) fading channel that is presented between the sensor and the controller. We assume channel state information at both the transmitter and the receiver, and allow the transmit power to vary with the channel state to obtain the minimum required average transmit power via optimal power adaptation. We consider both the case of independent and identically distributed fading and fading subject to a Markov chain. Based on the proposed necessary and sufficient conditions for mean-square stabilization, we show that the minimum average transmit power to ensure stabilizability can be obtained by solving a geometric program.

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arXiv2019

Feedback Passivation of Linear Systems with Fixed-Structured Controllers

This paper addresses the problem of designing an optimal output feedback controller with a specified controller structure for linear time-invariant (LTI) systems to maximize the passivity level for the closed-loop system, in both continuous-time (CT) and discrete-time (DT). Specifically, the set of controllers under consideration is linearly parameterized with constrained parameters. Both input feedforward passivity (IFP) and output feedback passivity (OFP) indices are used to capture the level of passivity. Given a set of stabilizing controllers, a necessary and sufficient condition is proposed for the existence of such fixed-structured output feedback controllers that can passivate the closed-loop system. Moreover, it is shown that the condition can be used to obtain the controller that maximizes the IFP or the OFP index by solving a convex optimization problem.

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arXiv2019

Data-driven identification of dissipative linear models for nonlinear systems

We consider the problem of identifying a dissipative linear model of an unknown nonlinear system that is known to be dissipative, from time domain input-output data. We first learn an approximate linear model of the nonlinear system using standard system identification techniques and then perturb the system matrices of the linear model to enforce dissipativity, while closely approximating the dynamical behavior of the nonlinear system. Further, we provide an analytical relationship between the size of the perturbation and the radius in which the dissipativity of the linear model guarantees local dissipativity of the unknown nonlinear system. We demonstrate the application of this identification technique to the problem of learning a dissipative model of a microgrid with high penetration of variable renewable energy sources.

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arXiv2019

Incentive Design for Temporal Logic Objectives

We study the problem of designing an optimal sequence of incentives that a principal should offer to an agent so that the agent's optimal behavior under the incentives realizes the principal's objective expressed as a temporal logic formula. We consider an agent with a finite decision horizon and model its decision-making process as a Markov decision process (MDP). Under certain assumptions, we present a polynomial-time algorithm to synthesize an incentive sequence that minimizes the cost to the principal. We show that if the underlying MDP has only deterministic transitions, the principal can hide its objective from the agent and still realize the desired behavior through incentives. On the other hand, an MDP with stochastic transitions may require the principal to share its objective with the agent. Finally, we demonstrate the proposed method in motion planning examples where a principal changes the optimal trajectory of an agent by providing incentives.

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