arXiv subjects

Vijay Gupta

Publications and source records attributed to Vijay Gupta.

At least 91 records · Page 5Linked to original sources

arXiv2019

Sequential Synthesis of Distributed Controllers for Cascade Interconnected Systems

We consider the problem of designing distributed controllers to ensure passivity of a large-scale interconnection of linear subsystems connected in a cascade topology. The control design process needs to be carried out at the subsystem-level with no direct knowledge of the dynamics of other subsystems in the interconnection. We present a distributed approach to solve this problem, where subsystem-level controllers are locally designed in a sequence starting at one end of the cascade using only the dynamics of the particular subsystem, coupling with the immediately preceding subsystem and limited information from the preceding subsystem in the cascade to ensure passivity of the interconnected system up to that point. We demonstrate that this design framework also allows for new subsystems to be compositionally added to the interconnection without requiring redesign of the pre-existing controllers.

eess.SY↗

arXiv2018

Better numerical approximation by Durrmeyer type operators

The main object of this paper is to construct new Durrmeyer type operators which have better features than the classical one. Some results concerning the rate of convergence and asymptotic formulas of the new operator are given. Finally, the theoretical results are analyzed by numerical examples.

math.NA↗

arXiv2018

Energy Absorption and Low Velocity Impact Response of Open-Cell Polyurea Foams

The energy absorption and impact attenuation of low density polyurea (PU) foams (140 - 220 kg/m3) is presented. The stress-strain behavior, energy absorption, cushioning efficiency, and energy return (resilience) are measured at a quasi-static strain rate using an Instron load frame. In addition, the low velocity impact attenuation of the polyurea foams at 5 J and 7 J impact energies were investigated according to the American Society for Testing and Materials (ASTM) test methods F1976. The polyurea foams were then compared with widely used ethylene vinyl acetate (EVA) and thermoplastic polyurethane (TPU) foam technologies at similar densities. The PU foams displayed a 5 % increase in cushioning efficiency and 30 % greater energy absorption over TPU and EVA foams under quasi-static compression. Under impact testing, PU foams resulted in a reduction of up to 28.6 % and 36.9 % in peak transmitted impact forces when compared to EVA and TPU foams of the same thickness (20 mm) at 5 J and 7 J, respectively. These properties should allow these materials to have a wide range of cushioning/impact applications, especially in protective body and headgear systems.

cond-mat.soft↗

arXiv2018

Reliability and Market Price of Energy in the Presence of Intermittent and Non-Dispatchable Renewable Energies

The intermittent nature of the renewable energies increases the operation costs of conventional generators. As the share of energy supplied by renewable sources increases, these costs also increase. In this paper, we quantify these costs by developing a market clearing price of energy in the presence of renewable energy and congestion constraints. We consider an electricity market where generators propose their asking price per unit of energy to an independent system operator (ISO). The ISO solve an optimization problem to dispatch energy from each generator to minimize the total cost of energy purchased on behalf of the consumers. To ensure that the generators are able to meet the load within a desired confidence level, we incorporate the notion of load variance using the Conditional Value-at-Risk (CVAR) measure in an electricity market and we derive the amount of committed power and market clearing price of energy as a function of CVAR. It is shown that a higher penetration of renewable energies may increase the committed power, market clearing price of energy and consumer cost of energy due to renewable generation uncertainties. We also obtain an upper-bound on the amount that congestion constraints can affect the committed power. We present descriptive simulations to illustrate the impact of renewable energy penetration and reliability levels on committed power by the non-renewable generators, difference between the dispatched and committed power, market price of energy and profit of renewable and non-renewable generators.

eess.SY↗

arXiv2018

Conic-sector-based analysis and control synthesis for linear parameter varying systems

