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 systems of partial differential equations
In the paper definitions of various kinds of stability and boundedness of solutions of linear controllable systems of partial differential equations are introduced and their interconnections are derived. By means of Ljapunov's functions theorems are proved which give necessary and sufficient conditions for particular kinds of stability and boundedness of the solutions.
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)...
Controlled diffusion processes.
Controlled functional differential equations : approximate and exact asymptotic tracking with prescribed transient performance
A tracking problem is considered in the context of a class of multi-input, multi-output, nonlinear systems modelled by controlled functional differential equations. The class contains, as a prototype, all finite-dimensional, linear, -input, -output, minimum-phase systems with sign-definite “high-frequency gain”. The first control objective is tracking of reference signals by the output of any system in : given , construct a feedback strategy which ensures that, for every (assumed bounded...
Controlled functional differential equations: approximate and exact asymptotic tracking with prescribed transient performance
A tracking problem is considered in the context of a class of multi-input, multi-output, nonlinear systems modelled by controlled functional differential equations. The class contains, as a prototype, all finite-dimensional, linear, m-input, m-output, minimum-phase systems with sign-definite “high-frequency gain". The first control objective is tracking of reference signals r by the output y of any system in : given , construct a feedback strategy which ensures that, for every r (assumed bounded with...
Controller design for bilinear systems with parametric uncertainties.
Controller design for bush-type 1-d wave networks∗
In this paper, we introduce a new method for feedback controller design for the complex distributed parameter networks governed by wave equations, which ensures the stability of the closed loop system. This method is based on the uniqueness theory of ordinary differential equations and cutting-edge approach in the graph theory, but it is not a simple extension. As a realization of this idea, we investigate a bush-type wave network. The well-posedness of the closed loop system is obtained via Lax-Milgram’s...
Controller design for bush-type 1-d wave networks
In this paper, we introduce a new method for feedback controller design for the complex distributed parameter networks governed by wave equations, which ensures the stability of the closed loop system. This method is based on the uniqueness theory of ordinary differential equations and cutting-edge approach in the graph theory, but it is not a simple extension. As a realization of this idea, we investigate a bush-type wave network. The well-posedness of the closed loop system is obtained via Lax-Milgram’s...