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Mathematics of Control, Signals, and Systems : Volume 29

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Lipschitz continuity of the value function in mixed-integer optimal control problems

Boundary local null-controllability of the Kuramoto–Sivashinsky equation

Optimal control of semi-Markov processes with a backward stochastic differential equations approach

Boundary controllability of a nonlinear coupled system of two Korteweg–de Vries equations with critical size restrictions on the spatial domain

On an invariance principle for differential-algebraic equations with jumps and its application to switched differential-algebraic equations

The converging-input converging-state property for Lur’e systems

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Boundary controllability of a nonlinear coupled system of two Korteweg–de Vries equations with critical size restrictions on the spatial domain

Content Provider	Springer Nature Link
Author	Pazoto, Ademir F. Gallego, Fernando A. Capistra Filho, Roberto A.
Copyright Year	2017
Abstract	This article is dedicated to improve the controllability results obtained by Cerpa and Pazoto (Commun Contemp Math 13:183–189, 2011) and by Micu et al. (Commun Contemp Math 11(5):779–827, 2009) for a nonlinear coupled system of two Korteweg–de Vries equations posed on a bounded interval. Initially, Micu et al. (2009) proved that the nonlinear system is exactly controllable by using four boundary controls without any restriction on the length L of the interval. Later on, in Cerpa and Pazoto (2011), two boundary controls were considered to prove that the same system is exactly controllable for small values of the length L and large time of control T. Here, we use the ideas contained in Capistrano-Filho et al. (Z Angew Math Phys 67(5):67–109, 2016) to prove that, with another configuration of four controls, it is possible to prove the existence of the so-called critical length phenomenon for the linear system, i.e., whether the system is controllable depends on the length of the spatial domain. In addition, when we consider only one control input, the boundary controllability still holds for suitable values of the length L and time of control T. In both cases, the control spaces are sharp due a technical lemma which reveals a hidden regularity for the solution of the adjoint system.
Ending Page	37
Page Count	37
Starting Page	1
File Format	PDF
ISSN	09324194
e-ISSN	1435568X
Journal	Mathematics of Control, Signals, and Systems
Issue Number	1
Volume Number	29
Language	English
Publisher	Springer London
Publisher Date	2017-01-28
Publisher Place	London
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.) KdV-like equations (Korteweg-de Vries) Gear–Grimshaw system Exact boundary controllability Critical set Systems Theory, Control Control, Robotics, Mechatronics Dirichlet boundary conditions Neumann boundary conditions Controllability Communications Engineering, Networks Stabilization of systems by feedback
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Applied Mathematics Signal Processing Control and Systems Engineering

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Neumann boundary controllability of the Gear–Grimshaw system with critical size restrictions on the spatial domain

Neumann Boundary Controllability of the Korteweg--de Vries Equation on a Bounded Domain

Boundary controllability of a nonlinear coupled system of two Korteweg-de Vries equations with critical size restrictions on the spatial domain

Stabilization of the Gear-Grimshaw system with weak damping

Internal controllability of the korteweg–de vries equation on a bounded domain

Exact Boundary Controllability of a coupled System of KdV Equations

Energy solutions for the fifth-order modified Korteweg de-Vries equations

Gardner's deformations of the graded Korteweg-de Vries equations revisited

Two dimensional KP systems and their solvability

Boundary controllability of a nonlinear coupled system of two Korteweg–de Vries equations with critical size restrictions on the spatial domain

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