相关论文: Minimal time impulse control of the heat equation
This paper investigates a minimal time control problem for the heat equation with multiple impulse controls. We first establish the maximum principles for this problem and then prove the equivalence between the minimal time impulse control…
This paper studies the time optimal control problem for systems of heat equations coupled by a pair of constant matrices. The control constraint is of the ball-type, while the target is the origin of the state space. We obtain an upper…
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…
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…
In this paper, we first design a time optimal control problem for the heat equation with sampled-data controls, and then use it to approximate a time optimal control problem for the heat equation with distributed controls. Our design is…
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…
This paper presents the equivalence between minimal time and minimal norm control problems for internally controlled heat equations. The target is an arbitrarily fixed bounded, closed and convex set with a nonempty interior in the state…
In this paper, optimal time control problems and optimal target control problems are studied for the approximately null-controllable heat equations. Compared with the existed results on these problems, the boundary of control variables are…
This paper studies a kind of minimal time control problems related to the exact synchronization for a controlled linear system of parabolic equations. Each problem depends on two parameters: the bound of controls and the initial state. The…
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…
This paper presents an equivalence theorem for three different kinds of optimal control problems, which are optimal target control problems, optimal norm control problems and optimal time control problems. Controlled systems in this study…
A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…
Our goal is to study controllability and observability properties of the 1D heat equation with internal control (or observation) set $\omega_{\varepsilon}=(x_{0}-\varepsilon, x_{0}+\varepsilon )$, in the limit $\varepsilon\rightarrow 0$,…
This paper develops a mathematical framework that aims to control the temperature and rotational speed in the activation process of a gas turbine in an optimal way. These controls influence the deformation and the stress in the component…
In this paper, we solve the problem of simultaneously driving in minimum time to arbitrary final conditions, N two level quantum systems subject to independent controls. The solution of this problem is obtained via an explicit description…
An optimal control problem for the continuity equation is considered. The aim of a "controller" is to maximize the total mass within a target set at a given time moment. The existence of optimal controls is established. For a particular…
The main aim of this paper is to provide a new feedback law for the heat equations in a bounded domain $\Omega $ with Dirichlet boundary condition. Two constraints will be compulsory: First, The controls are active in a subdomain of $\Omega…
In this paper, we study the impulse controllability of a multi-dimensional heat equation with dynamic boundary conditions in a bounded smooth domain. Using a recent approach based on finite-time stabilization, we show that the system is…
The minimum-time control problem consists in finding a control policy that will drive a given dynamic system from a given initial state to a given target state (or a set of states) as quickly as possible. This is a well-known challenging…
We show the existence and optimal regularity of the optimal temperature configuration in a problem in heat conduction with minimal temperature constraint, interior heating and exterior insulation. Regularity of the two free boundaries is…