Control of Reaction-Diffusion Systems

Löber, Jakob

doi:10.1007/978-3-319-46574-6_5

Cited by 2 publications

(2 citation statements)

References 51 publications

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“…If the coupling matrix B is not invertible, expression (7) for f Gold cannot be used. The question arises how to extend our approach to underactuated systems [37,55]. In the following example we assume a control acting on the activator u only while inhibitors v and w remain uncontrolled, i.e., f v,Gold (r, t) = f w,Gold (r, t) = 0.…”

Section: Position Control By a Single Control Signalmentioning

confidence: 99%

Control of traveling localized spots

Martens

Ryll

Löber

et al. 2021

Math. Model. Nat. Phenom.

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Traveling localized spots represent an important class of self-organized two- dimensional patterns in reaction-diffusion systems. We study open-loop control intended to guide a stable spot along a desired trajectory with desired velocity. Simultaneously, the spot's concentration profile does not change under control. For a given protocol of motion, we first express the control signal analytically in terms of the Goldstone modes and the propagation velocity of the uncontrolled spot. Thus, detailed information about the underlying nonlinear reaction kinetics is unnecessary. Then, we confirm the optimality of this solution by demonstrating numerically its equivalence to the solution of a regularized, optimal control problem. To solve the latter, the analytical expressions for the control are excellent initial guesses speeding-up substantially the otherwise time-consuming calculations.

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Section: Position Control By a Single Control Signalmentioning

confidence: 99%

Control of traveling localized spots

Martens

Ryll

Löber

et al. 2021

Math. Model. Nat. Phenom.

View full text Add to dashboard Cite

show abstract

“…If the coupling matrix B is not invertible, expression (7) for f Gold cannot be used. The question arises how to extend our approach to underactuated systems [36,52]. In the following example we assume a control acting on the activator u only while inhibitors v and w remain uncontrolled, i.e., f v,Gold (r, t) = f w,Gold (r, t) = 0.…”

Section: Position Control By a Single Control Signalmentioning

confidence: 99%

Control of traveling localized spots

Martens¹,

Ryll²,

Löber³

et al. 2017

Preprint

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Traveling localized spots represent an important class of selforganized two-dimensional patterns in reaction-diffusion systems. We study openloop control intended to guide a stable spot along a desired trajectory with desired velocity. Simultaneously, the spot's concentration profile does not change under control. For a given protocol of motion, we first express the control signal analytically in terms of the Goldstone modes and the propagation velocity of the uncontrolled spot. Thus, detailed information about the underlying nonlinear reaction kinetics is unnecessary. Then, we confirm the optimality of this solution by demonstrating numerically its equivalence to the solution of a regularized, optimal control problem. To solve the latter, the analytical expressions for the control are excellent initial guesses speeding-up substantially the otherwise timeconsuming calculations.

show abstract

Control of Reaction-Diffusion Systems

Cited by 2 publications

References 51 publications

Control of traveling localized spots

Control of traveling localized spots

Control of traveling localized spots

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