Related papers: Finite Codimensional Controllability, and Optimal …
Controlling the shapes of surfaces provides a novel way to direct self-assembly of colloidal particles on those surfaces and may be useful for material design. This motivates the investigation of an optimal control problem for surface shape…
We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…
We consider an optimal control problem governed by a rate-inde\-pendent system with non-convex energy. The state equation is approximated by means of viscous regularization w.r.t.\ to hierarchy of two different Hilbert spaces. The…
This paper is addressed to studying the exact controllability for stochastic transport equations by two controls: one is a boundary control imposed on the drift term and the other is an internal control imposed on the diffusion term. By…
In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Dirichlet or Neumann boundary controls. The main idea is to use…
The paper deals with the controllability of a degenerate beam equation. In particular, we assume that the left end of the beam is fixed, while a suitable control $f$ acts on the right end of it. As a first step we prove the existence of a…
In this paper we study an optimal control problem (OCP) associated to a linear elliptic equation {on a bounded domain $\Omega$}. The matrix-valued coefficients A of such systems is our control taken in L2 which in particular may comprise…
Following Demidovich's concept and definition of convergent systems, we analyze the optimal nonlinear damping control, recently proposed [1] for the second-order systems. Targeting the problem of output regulation, correspondingly tracking…
We propose a machine learning algorithm for solving finite-horizon stochastic control problems based on a deep neural network representation of the optimal policy functions. The algorithm has three features: (1) It can solve…
In the paper, the problems of approximate controllability are studied for the control system $w_t=\Delta w$, $w(0,x_2,t)=u(x_2,t)$, $x_1\in\mathbb R_+=(0,+\infty)$, $x_2\in\mathbb R$, $t\in(0,T)$, where $u$ is a control belonging to a…
We provide sufficient conditions for the approximate controllability of infinite-dimensional quantum control systems corresponding to form perturbations of the drift Hamiltonian modulated by a control function. We rely on previous results…
In this paper we study the exact boundary controllability for the following Boussinesq equation with variable physical parameters: \begin{array}{lll} \rho(x)y_{tt}=-(\sigma(x)y_{xx})_{xx}+(q(x)y_x)_x-(y^2)_{xx},&&t>0,~x\in(0,l),\\…
We study the exact controllability for spatially periodic water waves with surface tension, by localized exterior pressures applied to free surfaces. We prove that in any dimension, the exact controllability holds within arbitrarily short…
An iterative learning algorithm is presented for continuous-time linear-quadratic optimal control problems where the system is externally symmetric with unknown dynamics. Both finite-horizon and infinite-horizon problems are considered. It…
This paper deals with optimal control problems for systems affine in the control variable. We consider nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain…
This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…
In this paper it is considered a class of infinite-dimensional control systems in a variational setting. By using a Faedo-Galerkin method, a sequence of approximating finite dimensional controlled differential equations is defined. On each…
The objective of the paper is to investigate the approximate controllability property of a linear stochastic control system with values in a separable real Hilbert space. In a first step we prove the existence and uniqueness for the…
This article is devoted to studying the null controllability of evolution equations with memory terms. The problem is challenging not only because the state equation contains memory terms but also because the classical controllability…
This short book is the result of various master and summer school courses I have taught. The objective is to introduce the readers to mathematical control theory, both in finite and infinite dimension. In the finite-dimensional context, we…