Related papers: The solution classical and quantum feedback optima…
A scheme for generating a family of convex variational principles is developed, the Euler- Lagrange equations of each member of the family formally corresponding to the necessary conditions of optimal control of a given system of ordinary…
Simple, precise, and robust control is demanded for operating a large quantum information processor. However, existing routes to high-fidelity quantum control rely heavily on arbitrary waveform generators that are difficult to scale up.…
This paper addresses the numerical solution of backward stochastic differential equations (BSDEs) arising in stochastic optimal control. Specifically, we investigate two BSDEs: one derived from the Hamilton-Jacobi-Bellman equation and the…
We study optimal stochastic control problem for non-Markovian stochastic differential equations (SDEs) where the drift, diffusion coefficients, and gain functionals are path-dependent, and importantly we do not make any ellipticity…
In this paper, we study an optimal control problem of linear backward stochastic differential equation (BSDE) with quadratic cost functional under partial information. This problem is solved completely and explicitly by using a stochastic…
The classical maximum principle for optimal stochastic control states that if a control $\hat{u}$ is optimal, then the corresponding Hamiltonian has a maximum at $u=\hat{u}$. The first proofs for this result assumed that the control did not…
The optimal control problem for open quantum systems can be formulated as a time-dependent Lindbladian that is parameterized by a number of time-dependent control variables. Given an observable and an initial state, the goal is to tune the…
We present a formulation of feedback in quantum systems in which the best estimates of the dynamical variables are obtained continuously from the measurement record, and fed back to control the system. We apply this method to the problem of…
We present a theory of optimal control for McKean-Vlasov stochastic differential equations with infinite time horizon and discounted gain functional. We first establish the well-posedness of the state equation and of the associated control…
In this paper, a finite-horizon optimal control problem involving a dynamical system described by a linear Caputo fractional differential equation and a quadratic cost functional is considered. An explicit formula for the value functional…
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…
In this paper, the stochastic verification theorems for stochastic control problems of reflected forward-backward stochastic differential equations are studied. We carry out the work within the frameworks of classical and viscosity…
Recently two papers [K. Jacobs, Phys. Rev. A {\bf 67}, 030301(R) (2003); H. M. Wiseman and J. F. Ralph, New J. Physics {\bf 8}, 90 (2006)] have derived control strategies for rapid purification of qubits, optimized with respect to various…
In this paper, we are concerned with the classical solvability of a class of second-order Hamilton-Jacobi-Bellman equations (HJB equations) arising from stochastic optimal control problems with linear dynamics and uniformly convex cost…
Based on a recently developed notion of physical realizability for quantum linear stochastic systems, we formulate a quantum LQG optimal control problem for quantum linear stochastic systems where the controller itself may also be a quantum…
We consider a stochastic optimal control problem governed by a stochastic differential equation with delay in the control. Using a result of existence and uniqueness of a sufficiently regular mild solution of the associated…
We present a novel class of minimax optimal control problems with positive dynamics, linear objective function and homogeneous constraints. The proposed problem class can be analyzed with dynamic programming and an explicit solution to the…
We present a novel framework for optimal control in both classical and quantum systems. Our approach leverages the Dirac--Bergmann algorithm: a systematic method for formulating and solving constrained dynamical systems. In contrast to the…
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…
This paper, which is the natural continuation of a previous paper by the same authors, studies a class of optimal control problems with state constraints where the state equation is a differential equation with delays. This class includes…