Related papers: An optimal control-based numerical method for scal…
In this paper, we consider the optimal control problem for a class of evolution inclusions with Volterra type operators, which can be history-dependent. We establish the existence of a solution to the stated optimal control problem under…
We consider a state-constrained optimal control problem of a system of two non-local partial-differential equations, which is an extension of the one introduced in a previous work in mathematical oncology. The aim is to minimize the tumor…
Controlling electromagnetic energy is essential for an efficient and sustainable society. A key requirement is concentrating magnetic energy in a desired volume of space in order to either extract the energy to produce work or store it.…
We study the 2+1 dimensional XY model at nonzero chemical potential $\mu$ on deformed integration manifolds, with the aim of alleviating its sign problem. We investigate several proposals for the deformations, and considerably improve on…
Optical fields in metamaterial nanostructures can be separated into bright modes, whose dispersion is typically described by effective medium parameters, and dark fluctuating fields. Such combination of propagating and evanescent modes…
We study degenerate fully nonlinear free transmission problems, where the degeneracy rate varies in the domain. We prove optimal pointwise regularity depending on the degeneracy rate. Our arguments consist of perturbation methods, relating…
A general maximum principle is proved for optimal controls of abstract semilinear stochastic evolution equations. The control variable, as well as linear unbounded operators, acts in both drift and diffusion terms, and the control set need…
This paper investigates a space-time interface-fitted approximation of a moving-interface optimal control problem with energy regularization. We reformulate the optimality conditions into a variational problem involving both the state and…
This paper considers the stochastic linear quadratic optimal control problem in which the control domain is nonconvex. By the functional analysis and convex perturbation methods, we establish a novel maximum principle. The application of…
We prove a well-posedness result for two pseudo-parabolic problems, which can be seen as two models for the same electrical conduction phenomenon in heterogeneous media, neglecting the magnetic field. One of the problems is the…
We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…
Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must either confront the challenge of controlling errors in the discrete divergence of the magnetic field, or else be faced with…
A pivotal task in quantum metrology, and quantum parameter estimation in general, is to de- sign schemes that achieve the highest precision with given resources. Standard models of quantum metrology usually assume the dynamics is fixed, the…
In this paper, we consider optimal control problems derived by stochastic systems with delay, where control domains are non-convex and the diffusion coefficients depend on control variables. By an estimate of the integral of…
An optimal control problem associated to the Keller-Segel with logistic reaction system will be studied in $2D$ domains. The control acts in a bilinear form only in the chemical equation. The existence of optimal control and a necessary…
We propose a novel direct transcription and solution method for solving nonlinear, continuous-time dynamic optimization problems. Instead of forcing the dynamic constraints to be satisfied only at a selected number of points as in direct…
The benefits of transmission line switching are well-known in terms of reducing operational cost and improving system reliability of power systems. However, finding the optimal power network configuration is a challenging task due to the…
The numerical analysis of a family of distributed mixed optimal control problems governed by elliptic variational inequalities (with parameter $\alpha >0$) is obtained through the finite element method when its parameter $h\rightarrow 0$.…
We consider a nonlinear control system with vector-valued measures as controls and with dynamics depending on time delayed states. First, we introduce a notion of discontinuous, bounded variation solution associated with this system and…
Inverse problems of electric conductivity are studied that arise in the design of spherical shielding or cloaking shells and other functional devices used to control DC electric fields. The shells are considered consisting of a finite…