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.

Reconfiguration of the costly punishment network architecture in punishment decision-making.

Human costly punishment is rooted in multiple regions across large-scale functional systems, a collection of which constitutes the costly punishment network (CPN). Our previous study found that the CPN is intrinsically organized in an optimized and reliable manner to support individual costly punishment propensity. However, it remains unknown how the CPN is reconfigured in response to external cognitive demands in punishment decision-making. Here, we combined resting-state and task-functional magnetic resonance imaging to examine the task-related reconfigurations of intrinsic organizations of the CPN when participants made decisions of costly punishment in the Ultimatum Game. Although a strong consistency was observed in the overall pattern and each nodal profile between the intrinsic (task-free) and extrinsic (task-evoked) functional connectivity of the CPN, condition-general and condition-specific reconfigurations were also evident. Specifically, both unfair and fair conditions induced increases in functional connectivity between a few specific pairs of regions, and the unfair condition additionally induced increases in network efficiency of the CPN. Intriguingly, the specific changes in global efficiency of the CPN in the unfair condition were associated with individual differences in costly punishment after adjusting for the corresponding results in the fair condition, which were further identified for females but not for males. These findings were largely reproducible on independent samples. Collectively, our findings provide novel insights into how the CPN adaptively reconfigures its network architecture to support costly punishment.

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.

Nodal profile control for networks of geometrically exact beams

In this work, we consider networks of so-called geometrically exact beams, namely, shearable beams that may undergo large motions. The corresponding mathematical model, commonly written in terms of displacements and rotations expressed in a fixed basis (Geometrically Exact Beam model, or GEB), has a quasilinear governing system. However, the model may also be written in terms of intrinsic variables expressed in a moving basis attached to the beam (Intrinsic GEB model, or IGEB) and while the number of equations is then doubled, the latter model has the advantage of being of first-order, hyperbolic and only semilinear. First, for any network, we show the existence and uniqueness of semi-global in time classical solutions to the IGEB model (i.e., for arbitrarily large time intervals, provided that the data are small enough). Then, for a specific network containing a cycle, we address the problem of local exact controllability of nodal profiles for the IGEB model – we steer the solution to satisfy given profiles at one of the multiple nodes by means of controls applied at the simple nodes – by using the constructive method of Zhuang, Leugering and Li (2018) [52]. Afterwards, for any network, we show that the existence of a unique classical solution to the IGEB network implies the same for the corresponding GEB network, by using that these two models are related by a nonlinear transformation. In particular, this allows us to give corresponding existence, uniqueness and controllability results for the GEB network.

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.

Boundary controllability of a system modelling a partially immersed obstacle

In this paper, we address the problem of boundary controllability for the one-dimensional nonlinear shallow water system, describing the free surface flow of water as well as the flow under a fixed gate structure. The system of differential equations considered can be interpreted as a simplified model of a particular type of wave energy device converter called oscillating water column. The physical requirements naturally lead to the problem of exact controllability in a prescribed region. In particular, we use the concept of nodal profile controllability in which at a given point (the node) time-dependent profiles for the states are required to be reachable by boundary controls. By rewriting the system into a hyperbolic system with nonlocal boundary conditions, we at first establish the semi-global classical solutions of the system, then get the local controllability and nodal profile using a constructive method. In addition, based on this constructive process, we provide an algorithmic concept to calculate the required boundary control function for generating a solution for solving these control problem.

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.

Controllability and stabilization of a conservation law modeling a highly re-entrant manufacturing system

In this paper, we study the controllability and stabilization for a scalar conservation law modeling a highly re-entrant manufacturing system with local and nonlocal velocity. We prove a local state controllability result, i.e., there exists a control that drives the solution from any given initial condition to any desired final condition in a certain time period, provided that the initial and final data are both close to the origin. A local result on nodal profile controllability is also given, i.e., for any initial data and any given out-flux in a neighborhood of the origin, there exists a control under which the solution starts from any initial data reaches exactly any desired out-flux over a fixed time period. Besides, using a Lyapunov function approach, we can stabilize the system to the origin exponentially by output feedback control.

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.

Hybrid Method for Optimal Placement of Multiple SPV Based Multiple RDGs in Microgrid System

<p>A hybrid method has been suggested for optimal placement of multiple renewable distribution generations (RDGs) in microgrid system. The analytical approaches have not been appropriated for optimal placements of multiple solar photovoltaic (SPV) based on RDGs alone. In this work, hybridization of a fuzzy method and particle swarm optimization (PSO) search for the optimal placement of multiple RDGs in microgrid systems for decreasing the active power loss has been proposed. In this approach, the sizes of RDGs are evaluated at every bus by PSO method while the locations are determined by fuzzy based technique. The objective function (OBF) has been minimized under operating constraints. The improvements in nodal voltage profile have been observed. To confirm the proposed hybrid approach, results have been compared with bat algorithm (BA) technique and existing fast improved analytical (IA) method results. The suggested technique has been tested on 33-bus and 69-bus microgrid system.</p>

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.

Controllability for a scalar conservation law with nonlocal velocity

In this paper, we study the state controllability and nodal profile controllability for a scalar conservation law, with a nonlocal velocity, that models a highly re-entrant manufacturing system as encountered in semi-conductor production. We first prove a local state controllability result, i.e., there exists a control that drives the solution from any given initial data to any desired final data in a certain time period, provided that the initial and final data are both close to a given equilibrium ρ ¯ ⩾ 0 . We also obtain a global state controllability result for the same system, where there is no limitation on the distance between the initial and final data. Finally, we prove a nodal profile controllability result, i.e., there exists a control under which the solution starts from any initial data reaches exactly any given out-flux over a fixed time period.