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We consider Koopman operator theory in the context of nonlinear infinite-dimensional systems, where the operator is defined over a space of bounded continuous functionals. The properties of the Koopman semigroup are described and a…
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…
Managing power grids with the increasing presence of variable renewable energy-based (distributed) generation involves solving high-dimensional optimization tasks at short intervals. Linearizing the AC power flow (PF) constraints is a…
Strongly nonlinear flows, which commonly arise in geophysical and engineering turbulence, are characterized by persistent and intermittent energy transfer between various spatial and temporal scales. These systems are difficult to model and…
Koopman spectral analysis has attracted attention for understanding nonlinear dynamical systems by which we can analyze nonlinear dynamics with a linear regime by lifting observations using a nonlinear function. For analysis, we need to…
Koopman operator theory has proven to be a promising approach to nonlinear system identification and global linearization. For nearly a century, there had been no efficient means of calculating the Koopman operator for applied engineering…
There have been recent efforts that combine seemingly disparate methods, extremum seeking (ES) optimization and partial differential equation (PDE) backstepping, to address the problem of model-free optimization with PDE actuator dynamics.…
This paper presents a study of the Koopman operator theory and its application to optimal control of a multi-robot system. The Koopman operator, while operating on a set of observation functions of the state vector of a nonlinear system,…
Given the complexity and nonlinearity inherent in traffic dynamics within vehicular platoons, there exists a critical need for a modeling methodology with high accuracy while concurrently achieving physical analyzability. Currently, there…
Dynamical systems are ubiquitous and are often modeled using a non-linear system of governing equations. Numerical solution procedures for many dynamical systems have existed for several decades, but can be slow due to high-dimensional…
In this paper, we propose linear operator theoretic framework involving Koopman operator for the data-driven identification of power system dynamics. We explicitly account for noise in the time series measurement data and propose robust…
This paper studies two fundamental problems in power systems: the economic dispatch problem (EDP) and load shedding. For the EDP, an extension of the problem considering the transmission losses is presented. Because the optimization problem…
In this paper, a data-driven nonparametric approach is presented for forecasting the probability density evolution of stochastic dynamical systems. The method is based on stochastic Koopman operator and extended dynamic mode decomposition…
The control of legged robots, particularly humanoid and quadruped robots, presents significant challenges due to their high-dimensional and nonlinear dynamics. While linear systems can be effectively controlled using methods like Model…
Although multiple works have proposed energy-efficient resource allocation schemes for Massive Multiple-Input Multiple-Output (M-MIMO) system, most approaches overlook the potential of optimizing Power Amplifier (PA) transmission power…
In this paper, we present finite-dimensional port-Hamiltonian system (PHS) models of a gas pipeline and a network comprising several pipelines for the purpose of control design and stability analysis. Starting from the partial differential…
The path-integral control, which stems from the stochastic Hamilton-Jacobi-Bellman equation, is one of the methods to control stochastic nonlinear systems. This paper gives a new insight into nonlinear stochastic optimal control problems…
Representing and predicting high-dimensional and spatiotemporally chaotic dynamical systems remains a fundamental challenge in dynamical systems and machine learning. Although data-driven models can achieve accurate short-term forecasts,…
High penetrations of intermittent renewable energy resources in the power system require large balancing reserves for reliable operations. Aggregated and coordinated behind-the-meter loads can provide these fast reserves, but represent…
We consider the worst-case load-shedding problem in electric power networks where a number of transmission lines are to be taken out of service. The objective is to identify a pre-specified number of line outage that leads to the maximum…