We present a conic sector theorem for linear parameter varying (LPV) systems in which the traditional definition of conicity is violated for certain values of the parameter. We show that such LPV systems can be defined to be conic in an average sense if the parameter trajectories are restricted so that the system operates with such values of the parameter sufficiently rarely. We then show that such an average definition of conicity is useful in analyzing the stability of the system when it is connected in feedback with a conic system with appropriate conic properties. This can be regarded as an extension of the classical conic sector theorem. Based on this modified conic sector theorem, we design conic controllers that allow the closed-loop system to operate in nonconic parameter regions for brief periods of time. Due to this extra degree of freedom, these controllers lead to less conservative performance than traditional designs, in which the controller parameters are chosen based on the largest cone that the plant dynamics are contained in. We demonstrate the effectiveness of the proposed design in stabilizing a power grid with very high penetration of renewable energy while minimizing power transmission losses.

eess.SY↗

arXiv2018

Dynamic Pricing and Energy Management Strategy for EV Charging Stations under Uncertainties

This paper presents a dynamic pricing and energy management framework for electric vehicle (EV) charging service providers. To set the charging prices, the service providers faces three uncertainties: the volatility of wholesale electricity price, intermittent renewable energy generation, and spatial-temporal EV charging demand. The main objective of our work here is to help charging service providers to improve their total profits while enhancing customer satisfaction and maintaining power grid stability, taking into account those uncertainties. We employ a linear regression model to estimate the EV charging demand at each charging station, and introduce a quantitative measure for customer satisfaction. Both the greedy algorithm and the dynamic programming (DP) algorithm are employed to derive the optimal charging prices and determine how much electricity to be purchased from the wholesale market in each planning horizon. Simulation results show that DP algorithm achieves an increased profit (up to 9%) compared to the greedy algorithm (the benchmark algorithm) under certain scenarios. Additionally, we observe that the integration of a low-cost energy storage into the system can not only improve the profit, but also smooth out the charging price fluctuation, protecting the end customers from the volatile wholesale market.

eess.SP↗

arXiv2018

Placement of EV Charging Stations --- Balancing Benefits among Multiple Entities

This paper studies the problem of multi-stage placement of electric vehicle (EV) charging stations with incremental EV penetration rates. A nested logit model is employed to analyze the charging preference of the individual consumer (EV owner), and predict the aggregated charging demand at the charging stations. The EV charging industry is modeled as an oligopoly where the entire market is dominated by a few charging service providers (oligopolists). At the beginning of each planning stage, an optimal placement policy for each service provider is obtained through analyzing strategic interactions in a Bayesian game. To derive the optimal placement policy, we consider both the transportation network graph and the electric power network graph. A simulation software --- The EV Virtual City 1.0 --- is developed using Java to investigate the interactions among the consumers (EV owner), the transportation network graph, the electric power network graph, and the charging stations. Through a series of experiments using the geographic and demographic data from the city of San Pedro District of Los Angeles, we show that the charging station placement is highly consistent with the heatmap of the traffic flow. In addition, we observe a spatial economic phenomenon that service providers prefer clustering instead of separation in the EV charging market.

eess.SP↗

arXiv2018

Stochastic Dynamic Pricing for EV Charging Stations with Renewables Integration and Energy Storage

This paper studies the problem of stochastic dynamic pricing and energy management policy for electric vehicle (EV) charging service providers. In the presence of renewable energy integration and energy storage system, EV charging service providers must deal with multiple uncertainties --- charging demand volatility, inherent intermittency of renewable energy generation, and wholesale electricity price fluctuation. The motivation behind our work is to offer guidelines for charging service providers to determine proper charging prices and manage electricity to balance the competing objectives of improving profitability, enhancing customer satisfaction, and reducing impact on power grid in spite of these uncertainties. We propose a new metric to assess the impact on power grid without solving complete power flow equations. To protect service providers from severe financial losses, a safeguard of profit is incorporated in the model. Two algorithms --- stochastic dynamic programming (SDP) algorithm and greedy algorithm (benchmark algorithm) --- are applied to derive the pricing and electricity procurement policy. A Pareto front of the multiobjective optimization is derived. Simulation results show that using SDP algorithm can achieve up to 7% profit gain over using greedy algorithm. Additionally, we observe that the charging service provider is able to reshape spatial-temporal charging demands to reduce the impact on power grid via pricing signals.

