Searcharxiv⌕ Search

arXiv subjects

Vivek Khatana

Publications and source records attributed to Vivek Khatana.

17 recordsLinked to original sources
arXiv2026

Large-Signal Stability Analysis of Optimization-Based Secondary Control for Distributed Energy Resources

This article develops a large-signal stability analysis for a sampled-data optimization-based secondary controller for distributed energy resources (DERs) in power systems. The induced closed loop combines nonlinear inverter power-flow dynamics, filtered active and reactive power measurements, constrained optimization updates, and interpolation-based actuation between sampling instants. We study this optimization-in-the-loop nonlinear sampled-data system beyond local linearization. The analysis provides computable bounds on the voltage, filtered reactive power, and the secondary control input. We further characterize steady-state operating points and establish how the optimizer objectives and constraints connect voltage regulation with equal per-unitized reactive power sharing. Finally, input-to-state stability of the frequency dynamics is established with respect to DER voltages and control inputs. These results provide a rigorous mathematical foundation for sampled-data optimization-based secondary control of DERs.

eess.SY↗
arXiv2026

Storage and Transport Capacity Design for a Self-Reliable Two-Node Stochastic Resource System

We study a two-node stochastic resource system operating over a finite horizon. Each node experiences uncertain supply and demand and is equipped with finite storage. The objective is to ensure that resource levels remain within prescribed limits with high probability. To this end, we formulate a chance-constrained capacity-design problem in which resources can be exchanged through a capacity-limited transport link. We characterize the minimum storage required at each node, derive the optimal transport policy, and quantify the trade-off between storage and transport capacities. Our results show the existence of a critical transport-capacity threshold that enables full risk pooling between the nodes. Moreover, this threshold decreases with the operating horizon, implying that full-pooling performance can be achieved with progressively smaller transport capacity over longer horizons.

eess.SY↗
arXiv2025

Networked Control and Mean Field Problems Under Diagonal Dominance: Decentralized and Social Optimality

In this article, we employ an input-output approach to expand the study of cooperative multi-agent control and optimization problems characterized by mean-field interactions that admit decentralized and selfish solutions. The setting involves $n$ independent agents that interact solely through a shared cost function, which penalizes deviations of each agent from the group's average collective behavior. Building on our earlier results established for homogeneous agents, we extend the framework to nonidentical agents and show that, under a diagonal dominant interaction of the collective dynamics, with bounded local open-loop dynamics, the optimal controller for $H_\infty$ and $H_2$ norm minimization remains decentralized and selfish in the limit as the number of agents $n$ grows to infinity.

math.OC↗
arXiv2025

Wasserstein Distributionally Robust Adaptive Covariance Steering

We present a methodology for predictable and safe covariance steering control of uncertain nonlinear stochastic processes. The systems under consideration are subject to general uncertainties, which include unbounded random disturbances (aleatoric uncertainties) and incomplete model knowledge (state-dependent epistemic uncertainties). These general uncertainties lead to temporally evolving state distributions that are entirely unknown, can have arbitrary shapes, and may diverge unquantifiably from expected behaviors, leading to unpredictable and unsafe behaviors. Our method relies on an $\mathcal{L}_1$-adaptive control architecture that ensures robust control of uncertain stochastic processes while providing Wasserstein metric certificates in the space of probability measures. We show how these distributional certificates can be incorporated into the high-level covariance control steering to guarantee safe control. Unlike existing distributionally robust planning and control methodologies, our approach avoids difficult-to-verify requirements like the availability of finite samples from the true underlying distribution or an a priori knowledge of time-varying ambiguity sets to which the state distributions are assumed to belong.

eess.SY↗
arXiv2024

Guaranteeing Service in Connected Microgrids: Storage Planning and Optimal Power Sharing Policy

The integration of renewable energy sources (RES) into power distribution grids poses challenges to system reliability due to the inherent uncertainty in their power production. To address this issue, battery energy sources (BESs) are being increasingly used as a promising solution to counter the uncertainty associated with RES power production. During the overall system planning stage, the optimal capacity of the BES has to be decided. In the operational phase, policies on when to charge the BESs and when to use them to support loads must be determined so that the BES remains within its operating range, avoiding depletion of charge on one hand and remaining within acceptable margins of maximum charge on the other. In this paper, a stochastic control framework is used to determine battery capacity, for microgrids, which ensures that during the operational phase, BESs' operating range is respected with pre-specified high probability. We provide an explicit analytical expression of the required BESs energy capacity for a single microgrid with RES as the main power source. Leveraging insights from the single microgrid case, the article focuses on the design and planning of BESs for the two-microgrid scenario. In this setting, microgrids are allowed to share power while respecting the capacity constraints imposed by the power lines. We characterize the optimal power transfer policy between the microgrids and the optimal BES capacity for multiple microgrids. This provides the BES savings arising from connecting the microgrids.

