Numerical Simulation of Nonlocal Delayed Feedback Controller for Simple Bioreactors

Čiegis, Raimondas; Suboč, Olga; Čiegis, Remigijus

doi:10.15388/informatica.2018.165

Cited by 15 publications

(15 citation statements)

References 9 publications

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“…Another important aspect is that theoretical investigations in the numerical analysis are strongly influenced by practical applications in heat conductions [3], thermoelasticity [10], underground water flow [23], electrochemistry [5], and so on. In [7,14], some mathematical models with nonlocal conditions for bioreactors are described.…”

Section: Introductionmentioning

confidence: 99%

M-Matrices and Convergence of Finite Difference Scheme for Parabolic Equation With Integral Boundary Condition

Čiupaila

Sapagovas

Pupalaigė

2020

Mathematical Modelling and Analysis

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In the paper, the stability and convergence of difference schemes approximating semilinear parabolic equation with a nonlocal condition are considered. The proof is based on the properties of M-matrices, not requiring the symmetry or diagonal predominance of difference problem. The main presumption is that all the eigenvalues of the corresponding difference problem with nonlocal conditions are positive.

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Section: Introductionmentioning

confidence: 99%

M-Matrices and Convergence of Finite Difference Scheme for Parabolic Equation With Integral Boundary Condition

Čiupaila

Sapagovas

Pupalaigė

2020

Mathematical Modelling and Analysis

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“…Particulary, many problems in thermoelasticity can be formulated as nonlocal problems (see [3][4][5] and the references therein). Two of the latest new mathematical models in the biotechnology are presented in [6,7]. A separate class of such nonlocal models is boundary value problem for elliptic equation with nonlocal boundary conditions [8].…”

Section: Introductionmentioning

confidence: 99%

Finite difference method for boundary value problem for nonlinear elliptic equation with nonlocal conditions

et al. 2019

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In the paper the convergence of a finite difference scheme for two-dimensional nonlinear elliptic equation in the rectangular domain with the integral boundary condition is considered. The majorant is constructed for the error of the solution of the system of difference equations, and the estimation of this error is obtained. With this aim, the idea of application of the M-matrices for the theoretical investigation of the system of difference equations was developed. Main results for the convergence of the difference schemes are obtained considering the structure of the spectrum and properties of the M-matrices for a wider class of boundary value problems for nonlinear equations with nonlocal conditions. The main advantage of the suggested method is that the error of approximate solution is estimated in the maximum norm.

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“…In this paper, we continue the analysis of bioreactors based on the enzymatic conversion of substrate into the required product. In [3], the control loop was defined by using the relation how the amount of the drug produced in the bioreactor and delivered into a human body depends on the substrate concentration specified on the external boundary of the bioreactor. Only diffusion transport and nonlinear reaction processes were taken in account.…”

Section: Introductionmentioning

confidence: 99%

“…We note that the feedback control mechanism is used in many technological applications [11,12]. The recent developments of this technique for optimal control of processes in smart bioreactors is one of the interesting new theoretical and computational challenges [3,7,13].…”

Section: Introductionmentioning

confidence: 99%

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Numerical algorithms for solving the optimal control problem of simple bioreactors

Čiegis

2019

NAMC

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The modified nonlocal feedback controller is used to control the production of drugs in a simple bioreactor. This bioreactor is based on the enzymatic conversion of substrate into the required product. The dynamics of this device is described by a system of two nonstationary nonlinear diffusion–convection–reaction equations. The analysis of the influence of the convection transport is one the aims of this paper. The control loop is defined using the relation, which shows how the amount of the drug produced in the bioreactor and delivered into a human body depends on the substrate concentration specified on the external boundary of the bioreactor. The system of PDEs is solved by using the finite volume and finite difference methods, the control loop parameters are defined from the analysis of stationary linearized equations. The second aim of this paper is to solve the inverse problem and to determine optimal boundary conditions. These results enable us to estimate the potential accuracy of the proposed devices.

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Numerical Simulation of Nonlocal Delayed Feedback Controller for Simple Bioreactors

Cited by 15 publications

References 9 publications

M-Matrices and Convergence of Finite Difference Scheme for Parabolic Equation With Integral Boundary Condition

M-Matrices and Convergence of Finite Difference Scheme for Parabolic Equation With Integral Boundary Condition

Finite difference method for boundary value problem for nonlinear elliptic equation with nonlocal conditions

Numerical algorithms for solving the optimal control problem of simple bioreactors

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