Related papers: Optimal control of variable-exponent subdiffusion
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…
A general stochastic maximum principle is proved for optimal controls of semilinear stochastic evolution equations. Stochastic evolution operators, and the control with values in a general set enter into both drift and diffusion terms.
A solution to the optimal problem for determining vector fields which maximize (resp. minimize) the transition probabilities from one location to another for a class of reflecting diffusion processes is obtained in the present paper. The…
This paper details a methodology to transcribe an optimal control problem into a nonlinear program for generation of the trajectories that optimize a given functional by approximating only the highest order derivatives of a given system's…
We address the problem of reshaping light in the Schr\"odinger optics regime from the perspective of optimal control theory. In technological applications, Schr\"odinger optics is often used to model a slowly-varying amplitude of a…
We consider a bilinear optimal control for an evolution equation involving the fractional Laplace operator of order $0<s<1$. We first give some existence and uniqueness results for the considered evolution equation. Next, we establish some…
The Variation Evolving Method (VEM), which seeks the optimal solutions with the variation evolution principle, is further developed to be more flexible in solving the Optimal Control Problems (OCPs) with terminal constraint. With the…
This paper considers the problem of designing time-dependent, real-time control policies for controllable nonlinear diffusion processes, with the goal of obtaining maximally-informative observations about parameters of interest. More…
We investigate an optimal control problem which arises in the optimization of an amplification technique for misfolded proteins. The improvement of this technique may play a role in the detection of prion diseases. The model consists in a…
In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of the gradient discretisation method. Gradient schemes are defined for the optimality…
We consider the optimal control problem governed by diffusion convection reaction equation without control constraints. The proper orthogonal decomposition(POD) method is used to reduce the dimension of the problem. The POD method may be…
The problem of identifying the diffusion parameter appearing in a nonlocal steady diffusion equation is considered. The identification problem is formulated as an optimal control problem having a matching functional as the objective of the…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
A method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation…
We consider a class of (ill-posed) optimal control problems in which a distributed vector-valued control is enforced to pointwise take values in a finite set $\mathcal{M}\subset\mathbb{R}^m$. After convex relaxation, one obtains a…
We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis…
In this paper we present a method to approximate optimal feedback controls for stochastic reaction-diffusion equations. We derive two approximation results providing the theoretical foundation of our approach and allowing for explicit error…
In a ubiquitous $SU(2)$ dynamics, achieving the simultaneous optimal estimation of multiple parameters is significant but difficult. Using quantum control to optimize this $SU(2)$ coding unitary evolution is one of solutions. We propose a…
This article develops variational integrators for a class of underactuated mechanical systems using the theory of discrete mechanics. Further, a discrete optimal control problem is formulated for the considered class of systems and…
This paper presents an explicit solution to decentralized control of a class of spatially invariant systems. The problem of optimal $H_2$ decentralized control for cone causal systems is formulated. Using Parseval's identity, the optimal…