Controllability of the discrete-spectrum Schrödinger equation driven by an external field
Controllability of the Semilinear Heat Equation with Impulses and Delay on the State
In this paper we prove the interior approximate controllability of the following Semilinear Heat Equation with Impulses and Delay [...] where Ω is a bounded domain in RN(N ≥ 1), φ : [−r, 0] × Ω → ℝ is a continuous function, ! is an open nonempty subset of Ω, 1ω denotes the characteristic function of the set ! and the distributed control u be- longs to L2([0, τ]; L2(Ω; )). Here r ≥ 0 is the delay and the nonlinear functions f , Ik : [0, τ] × ℝ × ℝ → ℝ are smooth enough, such that [...] Under this...
Controllability of three-dimensional Navier–Stokes equations and applications
We formulate two results on controllability properties of the 3D Navier–Stokes (NS) system. They concern the approximate controllability and exact controllability in finite-dimensional projections of the problem in question. As a consequence, we obtain the existence of a strong solution of the Cauchy problem for the 3D NS system with an arbitrary initial function and a large class of right-hand sides. We also discuss some qualitative properties of admissible weak solutions for randomly forced NS...
Controllability of time-varying cellular neural networks.
Controllability of Urysohn integral inclusions of Volterra type.
Controllability on infinite time horizon for first and second order functional differential inclusions in Banach spaces
In this paper, we shall establish sufficient conditions for the controllability on semi-infinite intervals for first and second order functional differential inclusions in Banach spaces. We shall rely on a fixed point theorem due to Ma, which is an extension on locally convex topological spaces, of Schaefer's theorem. Moreover, by using the fixed point index arguments the implicit case is treated.
Controllability on real reductive Lie groups.
Controllability on the group of diffeomorphisms
Controllability, penalty and stiffness
Controllability problems for the 1-D wave equation on a half-axis with the Dirichlet boundary control
In this paper necessary and sufficient conditions of L∞-controllability and approximate L∞-controllability are obtained for the control system wtt = wxx − q2w, w(0,t) = u(t), x > 0, t ∈ (0,T), where q ≥ 0, T > 0, u ∈ L∞(0,T) is a control. This system is considered in the Sobolev spaces.
Controllability problems for the 1-D wave equation on a half-axis with the Dirichlet boundary control
In this paper necessary and sufficient conditions of L∞-controllability and approximate L∞-controllability are obtained for the control system wtt = wxx − q2w, w(0,t) = u(t), x > 0, t ∈ (0,T), where q ≥ 0, T > 0, u ∈ L∞(0,T) is a control. This system is considered in the Sobolev spaces.
Controllability problems for the 1-D wave equation on a half-axis with the Dirichlet boundary control
In this paper necessary and sufficient conditions of L∞-controllability and approximate L∞-controllability are obtained for the control system wtt = wxx − q2w, w(0,t) = u(t), x > 0, t ∈ (0,T), where q ≥ 0, T > 0, u ∈ L∞(0,T) is a control. This system is considered in the Sobolev spaces.
Controllability properties for the one-dimensional Heat equation under multiplicative or nonnegative additive controls with local mobile support
We discuss several new results on nonnegative approximate controllability for the one-dimensional Heat equation governed by either multiplicative or nonnegative additive control, acting within a proper subset of the space domain at every moment of time. Our methods allow us to link these two types of controls to some extend. The main results include approximate controllability properties both for the static and mobile control supports.
Controllability properties of a class of systems modeling swimming microscopic organisms
We consider a finite-dimensional model for the motion of microscopic organisms whose propulsion exploits the action of a layer of cilia covering its surface. The model couples Newton's laws driving the organism, considered as a rigid body, with Stokes equations governing the surrounding fluid. The action of the cilia is described by a set of controlled velocity fields on the surface of the organism. The first contribution of the paper is the proof that such a system is generically controllable...
Controllability results for first and second order evolution inclusions with nonlocal conditions
We prove controllability results for first and second order semilinear differential inclusions in Banach spaces with nonlocal conditions.
Controllability results for semilinear functional and neutral functional evolution equations with infinite delay.
Controllability theorem for nonlinear dynamical systems
Some sufficient conditions for controllability of nonlinear systems described by differential equation ẋ = f(t,x(t),u(t)) are given.
Controllable graphs
Controllable two dimensional neutral systems
Controllablity of a quantum particle in a 1D variable domain
We consider a quantum particle in a 1D infinite square potential well with variable length. It is a nonlinear control system in which the state is the wave function ϕ of the particle and the control is the length l(t) of the potential well. We prove the following controllability result : given close enough to an eigenstate corresponding to the length l = 1 and close enough to another eigenstate corresponding to the length l=1, there exists a continuous function with T > 0, such that l(0)...