Related papers: Minimax State Estimation for a Dynamic System Desc…
The concept of a minimax classifier is well-established in statistical decision theory, but its implementation via neural networks remains challenging, particularly in scenarios with imbalanced training data having a limited number of…
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…
In this paper, we propose an efficient semidefinite programming (SDP) approach to worst-case linear discriminant analysis (WLDA). Compared with the traditional LDA, WLDA considers the dimensionality reduction problem from the worst-case…
This paper considers point and interval estimation of the $\ell_q$ loss of an estimator in high-dimensional linear regression with random design. We establish the minimax rate for estimating the $\ell_{q}$ loss and the minimax expected…
We address a broad class of optimization problems of finding quantum measurements, which includes the problems of finding an optimal measurement in the Bayes criterion and a measurement maximizing the average success probability with a…
This paper deals with the asymptotic behavior and FEM error analysis of a class of strongly damped wave equations using a semidiscrete finite element method in spatial directions combined with a finite difference scheme in the time…
Given a task of predicting $Y$ from $X$, a loss function $L$, and a set of probability distributions $\Gamma$ on $(X,Y)$, what is the optimal decision rule minimizing the worst-case expected loss over $\Gamma$? In this paper, we address…
In this paper, two types of linear estimators are considered for three related estimation problems involving set-theoretic uncertainty pertaining to $\mathcal{H}_{2}$ and $\mathcal{H}_{\infty}$ balls of frequency-responses. The problems at…
The purpose of this work is the design and analysis of a reliable and efficient a posteriori error estimator for the so-called pointwise tracking optimal control problem. This linear-quadratic optimal control problem entails the…
We consider a distributed optimal control problem subject to a parabolic evolution equation as constraint. The control will be considered in the energy norm of the anisotropic Sobolev space $[H_{0;,0}^{1,1/2}(Q)]^\ast$, such that the state…
Predicting the behavior of a dynamical system from noisy observations of its past outputs is a classical problem encountered across engineering and science. For linear systems with Gaussian inputs, the Kalman filter -- the best linear…
We analyze the finite element discretization of distributed elliptic optimal control problems with variable energy regularization, where the usual $L^2(\Omega)$ norm regularization term with a constant regularization parameter $\varrho$ is…
Modeling and inference with multivariate sequences is central in a number of signal processing applications such as acoustics, social network analysis, biomedical, and finance, to name a few. The linear-Gaussian state-space model is a…
Developing a unified small-signal model for modern, large-scale power systems that remains accurate across a wide range of operating ranges presents a formidable challenge. Traditional methods, spanning mechanistic modeling, modal…
In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly…
Moving horizon estimation (MHE) is a widely studied state estimation approach in several practical applications. In the MHE problem, the state estimates are obtained via the solution of an approximated nonlinear optimization problem.…
In this paper, we present solvable, convex formulations of $H_2$-optimal state estimation and state-feedback control problems for a general class of linear Partial Differential Equations (PDEs) with one spatial dimension. These convex…
Reduced model spaces, such as reduced basis and polynomial chaos, are linear spaces $V_n$ of finite dimension $n$ which are designed for the efficient approximation of families parametrized PDEs in a Hilbert space $V$. The manifold…
A linear-quadratic (LQ, for short) optimal control problem is considered for mean-field stochastic differential equations with constant coefficients in an infinite horizon. The stabilizability of the control system is studied followed by…
State estimation is an important aspect in many robotics applications. In this work, we consider the task of obtaining accurate state estimates for robotic systems by enhancing the dynamics model used in state estimation algorithms.…