Boundary Controllability Of Nodal Profile Research Articles

Exact Boundary Controllability of Nodal Profile for Nonautonomous Quasilinear Hyperbolic Systems

Exact Boundary Controllability of Nodal Profile for Nonautonomous Quasilinear Hyperbolic Systems

Exact boundary controllability of nodal profile for the system of one-dimensional adiabatic flow

In this paper, we study the exact boundary controllability of nodal profile for the system of one-dimensional adiabatic flow by means of the specificity of the entropy S which is constant about the time t. By a constructive method, we realize the exact boundary controllability of nodal profile by controlling the velocity or the pressure on the side without the nodal profile. Moreover, for the case of the infinite time interval, under the suitable assumption, we can obtain that if the nodal profile and the given boundary function possess an exponential or polynomial decaying property, the boundary control possesses the same exponential or polynomial decaying property.

The Exact Boundary Controllability of Nodal Profile for Entropy Solutions to 1-D Quasilinear Hyperbolic Systems of Conservation Laws with Linearly Degenerate Negative (Resp., Positive) Characteristic Fields

The Exact Boundary Controllability of Nodal Profile for Entropy Solutions to 1-D Quasilinear Hyperbolic Systems of Conservation Laws with Linearly Degenerate Negative (Resp., Positive) Characteristic Fields

Exact Boundary Controllability of Nodal Profile for Quasilinear Hyperbolic Systems and Its Asymptotic Stability

Exact Boundary Controllability of Nodal Profile for Quasilinear Hyperbolic Systems and Its Asymptotic Stability

Global piecewise classical solutions to quasilinear hyperbolic systems on a tree-like network

In this paper, we discuss the existence, uniqueness and asymptotic stability of global piecewise [Formula: see text] solution to the mixed initial-boundary value problem for 1-D quasilinear hyperbolic systems on a tree-like network. Under the assumption of boundary dissipation, when the given boundary and interface functions possess suitably small [Formula: see text] norm, we obtain the existence and uniqueness of global piecewise [Formula: see text] solution. Moreover, when they further possess a polynomial or exponential decaying property with respect to [Formula: see text], then the corresponding global piecewise [Formula: see text] solution possesses the same or similar decaying property. These results will be used to show the asymptotic stability of the exact boundary controllability of nodal profile on a tree-like network.

Exact boundary controllability of partial nodal profile for network of strings

Based on the theory of exact boundary controllability of nodal profile for hyperbolic systems, the authors propose the concept of exact boundary controllability of partial nodal profile to expand the scope of applications. With the new concept, we can shorten the controllability time, save the number of controls, and increase the number of charged nodes with given nodal profiles. Furthermore, we introduce the concept of in-situ controlled node to deal with a new situation that one node can be charged and controlled simultaneously. The minimum number of boundary controls on the entire tree-like network is determined by using the concept of ‘degree of freedom of charged nodes’ introduced. And the concept of ‘control path’ is introduced to appropriately divide the network, so that we can determine the infimum of controllability time. General frameworks of constructive proof are given on a single interval, a star-like network, a chain-like network and a planar tree-like network for linear wave equation(s) with Dirichlet, Neumann, Robin and dissipative boundary conditions to establish a complete theory on the exact boundary controllability of partial nodal profile.

A cut-off method to realize the exact boundary controllability of nodal profile for Saint-Venant systems on general networks with loops

In this paper, we consider the exact boundary controllability of nodal profile for Saint-Venant systems on a network with loops. In the case with one object-node, the proposed cut-off method not only contains the results obtained in [13] on a special network with a triangle-like loop in a unified way, but also generalizes these results to general networks with loops. Based on the results in the case with one object-node, the proposed cut-off method can also be applied successfully to the case with several object-nodes.

Asymptotic stability of the exact boundary controllability of nodal profile for 1D quasi‐linear wave equations

In this paper, we consider the asymptotic stability of the exact boundary controllability of nodal profile for 1D quasi‐linear wave equations. First, for 1D quasi‐linear hyperbolic systems with zero eigenvalues, we establish the existence and uniqueness of semiglobal classical solution to the one‐sided mixed initial‐boundary value problem on a semibounded initial axis and discuss the asymptotic behavior of the corresponding solutions under different hypotheses on the initial data. Based on these results, we obtain the asymptotic stability of the exact boundary controllability of nodal profile for 1D quasi‐linear wave equations on a semibounded time interval.

