Related papers: Time-minimum control of quantum purity for 2-level…
In this study, we consider an optimal control problem driven by a stochastic differential equation with state constraints. Here, the state constraints mean the constraints about the path of state. In order to show the maximum principe for…
We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…
We consider an optimal control problem where the state is governed by a free boundary problem called the two-phase membrane problem and the control appears in the coefficients of the characteristic function of the positivity and negativity…
In this article, we investigate a time-optimal state-constrained bilevel optimal control problem whose lower-level dynamics feature a sweeping control process involving a {\it truncated normal cone}. By bilevel, it is meant that the…
We examine the minimization of a quadratic cost functional composed of the output and the final state of abstract infinite-dimensional evolution equations in view of existence of solutions and optimality conditions. While the initial value…
We propose an optimal control strategy to generate maximally entangled states in bipartite quantum systems. Leveraging the Pontryagin Principle, we derive time-dependent control fields that maximize the entanglement measure, specifically…
We consider a class of closed loop stochastic optimal control problems in finite time horizon, in which the cost is an expectation conditional on the event that the process has not exited a given bounded domain. An important difficulty is…
Hybrid quantum-classical algorithms hold great promise for solving quantum control problems on near-term quantum computers. In this work, we employ the hybrid framework that integrates digital quantum simulation with classical optimization…
Using optimal control, we establish and link the ultimate bounds in time (referred to as quantum speed limit) and energy of two- and three-level quantum nonlinear systems which feature 1:2 resonance. Despite the unreachable complete…
This paper is concerned with a constrained stochastic linear-quadratic optimal control problem, in which the terminal state is fixed and the initial state is constrained to lie in a stochastic linear manifold. The controllability of…
This paper investigates the optimal control of a bilinear damped wave equation over an infinite time horizon. We establish the well-posedness of the controlled system and derive uniform energy estimates. The existence of optimal controls is…
In this work, we address the problem of maximizing fidelity in a quantum state transformation process controlled in such a way as to keep decoherence within given bounds. We consider a three-level $\Lambda$-type atom subjected to Markovian…
A discrete-time method for solving problems in optimal quantum control is presented. Controlling the time discretized markovian dynamics of a quantum system can be reduced to a Markov-decision process. We demonstrate this method in this…
Using the Pontryagin maximum principle, the generic structure of optimal policies is deduced for typical quantum control tasks involving coherent lasers, magnetic fields and reservoir engineering. In addition, the periodic optimization is…
In this paper we discuss the optimal control of a quasilinear parabolic state equation. Its form is leaned on the kind of problems arising for example when controlling the anisotropic Allen-Cahn equation as a model for crystal growth.…
We study the singularities for minimum time control-affine problems in 4D with 2D controls. After regularization, the problem boils down to the study of a bifurcation around some nilpotent equilibrium in the singular locus. We show that the…
Numerical ``direct'' approaches to time-optimal control often fail to find solutions that are singular in the sense of the Pontryagin Maximum Principle, performing better when searching for saturated (bang-bang) solutions. In previous work…
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…
In this study, we investigate the optimal control of the Landau-Lifshitz-Bloch equation within confined domains in $\mathbb R^n$ for $n= 2, 3.$ We establish the existence of strong solutions for dimensions $n=1, 2, 3$ under suitable growth…
Optimal control of two-qubit quantum systems attracts high interest due to applications ranging from two-qubit gate generation to optimization of receiver for transferring coherence matrices along spin chains. State preparation and…