eess.SP↗

arXiv2018

A Consumer Behavior Based Approach to Multi-Stage EV Charging Station Placement

This paper presents a multi-stage approach to the placement of charging stations under the scenarios of different electric vehicle (EV) penetration rates. The EV charging market is modeled as the oligopoly. A consumer behavior based approach is applied to forecast the charging demand of the charging stations using a nested logit model. The impacts of both the urban road network and the power grid network on charging station planning are also considered. At each planning stage, the optimal station placement strategy is derived through solving a Bayesian game among the service providers. To investigate the interplay of the travel pattern, the consumer behavior, urban road network, power grid network, and the charging station placement, a simulation platform (The EV Virtual City 1.0) is developed using Java on Repast.We conduct a case study in the San Pedro District of Los Angeles by importing the geographic and demographic data of that region into the platform. The simulation results demonstrate a strong consistency between the charging station placement and the traffic flow of EVs. The results also reveal an interesting phenomenon that service providers prefer clustering instead of spatial separation in this oligopoly market.

eess.SP↗

arXiv2017

Dissipativity of system abstractions obtained using approximate input-output simulation

This work focuses on the invariance of important properties between continuous and discrete models of systems which can be useful in the control design of large-scale systems and their software implementations. In particular, this paper discusses the relationships between the QSR dissipativity of a continuous state dynamical system and of its abstractions obtained through approximate input-output simulation relations. First, conditions to guarantee the dissipativity of the continuous system from its abstractions are provided. The reverse problem of determining the Q, S and R dissipativity matrices of the abstract system from that of the continuous system is also considered. Results characterizing the change in the dissipativity matrices are provided when the system abstraction is obtained. Since, under certain conditions, QSR dissipative systems are known to be stable, the results of this paper can be used to construct stable system abstractions as well. In the second part of this paper, we analyze the dissipativity of the approximate feedback composition of a continuous dynamical system and a discrete controller. We present illustrative examples to demonstrate the results of this paper.

eess.SY↗

arXiv2017

A Note on Jain modified Phillips operators

In the present article we define the Phillips type modification of the generalized Szász-Mirakjan operators. Moments, recurrence formulas, and other identities are established for these operators. Approximation properties are also obtained with use of the Boham-Korovkin theorem.

math.CA↗

arXiv2017

Encoding Multi-Resolution Brain Networks Using Unsupervised Deep Learning

The main goal of this study is to extract a set of brain networks in multiple time-resolutions to analyze the connectivity patterns among the anatomic regions for a given cognitive task. We suggest a deep architecture which learns the natural groupings of the connectivity patterns of human brain in multiple time-resolutions. The suggested architecture is tested on task data set of Human Connectome Project (HCP) where we extract multi-resolution networks, each of which corresponds to a cognitive task. At the first level of this architecture, we decompose the fMRI signal into multiple sub-bands using wavelet decompositions. At the second level, for each sub-band, we estimate a brain network extracted from short time windows of the fMRI signal. At the third level, we feed the adjacency matrices of each mesh network at each time-resolution into an unsupervised deep learning algorithm, namely, a Stacked De- noising Auto-Encoder (SDAE). The outputs of the SDAE provide a compact connectivity representation for each time window at each sub-band of the fMRI signal. We concatenate the learned representations of all sub-bands at each window and cluster them by a hierarchical algorithm to find the natural groupings among the windows. We observe that each cluster represents a cognitive task with a performance of 93% Rand Index and 71% Adjusted Rand Index. We visualize the mean values and the precisions of the networks at each component of the cluster mixture. The mean brain networks at cluster centers show the variations among cognitive tasks and the precision of each cluster shows the within cluster variability of networks, across the subjects.