eess.SY↗
arXiv2024

A Distributed Malicious Agent Detection Scheme for Resilient Power Apportioning in Microgrids

We consider the framework of distributed aggregation of Distributed Energy Resources (DERs) in power networks to provide ancillary services to the power grid. Existing aggregation schemes work under the assumption of trust and honest behavior of the DERs and can suffer when that is not the case. In this article, we develop a distributed detection scheme that allows the DERs to detect and isolate the maliciously behaving DERs. We propose a model for the maliciously behaving DERs and show that the proposed distributed scheme leads to the detection of the malicious DERs. Further, augmented with the distributed power apportioning algorithm the proposed scheme provides a framework for resilient distributed power apportioning for ancillary service dispatch in power networks. A controller-hardware-in-the-loop (CHIL) experimental setup is developed to evaluate the performance of the proposed resilient distributed power apportioning scheme on an 8-commercial building distribution network (Central Core) connected to a 55 bus distribution network (External Power Network) based on the University of Minnesota Campus. A diversity of DERs and loads are included in the network to generalize the applicability of the framework. The experimental results corroborate the efficacy of the proposed resilient distributed power apportioning for ancillary service dispatch in power networks.

eess.SY↗
arXiv2024

A Plug and Play Distributed Secondary Controller for Microgrids with Grid-Forming Inverters

A distributed controller for secondary control problems in microgrids with grid-forming (GFM) inverter-based resources (IBRs) is developed. The controller is based on distributed optimization and is synthesized and implemented distributively enabling each GFM IBR to utilize decentralized measurements and the neighborhood information in the communication network. We present a convergence analysis establishing voltage regulation and reactive power sharing properties. A controller-hardware-in-the-loop experiment is conducted to evaluate the performance of the proposed controller. The experimental results corroborate the efficacy of the proposed distributed controller for secondary control.

eess.SY↗
arXiv2024

Distributed Difference of Convex Optimization

In this article, we focus on solving a class of distributed optimization problems involving $n$ agents with the local objective function at every agent $i$ given by the difference of two convex functions $f_i$ and $g_i$ (difference-of-convex (DC) form), where $f_i$ and $g_i$ are potentially nonsmooth. The agents communicate via a directed graph containing $n$ nodes. We create smooth approximations of the functions $f_i$ and $g_i$ and develop a distributed algorithm utilizing the gradients of the smooth surrogates and a finite-time approximate consensus protocol. We term this algorithm as DDC-Consensus. The developed DDC-Consensus algorithm allows for non-symmetric directed graph topologies and can be synthesized distributively. We establish that the DDC-Consensus algorithm converges to a stationary point of the nonconvex distributed optimization problem. The performance of the DDC-Consensus algorithm is evaluated via a simulation study to solve a nonconvex DC-regularized distributed least squares problem. The numerical results corroborate the efficacy of the proposed algorithm.

math.OC↗
arXiv2024

Adaptive Online Model Update Algorithm for Predictive Control in Networked Systems

In this article, we introduce an adaptive online model update algorithm designed for predictive control applications in networked systems, particularly focusing on power distribution systems. Unlike traditional methods that depend on historical data for offline model identification, our approach utilizes real-time data for continuous model updates. This method integrates seamlessly with existing online control and optimization algorithms and provides timely updates in response to real-time changes. This methodology offers significant advantages, including a reduction in the communication network bandwidth requirements by minimizing the data exchanged at each iteration and enabling the model to adapt after disturbances. Furthermore, our algorithm is tailored for non-linear convex models, enhancing its applicability to practical scenarios. The efficacy of the proposed method is validated through a numerical study, demonstrating improved control performance using a synthetic IEEE test case.

eess.SY↗
arXiv2023

Transactive Framework for Dynamic Energy Storage Allocation for Critical Load Management

