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This paper presents a new aggregate power tracking control scheme for populations of thermostatically controlled loads (TCLs). The control design is carried out in the framework of partial differential equations (PDEs) based on a…

To respond to volatility and congestion in the power grid, demand response (DR) mechanisms allow for shaping the load compared to a base load profile. When tapping on a large population of heterogeneous appliances as a DR resource, the…

We propose a novel decomposition framework for the distributed optimization of Difference Convex (DC)-type nonseparable sum-utility functions subject to coupling convex constraints. A major contribution of the paper is to develop for the…

We propose a combined global-local control approach to regulate voltage and minimize power losses in distribution networks with high integration of distributed energy resources (DERs). Local controllers embed the fast acting proportional…

Recent years have seen the emergence of nonlinear methods for solving partial differential equations (PDEs), such as physics-informed neural networks (PINNs). While these approaches often perform well in practice, their theoretical analysis…

Given a data set and a subset of labels the problem of semi-supervised learning on point clouds is to extend the labels to the entire data set. In this paper we extend the labels by minimising the constrained discrete $p$-Dirichlet energy.…

This paper is concerned with the problem of coordinating a set of distributed energy resources (DERs) in a lossy power distribution system to provide frequency regulation services to a bulk power grid with the explicit consideration of…

We propose an Exponential DG approach for numerically solving partial differential equations (PDEs). The idea is to decompose the governing PDE operators into linear (fast dynamics extracted by linearization) and nonlinear (the remaining…

This paper presents a novel partial differential equation (PDE)-based framework for controlling an ensemble of robots, which have limited sensing and actuation capabilities and exhibit stochastic behaviors, to perform mapping and coverage…

Integrating Distributed Energy Resources (DERs) with peer-to-peer (P2P) energy trading offers promising solutions for grid modernization by incentivizing prosumers to participate in mitigating peak demand. However, this integration also…

In most biological studies and processes, cell proliferation and population dynamics play an essential role. Due to this ubiquity, a multitude of mathematical models has been developed to describe these processes. While the simplest models…

We present a hierarchical model predictive control approach for large-scale systems based on dual decomposition. The proposed scheme allows coupling in both dynamics and constraints between the subsystems and generates a primal feasible…

Aggregate load modeling is of fundamental importance for systematic analysis and design of various demand response strategies. Instead of keeping track of the trajectories of individual loads, the aggregate modeling problem focuses on…

We introduce a novel and scalable Bayesian framework for multivariate-density-density regression (DDR), designed to model relationships between multivariate distributions. Our approach addresses the critical issue of distributions residing…

Power systems dominated by converter-interfaced distributed energy resources (DERs) typically exhibit weaker damping capabilities and lower inertia, compromising system stability. Although individual DER controllers are evolving to provide…

This paper investigates the robust optimal control of sampled-data stochastic systems with multiplicative noise and distributional ambiguity. We consider a class of discrete-time optimal control problems where the controller \emph{jointly}…

As we transition towards a power grid that is increasingly based on renewable resources like solar and wind, the intelligent control of distributed energy resources (DER) including photovoltaic (PV) arrays, controllable loads, energy…

Distributed energy resources (DERs) can serve as non-wire alternatives to capacity expansion by managing peak load to avoid or defer traditional expansion projects. In this paper, we study a planning problem that co-optimizes DERs…

Existing large-scale optimization schemes are challenged by both scalability and cyber-security. With the favorable scalability, adaptability, and flexibility, decentralized and distributed optimization paradigms are widely adopted in…

We study differentially private (DP) algorithms for stochastic non-convex optimization. In this problem, the goal is to minimize the population loss over a $p$-dimensional space given $n$ i.i.d. samples drawn from a distribution. We improve…