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Bounding the correlations predicted by quantum theory is an important challenge in quantum information science. Today's leading approach is semidefinite programming relaxations, but existing methods still cannot account for many relevant…
Time domain simulation is the basis of dynamic security assessment for power systems. Traditionally, numerical integration methods are adopted by simulation software to solve nonlinear power system differential-algebraic equations about any…
This paper studies a fundamental problem in convex optimization, which is to solve semidefinite programming (SDP) with high accuracy. This paper follows from the existing robust SDP-based interior point method analysis due to [Huang, Jiang,…
This paper introduces a Fault Diagnosis (Detection, Isolation, and Estimation) method using Set-Membership Estimation (SME) designed for a class of nonlinear systems that are linear to the fault parameters. The methodology advances fault…
This paper studies how to solve semi-infinite polynomial programming (SIPP) problems by semidefinite relaxation method. We first introduce two SDP relaxation methods for solving polynomial optimization problems with finitely many…
Power systems are highly complex, large-scale engineering systems subject to many uncertainties, which makes accurate mathematical modeling challenging. This paper proposes a novel, centralized dynamic state estimator for power systems that…
The multireference alignment problem consists of estimating a signal from multiple noisy shifted observations. Inspired by existing Unique-Games approximation algorithms, we provide a semidefinite program (SDP) based relaxation which…
Probabilistic optimal power flow (POPF) is an important analytical tool to ensure the secure and economic operation of power systems. POPF needs to solve enormous nonlinear and nonconvex optimization problems. The huge computational burden…
Dynamic state and parameter estimation methods for dynamic security assessment in power systems are becoming increasingly important for system operators. Usually, the data used for this type of applications stems from phasor measurement…
Efficient and accurate state estimation is essential for the optimal management of the future smart grid. However, to meet the requirements of deploying the future grid at a large scale, the state estimation algorithm must be able to…
Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its…
AC State Estimation (ACSE) is widely recognized as a practical approach for determining the grid states in steady-state conditions. It serves as a fundamental analysis to ensure grid security and is a reference for market dispatch. As grid…
A new framework for nonlinear system identification is presented in terms of optimal fitting of stable nonlinear state space equations to input/output/state data, with a performance objective defined as a measure of robustness of the…
Distance measurements demonstrate distinctive scalability when used for relative state estimation in large-scale multi-robot systems. Despite the attractiveness of distance measurements, multi-robot relative state estimation based on…
Increasing frequency and intensity of extreme weather events motivates the assessment of power system resilience. The random nature of power system failures during these events mandates probabilistic resilience assessment, but…
This paper considers the state estimation problem for nonlinear dynamic systems with unknown but bounded noises. Set membership filter (SMF) is a popular algorithm to solve this problem. In the set membership setting, we investigate the…
With high penetrations of renewable generation and variable loads, there is significant uncertainty associated with power flows in DC networks such that stability and operational constraint satisfaction are of concern. Most existing DC…
Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…
Quantum steering, an intermediate quantum correlation lying between entanglement and nonlocality, has emerged as a critical quantum resource for a variety of quantum information processing tasks such as quantum key distribution and true…
The use of convex relaxations has lately gained considerable interest in Power Systems. These relaxations play a major role in providing global optimality guarantees for non-convex optimization problems. For the Optimal Power Flow (OPF)…