Related papers: Optimal Actuator Location of the Minimum Norm Cont…
In this paper, we study optimal actuator location of the minimum norm controls for a multi-dimensional heat equation with control defined in the space $L^p(0,T;L^2(\Omega))$. The actuator domain $\omega$ is quite general in the sense that…
This paper focuses on investigating the optimal actuator location for achieving minimum norm controls in the context of approximate controllability for degenerate parabolic equations. We propose a formulation of the optimization problem…
This paper aims to provide directly the observability inequality of backward stochastic heat equations for measurable sets. As an immediate application, the null controllability of the forward heat equations is obtained. Moreover, an…
We consider the actuator placement problem for linear systems. Specifically, we aim to identify an actuator which requires the least amount of control energy to drive the system from an arbitrary initial condition to the origin in the worst…
This paper is concerned with impulse approximate controllability for stochastic evolution equations with impulse controls. As direct applications, we formulate captivating minimal norm and time optimal control problems; The minimal norm…
We consider the time-varying actuator placement in continuous time, where the goal is to maximize the trace of the controllability Grammian. A natural relaxation of the problem is to allow the binary $\{0,1\}$ variable indicating whether an…
This paper establishes the tractability of finding the optimal Nash equilibrium, as well as the optimal social solution, to a discrete congestion game using a gate-model quantum computer. The game is of the type originally posited by…
This paper investigates the norm and time optimal control problems for stochastic heat equations. We begin by presenting a characterization of the norm optimal control, followed by a discussion of its properties. We then explore the…
The paper is concerned with a kind of minimal time control problem for the heat equation with impulse controls. The purpose of such a problem is to find an optimal impulse control (among certain control constraint set) steering the solution…
We are concerned with the optimal control problem of the well known nonlocal thermistor problem, i.e., in studying the heat transfer in the resistor device whose electrical conductivity is strongly dependent on the temperature. Existence of…
An optimal boundary control problem for the one-dimensional heat equation is considered. The objective functional includes a standard quadratic terminal observation, a Tikhonov regularization term with regularization parameter $\nu$, and…
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…
The relaxation of a system to a steady state is a central point of interest in many attempts to advance control over the quantum world. In this paper, we consider control through instantaneous Gaussian unitary operations on the ubiquitous…
We consider the mean-field game where each agent determines the optimal time to exit the game by solving an optimal stopping problem with reward function depending on the density of the state processes of agents still present in the game.…
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 a network of residential heating systems in which several prosumers satisfy their heating and hot water demand using solar thermal collectors and services of a central producer. Overproduction of heat can either be stored in a…
We consider a stochastic optimal control problem for an heat equation with boundary noise and boundary controls. Under suitable assumptions on the coefficients, we prove existence of optimal controls in strong sense by solving the…
We address the problem of minimal actuator placement in linear systems so that the volume of the set of states reachable with one unit or less of input energy is lower bounded by a desired value. First, following the recent work of…
We give the solution to the minimum-energy control problem for linear stochastic systems. The problem is as follows: given an exactly controllable system, find the control process with the minimum expected energy that transfers the system…
In this paper, we study a certain approximation property for a time optimal control problem of the heat equation with $L^\infty$-potential. We prove that the optimal time and the optimal control to the same time optimal control problem for…