Increased penetration of Distributed Energy Resources (DER) and Renewable Energy Systems (RES) transforming the conventional distribution grid into a transactive framework supervised by a distribution system operator (DSO). Although the emerging transactive energy management techniques improve the grid reliability, the inherent uncertainty of RES poses a challenge in meeting the power demand of the critical infrastructure in the microgrid unless sufficient battery energy storage is maintained. However, maintaining expensive battery storage increases the operating cost of the DSO. In this article, we propose a cost-effective dynamic resource allocation strategy to optimize the battery reserve requirement while ensuring the critical demand is met with a provable guarantee. Our proposed scheme enables the DSO to optimize the RES and battery reserve allocation to eliminate the risk of over or underproduction. We present numerical simulations under three different scenarios of multiple microgrids with uncertain renewable generation. The simulation results demonstrate the efficacy of the proposed transactive stochastic control algorithm.

eess.SY↗
arXiv2022

Distributed Average Consensus Over Noisy Communication Links in Directed Graphs

Motivated by the needs of resiliency, scalability, and plug-and-play operation, distributed decision-making is becoming increasingly prevalent. The problem of achieving consensus in a multi-agent system is at the core of distributed decision-making. In this article, we study the problem of achieving average consensus over a directed multi-agent network when the communication links are corrupted with noise. We propose an algorithm where each agent updates its estimates based on the local mixing of information and adds its weighted noise-free initial information to its updates during every iteration. We demonstrate that with appropriately designed weights the agents achieve consensus under additive communication noise. We establish that when the communication links are noiseless the proposed algorithm moves towards consensus at a geometric rate. Under communication noise, we prove that the agent estimates reach a consensus value almost surely. We present numerical experiments to corroborate the efficacy of the proposed algorithm under different noise realizations and various algorithm parameters.

cs.DC↗
arXiv2022

DC-DistADMM: ADMM Algorithm for Constrained Distributed Optimization over Directed Graphs

This article reports an algorithm for multi-agent distributed optimization problems with a common decision variable, local linear equality and inequality constraints and set constraints with convergence rate guarantees. \textcolor{black}{The algorithm accrues all the benefits of the Alternating Direction Method of Multipliers (ADMM) approach}. It also overcomes the limitations of existing methods on convex optimization problems with linear inequality, equality and set constraints by allowing directed communication topologies. Moreover, the algorithm can be synthesized distributively. The developed algorithm has: (i) a $O(1/k)$ rate of convergence, where $k$ is the iteration counter, when individual functions are convex but not-necessarily differentiable, and (ii) a geometric rate of convergence to any arbitrary small neighborhood of the optimal solution, when the objective functions are smooth and restricted strongly convex at the optimal solution. The efficacy of the algorithm is evaluated by a comparison with state-of-the-art constrained optimization algorithms in solving a constrained distributed $\ell_1$-regularized logistic regression problem, and unconstrained optimization algorithms in solving a $\ell_1$-regularized Huber loss minimization problem. Additionally, a comparison of the algorithm's performance with other algorithms in the literature that utilize multiple communication steps is provided.

eess.SY↗
arXiv2021

Gradient-Consensus: Linearly Convergent Distributed Optimization Algorithm over Directed Graphs

In this article, we propose a new approach, optimize then agree for minimizing a sum $ f = \sum_{i=1}^n f_i(x)$ of convex objective functions over a directed graph. The optimize then agree approach decouples the optimization step and the consensus step in a distributed optimization framework. The key motivation for optimize then agree is to guarantee that the disagreement between the estimates of the agents during every iteration of the distributed optimization algorithm remains under any apriori specified tolerance; existing algorithms do not provide such a guarantee which is required in many practical scenarios. In this method, each agent during each iteration maintains an estimate of the optimal solution and, utilizes its locally available gradient information along with a finite-time approximate consensus protocol to move towards the optimal solution (hence the name Gradient-Consensus algorithm). We establish that the proposed algorithm has a global R-linear rate of convergence if the aggregate function $f$ is strongly convex and Lipschitz differentiable. We also show that under the relaxed assumption of $f_i$'s being convex and Lipschitz differentiable, the objective function error residual decreases at a Q-linear rate (in terms of the number of gradient computation steps) until it reaches a small value, which can be managed using the tolerance value specified on the finite-time approximate consensus protocol; no existing method in the literature has such strong convergence guarantees when $f_i$ are not necessarily strongly convex functions. The communication overhead for the improved guarantees on meeting constraints and better convergence of our algorithm is $O(k\log k)$ iterates in comparison to $O(k)$ of the traditional algorithms. Further, we numerically evaluate the performance of the proposed algorithm by solving a distributed logistic regression problem.

eess.SY↗
arXiv2020

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

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

eess.SY↗
arXiv2020

On Mitigating the Uncertainty in Renewable Generation in Distribution Microgrids

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

eess.SY↗
arXiv2019

Distributed finite-time termination for consensus algorithm in switching topologies

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

eess.SY↗