Robust optimization of delay differential equations with state and parameter dependent delays

Otten, Jonas; Mönnigmann, Martin

doi:10.1109/cdc.2016.7798469

Cited by 2 publications

(4 citation statements)

References 14 publications

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“…Lemma 1 (augmented system modified Hopf [1]). Assume x(c) is a steady state for parameter values α (c) .…”

Section: Augmented System Of Modified Hopf Manifoldmentioning

confidence: 99%

“…The following proposition is stated in [1], but only a sketch of the proof was given there. It is the purpose of the present document to state a complete proof.…”

Section: Augmented System Of Modified Hopf Manifoldmentioning

confidence: 99%

“…

This document states the normal vector system for modified Hopf boundaries of delay differential systems with state and parameter dependent delays. Specifically, it states the proof for Proposition 1 in the paper entitled Robust optimization of delay differential equations with state and parameter dependent delays by the same authors [1].

…”

mentioning

confidence: 99%

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Normal Vectors on Modified Hopf Manifolds of Delay Differential Equations

Otten,

Mönnigmann

2019

Preprint

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“…Lemma 1 (augmented system modified Hopf [1]). Assume x(c) is a steady state for parameter values α (c) .…”

Section: Augmented System Of Modified Hopf Manifoldmentioning

confidence: 99%

“…The following proposition is stated in [1], but only a sketch of the proof was given there. It is the purpose of the present document to state a complete proof.…”

Section: Augmented System Of Modified Hopf Manifoldmentioning

confidence: 99%

See 1 more Smart Citation

Normal Vectors on Modified Hopf Manifolds of Delay Differential Equations

Otten,

Mönnigmann

2019

Preprint

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“…Mönnigmann and Marquardt incorporated these normal vectors to state robustness in economic optimization problems [20]. Their normal vector approach has been extended in different contexts, for example, to achieve specified transient behavior [11], to the stability of periodically operated systems [12] and, more recently, to delayed systems [13,21,22]. The Lang-Kobayashi type laser diode models, which serve as examples in the present paper, belong to the latter problem class.…”

Section: Introductionmentioning

confidence: 99%

A method for the optimization of nonlinear systems with delays that guarantees stability and robustness

Otten,

Mönnigmann

2019

Preprint

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We present a method for the steady state optimization of nonlinear delay differential equations. The method ensures stability and robustness, where a system is called robust if it remains stable despite uncertain parameters. Essentially, we ensure stability of all steady states of the nonlinear system on the steady state manifold that results from the variation of the uncertain parameters. The uncertain parameters are characterized by finite intervals, which may be interpreted as error bars and therefore are of immediate practical relevance. Stability despite uncertain parameters can be guaranteed by enforcing a lower bound on the distance of the optimal steady state to submanifolds of saddle-node and Hopf bifurcations on the steady state manifold. We derive constraints that ensure this distance. The proposed method differs from previous ones in that stability and robustness are guaranteed with constraints instead of with the cost function. Because the cost function is not required to enforce stability and robustness, it can be used to state economic or similar goals, which is natural in applications. We illustrate the proposed method by optimizing a laser diode. The optimization finds a steady state of maximum intensity while guaranteeing asymptotic or exponential stability despite uncertain model parameters.

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Robust optimization of delay differential equations with state and parameter dependent delays

Cited by 2 publications

References 14 publications

Normal Vectors on Modified Hopf Manifolds of Delay Differential Equations

Normal Vectors on Modified Hopf Manifolds of Delay Differential Equations

A method for the optimization of nonlinear systems with delays that guarantees stability and robustness

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