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Hierarchical optimization architectures are used in power systems to manage disturbances and phenomena that arise at multiple spatial and temporal scales. We present a graph modeling abstraction for representing such architectures and an…
The modified nodal analysis (MNA) is probably the most widely used formulation for the modeling and simulation of electric circuits. Its conventional form uses electric node potentials and currents across inductors and voltage sources as…
What is the best representation for doing euclidean geometry on computers? These notes from a SIGGRAPH 2019 short course entitled "Geometric algebra for computer graphics" introduce projective geometric algebra (PGA) as a modern framework…
Geometrical optics (GO) is widely used for reduced modeling of waves in plasmas but fails near reflection points, where it predicts a spurious singularity of the wave amplitude. We show how to avoid this singularity by adopting a different…
Massive multiple-input multiple-output (MIMO) systems are cellular networks where the base stations (BSs) are equipped with unconventionally many antennas, deployed on co-located or distributed arrays. Huge spatial degrees-of-freedom are…
In the design of electromagnetic devices the accurate representation of the geometry plays a crucial role in determining the device performance. For accelerator cavities, in particular, controlling the frequencies of the eigenmodes is…
The adiabatic geometric phases for general three state systems are discussed. An explicit parameterization for space of states of these systems is given. The abelian and non-abelian connection one-forms or vector potentials that would…
In this work, we utilize discrete geometric mechanics to derive a 2nd-order variational integrator so as to simulate rigid body dynamics. The developed integrator is to simulate the motion of a free rigid body and a quad-rotor. We…
Cross-grating phase microscopy (CGM) is a quantitative phase microscopy technique based on the association of a 2-dimensional diffraction grating (cross-grating) and a regular camera sensor, separated by a millimetric distance. This simple…
This paper introduces a new approach for output feedback stabilization of SISO systems which, unlike most of the techniques found in the literature, does not use high-gain observers and control input saturation to achieve separation between…
We present a method and tool for evaluating the placement of Distributed Energy Resources (DER) on distribution circuits in order to control voltages and power flows. Our previous work described Phasor-Based Control (PBC), a novel control…
In this paper, we define the phase response for a class of multi-input multi-output (MIMO) linear time-invariant (LTI) systems whose frequency responses are (semi-)sectorial at all frequencies. The newly defined phase concept subsumes the…
We present a combination of analytical and numerical calculations for the critical behavior of a supersymmetric non-linear $\sigma$-model within the context of the localization transition of a disordered one-electron system. As a result, we…
The proportional-integral-derivative (PID) controller and its variants are widely used in control engineering, but they often rely on linearization around equilibrium points and empirical parameter tuning, making them ineffective for…
This paper presents a new view of multi-user (MU) hybrid massive multiple-input and multiple-output (MIMO) systems from array signal processing perspective. We first show that the instantaneous channel vectors corresponding to different…
The widespread deployment of power electronic technologies is transforming modern power systems into fast, nonlinear, and heterogeneous networks. Conventional modeling and control approaches, rooted in quasi-static analysis and centralized…
Sliding mode control (SMC) is a robust and computationally efficient model-based controller design technique for highly nonlinear systems, in the presence of model and external uncertainties. However, the implementation of the conventional…
Geometric algebra (GA) is a mathematical tool for geometric computing, providing a framework that allows a unified and compact approach to geometric relations which in other mathematical systems are typically described using different more…
Data with features of volume, velocity, variety, and veracity are challenging traditional tools to extract useful analysis for decision-making. By integrating high-dimensional analysis with visualization, this paper develops a 3D power-map…
Accurate phase connectivity information is essential for advanced monitoring and control applications in power distribution systems. The existing data-driven approaches for phase identification lack precise physical interpretation and…