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We present a theoretical study of the optimal control of a qubit interacting with a structured environment. We consider a model system in which the bath is a bosonic reservoir at zero temperature and the qubit frequency is the only control…
The main purpose of this article is to prove a logarithmic convexity estimate for the solution of a linear heat equation subject to dynamic boundary conditions in a bounded convex domain. As an application, we prove the impulsive null…
We investigate a control process described by a linear system of ordinary differential equations with a noise of special type acting to the control parameter. As the cost functional the probability of the final state vector to enter to a…
Turnpikes have recently gained significant research interest in optimal control, since they allow for pivotal insights into the structure of solutions to optimal control problems. So far, mainly steady state solutions which serve as optimal…
A general maximum principle is proved for optimal controls of abstract semilinear stochastic evolution equations. The control variable, as well as linear unbounded operators, acts in both drift and diffusion terms, and the control set need…
Deterministic optimal impulse control problem with terminal state constraint is considered. Due to the appearance of the terminal state constraint, the value function might be discontinuous in general. The main contribution of this paper is…
In this article, we study the existence of insensitizing controls for a nonlinear reaction-diffusion equation with dynamic boundary conditions. Here, we have a partially unknown data of the system, and the problem consists in finding…
In this paper we consider an energy storage optimization problem in finite time in a model with partial information that allows for a changing economic environment. The state process consists of the storage level controlled by the storage…
We consider a control problem where the system is driven by a decoupled as well as a coupled forward-backward stochastic differential equation. We prove the existence of an optimal control in the class of relaxed controls, which are…
The study is devoted to mathematical modeling and optimal control design of longitudinal motions of a rectilinear elastic rod. The control inputs are a force, which is normal to the cross section and distributed piecewise constantly along…
We focus on optimal control problems governed by elliptic, quasilinear PDEs. Though there are various examples of such problems in the literature, we make an attempt at describing some general principles by dealing with three basic…
In the paper, problems of controllability, approximate controllability, reachability and approximate reachability are studied for the control system $w_t=w_{xx}$, $w(0,\cdot)=u$, $x>0$, $t\in(0,T)$, where $u\in L^\infty(0,T)$ is a control.…
Most modern control systems are switched, meaning they have continuous as well as discrete decision variables. Switched systems often have constraints called dwell-time constraints (e.g., cycling constraints in a heat pump) on the switching…
The scheme of online optimization as a feedback controller is widely used to steer the states of a physical system to the optimal solution of a predefined optimization problem. Such methods focus on regulating the physical states to the…
Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for…
Problem of damping of an arbitrary number of linear oscillators under common bounded control is considered. We are looking for a feedback control steering the system to the equilibrium. The obtained control is asymptotically optimal: the…
In this paper, we investigate the existence and uniqueness of solutions for a class of evolutionary integral equations perturbed by a noise arising in the theory of heat conduction. As a motivation of our results, we study an optimal…
We consider the optimal control problem of minimizing some quadratic functional over all possible solutions of an internally controlled multi-dimensional heat equation with a periodic terminal state constraint. This problem has a unique…
Transferring a physical system from an initial to a final state while minimizing energetic losses is an interdisciplinary control problem that bridges stochastic thermodynamics and optimal transport theory. Recent research typically…
In this paper, a sub-optimal boundary control strategy for a free boundary problem is investigated. The model is described by a non-smooth convection-diffusion equation. The control problem is addressed by an instantaneous strategy based on…