stat.ML↗

arXiv2017

Trade-Offs in Stochastic Event-Triggered Control

This paper studies the optimal output-feedback control of a linear time-invariant system where a stochastic event-based scheduler triggers the communication between the sensor and the controller. The primary goal of the use of this type of scheduling strategy is to provide significant reductions in the usage of the sensor-to-controller communication and, in turn, improve energy expenditure in the network. In this paper, we aim to design an admissible control policy, which is a function of the observed output, to minimize a quadratic cost function while employing a stochastic event-triggered scheduler that preserves the Gaussian property of the plant state and the estimation error. For the infinite horizon case, we present analytical expressions that quantify the trade-off between the communication cost and control performance of such event-triggered control systems. This trade-off is confirmed quantitatively via numerical examples.

eess.SY↗

arXiv2017

On Passivity of Fractional Order Systems

We generalize notions of passivity and dissipativity to fractional order systems. Similar to integer order systems, we show that the proposed definitions generate analogous stability and compositionality properties for fractional order systems as well. We also study the problem of passivating a fractional order system through a feedback controller. Numerical examples are presented to illustrate the concepts.

math.DS↗

arXiv2017

Provably Safe Cruise Control of Vehicular Platoons

We synthesize performance-aware safe cruise control policies for longitudinal motion of platoons of autonomous vehicles. Using set-invariance theories, we guarantee infinite-time collision avoidance in the presence of bounded additive disturbances, while ensuring that the length and the cruise speed of the platoon are bounded within specified ranges. We propose (i) a centralized control policy, and (ii) a distributed control policy, where each vehicle's control decision depends solely on its relative kinematics with respect to the platoon leader. Numerical examples are included.

eess.SY↗

arXiv2017

Data-Injection Attacks in Stochastic Control Systems: Detectability and Performance Tradeoffs

Consider a stochastic process being controlled across a communication channel. The control signal that is transmitted across the control channel can be replaced by a malicious attacker. The controller is allowed to implement any arbitrary detection algorithm to detect if an attacker is present. This work characterizes some fundamental limitations of when such an attack can be detected, and quantifies the performance degradation that an attacker that seeks to be undetected or stealthy can introduce.

math.OC↗

arXiv2017

A Reputation-Based Contract for Repeated Crowdsensing with Costly Verification

We study a setup in which a system operator hires a sensor to exert costly effort to collect accurate measurements of a value of interest over time. At each time, the sensor is asked to report his observation to the operator, and is compensated based on the accuracy of this observation. Since both the effort and observation are private information for the sensor, a naive payment scheme which compensates the sensor based only on his self-reported values will lead to both shirking and falsification of outcomes by the sensor. We consider the problem of designing an appropriate compensation scheme to incentivize the sensor to at once exert costly effort and truthfully reveal the resulting observation. To this end, we formulate the problem as a repeated game and propose a compensation scheme that employs stochastic verification by the operator coupled with a system of assigning reputation to the sensor. In particular, our proposed payment scheme compensates the sensor based on both the effort in the current period as well as the history of past behavior. We show that by using past behavior in determining present payments, the operator can both incentivize higher effort as well as more frequent truthtelling by the sensor and decrease the required verification frequency.

math.OC↗

arXiv2017

A Contract Design Approach for Phantom Demand Response

We design an optimal contract between a demand response aggregator (DRA) and power grid customers for incentive-based demand response. We consider a setting in which the customers are asked to reduce their electricity consumption by the DRA and they are compensated for this demand curtailment. However, given that the DRA must supply every customer with as much power as she desires, a strategic customer can temporarily increase her base load in order to report a larger reduction as part of the demand response event. The DRA wishes to incentivize the customers both to make costly effort to reduce load and to not falsify the reported load reduction. We model this problem as a contract design problem and present a solution. The proposed contract consists of two parts: a part that depends on (the possibly inflated) load reduction as measured by the DRA and another that provides a share of the profit that accrues to the DRA through the demand response event to the customers. Since this profit accrues due to the total load reduction because of the actions taken by all the customers, the interaction among the customers also needs to be carefully included in the contract design. The contract design and its properties are presented and illustrated through examples.

math.OC↗