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In this paper, we consider the mixed optimal control of a linear stochastic system with a quadratic cost functional, with two controllers-one can choose only deterministic time functions, called the deterministic controller, while the other…

Optimization and Control · Mathematics 2017-08-23 Ying Hu , Shanjian Tang

The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…

Optimization and Control · Mathematics 2023-04-06 Caroline Geiersbach , Teresa Scarinci

The study is devoted to mathematical modeling and optimal control design of longitudinal motions of a rectilinear elastic rod. The control inputs are a force, which is normal to the cross section and distributed piecewise constantly along…

Optimization and Control · Mathematics 2022-07-22 Georgy Kostin , Alexander Gavrikov

The present paper represents a continuation of our previous one. There, a continuous dependence result for the solution of an elliptic variational-hemivariational inequality was obtained and then used to prove the existence of optimal pairs…

Analysis of PDEs · Mathematics 2019-12-25 Yi-bin Xiao , Mircea Sofonea

Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through…

Optimization and Control · Mathematics 2020-08-26 Guozhi Dong , Michael Hintermueller , Kostas Papafitsoros

We deal with the problem of parameter estimation in stochastic differential equations (SDEs) in a partially observed framework. We aim to design a method working for both elliptic and hypoelliptic SDEs, the latters being characterized by…

Optimization and Control · Mathematics 2021-08-13 Quentin Clairon , Adeline Samson

This paper studies the partially observed stochastic optimal control problem for systems with state dynamics governed by partial differential equations (PDEs) that leads to an extremely large problem. First, an open-loop deterministic…

Optimization and Control · Mathematics 2017-11-06 Dan Yu , Mohammadhussein Rafieisakhaei , Suman Chakravorty

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…

Optimization and Control · Mathematics 2024-04-29 Sachin Shivakumar , Matthew Peet

In this paper, we are concerned with a stochastic optimal control problem of mean-field type under partial observation, where the state equation is governed by the controlled nonlinear mean-field stochastic differential equation, moreover…

Optimization and Control · Mathematics 2016-11-15 Maonin Tang , Qingxin Meng

We consider optimal control of the scalar wave equation where the control enters as a coefficient in the principal part. Adding a total variation penalty allows showing existence of optimal controls, which requires continuity results for…

Optimization and Control · Mathematics 2021-09-28 Christian Clason , Karl Kunisch , Philip Trautmann

In this paper, we carry out the numerical analysis of a nonsmooth quasilinear elliptic optimal control problem, where the coefficient in the divergence term of the corresponding state equation is not differentiable with respect to the state…

Numerical Analysis · Mathematics 2024-02-23 Christian Clason , Vu Huu Nhu , Arnd Rösch

We investigate $C^1$ finite element methods for one dimensional elliptic distributed optimal control problems with pointwise constraints on the derivative of the state formulated as fourth order variational inequalities for the state…

Numerical Analysis · Mathematics 2020-06-29 Susanne C. Brenner , Li-Yeng Sung , Winnifried Wollner

We design and analyze solution techniques for a linear-quadratic optimal control problem involving the integral fractional Laplacian. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates…

Optimization and Control · Mathematics 2020-10-09 Marta D'Elia , Christian Glusa , Enrique Otarola

This paper characterizes the solution to a finite horizon min-max optimal control problem where the system is linear and discrete-time with control and state constraints, and the cost quadratic; the disturbance is negatively costed, as in…

Optimization and Control · Mathematics 2017-10-13 D. Q. Mayne , S. V. Rakovic , R. B. Vinter , E. C. Kerrigan

We consider a specific type of nonlinear partial differential equations (PDE) that appear in mathematical finance as the result of solving some optimization problems. We review some existing in the literature examples of such problems, and…

Computational Finance · Quantitative Finance 2015-10-19 Andrey Itkin

In this work, we study a boundary control problem for the evolutionary Navier-Stokes equations, under mixed boundary conditions, in two dimensions. The cost functional here considered is of quadratic type, depending on both state and…

Optimization and Control · Mathematics 2024-10-02 Telma Guerra , Irene Marín-Gayte , Jorge Tiago

This paper is concerned with an optimal control problem subject to the $H^1$-critical defocusing semilinear wave equation on a smooth and bounded domain in three spatial dimensions. Due to the criticality of the nonlinearity in the wave…

Optimization and Control · Mathematics 2019-07-08 Karl Kunisch , Hannes Meinlschmidt

We consider fractional order optimal control problems in which the dynamic control system involves integer and fractional order derivatives and the terminal time is free. Necessary conditions for a state/control/terminal-time triplet to be…

Optimization and Control · Mathematics 2013-11-01 Shakoor Pooseh , Ricardo Almeida , Delfim F. M. Torres

This paper studies the partially observed stochastic optimal control problem for systems with state dynamics governed by Partial Differential Equations (PDEs) that leads to an extremely large problem. First, an open-loop deterministic…

Systems and Control · Computer Science 2017-07-12 Dan Yu , Mohammadhussein Rafieisakhaei , Suman Chakravorty

In this paper, we consider linear quadratic optimal control with mean-field type for discrete-time stochastic systems with state and control dependent noise. An optimal control problem is studied for a linear mean-field stochastic…

Optimization and Control · Mathematics 2022-10-06 Arzu Ahmadova , Nazim I. Mahmudov