Related papers: On the Attainable set for Temple Class Systems wit…
In this paper we give a direct proof that for a restricted affine control system on a connected manilfold M, the associated reachable sets up to time t varies continuously with the Haudorff metric.
This work is concerned with two optimisation problems that we tackle from a qualitative perspective. The first one deals with quantitative inequalities for spectral optimisation problems for Schr\"{o}dinger operators in general domains, the…
We study the controllability of the multidimensional wave equation in a bounded domain with Dirichlet boundary condition, in which the support of the control is allowed to change over time. The exact controllability is reduced to the proof…
We study a mixed boundary value problem for the quasilinear elliptic equation $\mathop{\rm div}\mathcal{A}(x,\nabla u(x))=0$ in an open infinite circular half-cylinder with prescribed continuous Dirichlet data on a part of the boundary and…
In this paper we present a survey concerning unconstrained free boundary problems of type $$ \left\{ \begin{array}{ll} F_1(D^2u,\nabla u,u,x)=0 & \text{in }B_1 \cap \Omega ,\\ F_2 (D^2 u,\nabla u,u,x)=0 & \text{in }B_1\setminus\Omega ,\\ u…
We make two remarks about the null-controllability of the heat equation with Dirichlet condition in unbounded domains. Firstly, we give a geometric necessary condition (for interior null-controllability in the Euclidean setting)which…
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 paper we study boundary controllability of the Korteweg-de Vries (KdV) equation posed on a finite domain $(0,L)$ with the Neumann boundary conditions: u_t+u_x+uu_x+u_{xxx}=0 in (0,L)x(0,T), u_{xx}(0,t)=0, u_x(L,t)=h(t),…
This paper introduces a new variational formulation for Dirichlet boundary control problem of elliptic partial differential equations, based on observations that the state and adjoint state are related through the control on the boundary of…
Estimating the reachable set of a dynamical system is a fundamental problem in control theory, particularly when control inputs are bounded. Direct simulation using randomly sampled admissible controls often leads to trajectories that…
This paper studies the existence of solutions and, in particular, the well-posedness of a class of boundary control systems. Our main result provides explicit and verifiable conditions on the system data that guarantee continuous dependence…
Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…
We establish existence and uniqueness results for initial boundary value problems with nearly incompressible vector fields. We then apply our results to establish well-posedness of the initial-boundary value problem for the Keyfitz and…
We study problems of optimal boundary control with systems governed by linear hyperbolic partial differential equations. The objective function is quadratic and given by an integral over the finite time interval $(0,\, T)$ that depends on…
We consider optimal control problems involving two constraint sets: one comprised of linear ordinary differential equations with the initial and terminal states specified and the other defined by the control variables constrained by simple…
In the paper, the problems of controllability and approximate controllability are studied for the control system $w_t=\Delta w$, $w_{x_1}(0,x_2,t)=u(t)\delta(x_2)$, $x_1>0$, $x_2\in\mathbb R$, $t\in(0,T)$, where $u\in L^\infty(0,T)$ is a…
Motivated by the control of invasive biological populations, we consider a class of optimization problems for moving sets $t\mapsto \Omega(t)\subset\mathbb{R}^2$. Given an initial set $\Omega_0$, the goal is to minimize the area of the…
In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we…
This paper is concerned with the Neumann initial-boundary value problem for the two-species chemotaxis system with consumption of chemoattractant \begin{equation*} u_t=\Delta u-\chi_1\nabla\cdot(u\nabla w), \end{equation*} \begin{equation*}…
This paper introduces control barrier functions for discrete-time systems, which can be shown to be necessary and sufficient for controlled invariance of a given set. Moreover, we propose nonlinear discrete-time control barrier functions…