Asymptotic stability of the exact boundary controllability of nodal profile for quasilinear hyperbolic systems

In this paper, we consider the asymptotic stability of the exact boundary controllability of nodal profile for quasilinear hyperbolic systems. We will prove that if the nodal profile and the given boundary function possess an exponential or polynomial decaying property, then the boundary control function and the solution to the corresponding mixed initial-boundary value problem will possess the same decaying property.

Exact boundary controllability of nodal profile for Saint-Venant system on a network with loops

The exact boundary controllability for hyperbolic systems can not be realized generally on a network with loops (see [16]). In this paper we consider the exact boundary controllability of nodal profile on a network with loops. Precisely speaking, on a network with a triangle-like loop, when nodal profiles are given at various kinds of nodes, different constructive methods can be used to get the corresponding exact boundary controllability of nodal profile for Saint-Venant system by means of boundary controls acting on suitable nodes, respectively. This reveals that the exact boundary controllability of nodal profile is quite different from the usual exact boundary controllability, and has relatively distinctive behaviors and characters.

Exact internal controllability of nodal profile for first order quasilinear hyperbolic systems

For 1-D first order quasilinear hyperbolic systems without zero eigenvalues, based on the theory of semi-global C1 solution, by means of the results on both the exact boundary controllability and the exact boundary controllability of nodal profile, using an extension method, the exact controllability of nodal profile can be obtained purely with the help of internal controls. Moreover, using a perturbation method, by adding suitable internal controls to the part of equations corresponding to zero eigenvalues, the corresponding exact internal controllability of nodal profile for 1-D first order quasilinear hyperbolic systems with zero eigenvalues can be also obtained.

Exact controllability of nodal profile for 1‐D first order quasilinear hyperbolic systems with internal controls

For 1‐D first order quasilinear hyperbolic systems without zero eigenvalues, based on the theory of exact boundary controllability of nodal profile, using an extension method, the exact controllability of nodal profile can be realized in a shorter time by means of additional internal controls acting on suitably small space‐time domains. On the other hand, using a perturbation method, the exact controllability of nodal profile for 1‐D first order quasilinear hyperbolic systems with zero eigenvalues can be realized by additional internal controls to the part of equations corresponding to zero eigenvalues. Furthermore, by adding suitable internal controls to all the equations on suitable domains, the exact controllability of nodal profile for systems with zero eigenvalues can be realized in a shorter time.

Exact boundary controllability of nodal profile for quasilinear wave equations in a planar tree‐like network of strings

Based on the theory of semi‐global piecewise C2 solutions to 1D quasilinear wave equations, the local exact boundary controllability of nodal profile for quasilinear wave equations in a planar tree‐like network of strings with general topology is obtained by a constructive method. The principles of providing nodal profiles and of choosing and transferring boundary controls are presented, respectively. Copyright © 2013 John Wiley & Sons, Ltd.

Exact boundary controllability of nodal profile for unsteady flows on a tree-like network of open canals

The lack of boundary controls is often encountered in practical applications and causes a crucial difficulty for realizing the exact boundary controllability. In this paper, taking the Saint-Venant system as example, by means of a global constructive method based on the theory on the semi-global C1 solution to quasilinear hyperbolic systems, we establish the exact boundary controllability of nodal profile for unsteady flows on a tree-like network of open canals. The principles of providing the nodal profiles, of choosing the boundary controls and of transferring the boundary controls are presented, respectively.

Exact boundary controllability of nodal profile for 1-D quasilinear wave equations

The local exact boundary controllability for 1-D quasilinear wave equations has been obtained by means of a constructive method with modular structure (see [12, 19]). In this Chapter, we will show that, based on the results given in Chap. 2, this constructive method can be elegantly modified to get the local exact boundary controllability of nodal profile for 1-D quasilinear wave equations (see Wang [21]).

Exact boundary controllability of nodal profile for quasilinear hyperbolic systems in a tree-like network

In this paper, the exact boundary controllability of nodal profile is established for quasilinear hyperbolic systems with general nonlinear boundary and interface conditions in a tree-like network with general topology. The basic principles for giving nodal profiles and for choosing boundary controls are presented, respectively. Copyright © 2011 John Wiley & Sons, Ltd.

Exact boundary controllability of nodal profile for quasilinear hyperbolic systems

In this paper the exact boundary controllability of nodal profile, originally proposed by M. Gugat et al., is studied for general 1-D quasilinear hyperbolic systems with general nonlinear boundary conditions. Copyright © 2010 John Wiley & Sons, Ltd.