Related papers: Equivalence between minimal time and minimal norm …
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…
In this paper, we establish the equivalence of minimal time and minimal norm control problems for semilinear heat equations in which the controls are distributed internally in an open subset of the state domain. As an application, the…
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…
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…
This paper builds up two equivalence theorems for different kinds of optimal control problems of internally controlled Schr\"{o}dinger equations. The first one concerns with the equivalence of the minimal norm and the minimal time control…
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…
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 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 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 time optimal internal control problem governed by the heat equation in $\Omega\times [0,\infty)$. In the problem, the target set $S$ is nonempty in $L^2(\Omega)$, the control set $U$ is closed, bounded and nonempty…
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 $\varepsilon\rightarrow 0$,…
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…
In this paper, minimal time and minimal norm control problems are studied. The target sets considered are the origin of state spaces and controls are point-wisely bounded functions. The system stuided in this paper is assumed to have no the…
In this paper, we study two subjects on internally controlled heat equations with time varying potentials: the attainable subspaces and the bang-bang property for some time optimal control problems. We present some equivalent…
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…
The paper is devoted to introducing an approach to compute the approximate minimum time function of control problems which is based on reachable set approximation and uses arithmetic operations for convex compact sets. In particular, in…
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…
In this article we study the internal controllability of 1D linear hyperbolic balance laws when the number of controls is equal to the number of state variables. The controls are supported in space in an arbitrary open subset. Our main…
This paper is concerned with the open-loop time-consistent solution of time-inconsistent mean-field stochastic linear-quadratic optimal control. Different from standard stochastic linear-quadratic problems, both the system matrices and the…
In the first part of this paper we introduced an algorithm that uses reachable set approximation to approximate the minimum time function of linear control problems. To illustrate the error estimates and to demonstrate differences to other…