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Optimal control theory is a promising candidate for a drastic improvement of the performance of quantum information tasks. We explore its ultimate limit in paradigmatic cases, and demonstrate that it coincides with the maximum speed limit…
In this work, we investigate the optimal control problem for continuous-time Markov decision processes with the random impact of the environment. We provide conditions to show the existence of optimal controls under finite-horizon criteria.…
For linear infinite systems the approximate controllability problem by control constraints is considered. Controllability conditions represented via system parameters are obtained. Partial differential control systems and control systems…
We study a time-inconsistent singular stochastic control problem for a general one-dimensional diffusion, where time-inconsistency arises from a non-exponential discount function. To address this, we adopt a game-theoretic framework and…
This paper is devoted to studying an infinite time horizon stochastic recursive control problem with jumps, where infinite time horizon stochastic differential equation and backward stochastic differential equation with jumps describe the…
Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an…
This paper is concerned with a discounted stochastic optimal control problem for regime switching diffusion in an infinite horizon. First, as a preliminary with particular interests in its own right, the global well-posedness of infinite…
The goal of this paper is to solve a class of stochastic optimal control problems numerically, in which the state process is governed by an It\^o type stochastic differential equation with control process entering both in the drift and the…
We prove existence of optimal control for the deterministic and stochastic shallow lake problem without any restrictions on the parameter space and we establish a generalization of the Arrhenius Law in the case of noise-dependent…
This paper derives an optimal control strategy for a simple stochastic dynamical system with constant drift and an additive control input. Motivated by the example of a physical system with an unexpected change in its dynamics, we take the…
In this paper we study the optimality condition for the Venttsel boundary control of a parabolic equation, that is, the state of the dynamic system is governed by a parabolic equation together with an initial condition while the control is…
In this work, we consider the two dimensional tidal dynamics equations in a bounded domain and address some optimal control problems like total energy minimization, minimization of dissipation of energy of the flow, etc. We also examine an…
This paper proposes an optimal control problem for a parabolic equation with a nonlocal nonlinearity. The system is described by a parabolic equation involving a nonlinear term that depends on the solution and its integral over the domain.…
We prove a maximum principle of optimal control of stochastic delay equations on infinite horizon. We establish first and second sufficient stochastic maximum principles as well as necessary conditions for that problem. We illustrate our…
We present a general approach to prove existence of solutions for optimal control problems not based on typical convexity conditions which quite often are very hard, if not impossible, to check. By taking advantage of several relaxations of…
We establish the existence of both optimal relaxed controls and strict optimal controls for systems driven by Reflected Stochastic Differential Equations RSDEs. Our approach is based on weak convergence techniques for the associated RSDEs…
In this paper we study the stochastic control problem of partially observed (multi-dimensional) stochastic system driven by both Brownian motions and fractional Brownian motions. In the absence of the powerful tool of Girsanov…
We prove two duality descriptions of the value function for a generic stochastic optimal problem. These descriptions also hold when the diffusion is controlled, a case left open by the literature so far.
Parameter control aims at realizing performance gains through a dynamic choice of the parameters which determine the behavior of the underlying optimization algorithm. In the context of evolutionary algorithms this research line has for a…
While feedback control has many applications in quantum systems, finding optimal control protocols for this task is generally challenging. So-called "verification theorems" and "viscosity solutions" provide two useful tools for this…