Related papers: An Optimal Control Approach to Gradient-Index Desi…
Recent studies of the dynamically assisted Schwinger effect have shown that particle production is significantly enhanced by a proper choice of the electric field. We demonstrate that optimal control theory provides a systematic means of…
It is control that turns scientific knowledge into useful technology: in physics and engineering it provides a systematic way for driving a system from a given initial state into a desired target state with minimized expenditure of energy…
In this paper we discuss optimality conditions for abstract optimization problems over complex spaces. We then apply these results to optimal control problems with a semigroup structure. As an application we detail the case when the state…
The control-affine Schr\"odinger bridge concerns with a stochastic optimal control problem. Its solution is a controlled evolution of joint state probability density subject to a control-affine It\^o diffusion with a given deadline…
We consider the inverse problem of the determining the potential in the dynamical Schr\"odinger equation on the interval by the measurement on the whole boundary. Provided that source is \emph{generic} using the Boundary Control method we…
The problem of quantum state preparation is one of the main challenges in achieving the quantum advantage. Furthermore, classically, for multi-level problems, our ability to solve the corresponding quantum optimal control problems is rather…
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…
We formulate and analyse an optimal control problem for the coagulation-fragmentation equation, where a scalar, time-dependent control modulates the coagulation rate by multiplying the coagulation kernel. The objective functional consists…
In this paper, we consider an optimal bilinear control problem for the nonlinear Schr\"{o}dinger equations with singular potentials. We show well-posedness of the problem and existence of an optimal control. In addition, the first order…
Controlling the shapes of surfaces provides a novel way to direct self-assembly of colloidal particles on those surfaces and may be useful for material design. This motivates the investigation of an optimal control problem for surface shape…
Achieving quantum-limited motional control of optically trapped particles beyond the sub-micrometer scale is an outstanding problem in levitated optomechanics. A key obstacle is solving the light scattering problem and identifying particle…
We apply innovative mathematical tools coming from optimal control theory to improve theoretical and experimental techniques in Magnetic Resonance Imaging (MRI). This approach allows us to explore and to experimentally reach the physical…
The spectrum of a Schr\"odinger operator with periodic potential generally consists of bands and gaps. In this paper, for fixed m, we consider the problem of maximizing the gap-to-midgap ratio for the m-th spectral gap over the class of…
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…
In this paper, we introduce a novel pseudospectral method for the numerical solution of optimal control problems governed by a parabolic distributed parameter system. The infinite-dimensional optimal control problem is reduced into a…
We propose a variational formulation of an inverse problem in continuous-time stochastic control, aimed at identifying control costs consistent with a given distribution over trajectories. The formulation is based on minimizing the…
In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former.…
In this paper we study and solve an optimal control problem motivated by applications in quantum and classical physics. Although apparently simple, this optimal control problem is not easy to solve and we resort to various elaborated…
This work investigates the optimal control of the variable-exponent subdiffusion, which extends the work [Gunzburger and Wang, {\it SIAM J. Control Optim.} 2019] to the variable-exponent case to account for the multiscale and crossover…
A crucial problem in shape deformation analysis is to determine a deformation of a given shape into another one, which is optimal for a certain cost. It has a number of applications in particular in medical imaging. In this article we…