Delay-independent sliding mode control for a class of quasi-linear parabolic distributed parameter systems with time-varying delay

Xing, Haiyan; Li, Donghai; Gao, Cunchen; Kao, Yonggui

doi:10.1016/j.jfranklin.2012.12.007

Cited by 18 publications

(16 citation statements)

References 26 publications

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“…Moreover, the theoretical development in Hilbert spaces or for PDE systems has only taken the attention in the last ten years. In this regard, we can cite the papers [8,33,44] concerning the control of semilinear PDE systems.…”

Section: Introductionmentioning

confidence: 99%

Sliding Mode Control for a Phase Field System Related to Tumor Growth

et al. 2017

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In the present contribution we study the sliding mode control (SMC) problem for a diffuse interface tumor growth model coupling a viscous Cahn-Hilliard type equation for the phase variable with a reaction-diffusion equation for the nutrient. First, we prove the well-posedness and some regularity results for the state system modified by the state-feedback control law. Then, we show that the chosen SMC law forces the system to reach within finite time the sliding manifold (that we chose in order that the tumor phase remains constant in time). The feedback control law is added in the Cahn-Hilliard type equation and leads the phase onto a prescribed target ϕ * in finite time.

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Section: Introductionmentioning

confidence: 99%

Sliding Mode Control for a Phase Field System Related to Tumor Growth

et al. 2017

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“…The second step is to design a SMC law that forces a linear combination of the system trajectories to reach the sliding surface − η ∗ in a finite time. SMCs are useful in many applications: we cite previous studies concerning the control of semilinear PDE systems and the recent contribution, where a sliding mode approach is applied for the first time to phase field systems of Caginalp type. We also mention the analysis developed in other studies: in particular, the second contribution is devoted to a conserved phase field system with a SMC feedback law for the internal energy in the temperature equation.…”

Section: Introductionmentioning

confidence: 99%

Sliding mode control for a diffuse interface tumor growth model coupling a Cahn–Hilliard equation with a reaction–diffusion equation

Colturato

2020

Math Methods in App Sciences

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We consider the sliding mode control (SMC) problem for a diffuse interface tumor growth model coupling a Cahn–Hilliard equation with a reaction–diffusion equation perturbed by a maximal monotone nonlinearity. We prove existence and regularity of strong solutions and, under further assumptions, a uniqueness result. Then, we show that the chosen SMC law forces the system to reach within finite time a sliding manifold that we chose in order that the tumor phase remains constant in time.

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“…While in some early works [27][28][29] only special classes of evolutions were considered, the theoretical development in a general Hilbert space setting or for PDE systems has gained attention only in the last ten years. In this respect, we can quote the papers [6], [23], and [35] dealing with sliding modes control for semilinear PDEs. In particular, in [6] the stabilization problem of a one-dimensional unstable heat conduction system (rod) modeled by a parabolic partial differential equation, powered with a Dirichlet type actuator from one of the boundaries was considered.…”

Section: Introductionmentioning

confidence: 99%

Sliding Mode Control for a Nonlinear Phase-Field System

Barbu¹,

Colli²,

Gilardi³

et al. 2017

SIAM J. Control Optim.

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In the present contribution the sliding mode control (SMC) problem for a phasefield model of Caginalp type is considered. First we prove the well-posedness and some regularity results for the phase-field type state systems modified by the statefeedback control laws. Then, we show that the chosen SMC laws force the system to reach within finite time the sliding manifold (that we chose in order that one of the physical variables or a combination of them remains constant in time). We study three different types of feedback control laws: the first one appears in the internal energy balance and forces a linear combination of the temperature and the phase to reach a given (space dependent) value, while the second and third ones are added in the phase relation and lead the phase onto a prescribed target. While the control law is non-local in space for the first two problems, it is local in the third one, i.e., its value at any point and any time just depends on the value of the state.

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Delay-independent sliding mode control for a class of quasi-linear parabolic distributed parameter systems with time-varying delay

Cited by 18 publications

References 26 publications

Sliding Mode Control for a Phase Field System Related to Tumor Growth

Sliding Mode Control for a Phase Field System Related to Tumor Growth

Sliding mode control for a diffuse interface tumor growth model coupling a Cahn–Hilliard equation with a reaction–diffusion equation

Sliding Mode Control for a Nonlinear Phase-Field System

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