Funnel control of nonlinear systems

Berger, Toby; Ilchmann, Achim; Ryan, E. P.

doi:10.1007/s00498-021-00277-z

Cited by 56 publications

(67 citation statements)

References 54 publications

(122 reference statements)

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“…As an illustration of the method, they consider a mass-spring system mounted on a car. Note that a newly survey for funnel control for different types of systems can be found in Berger et al (2021c). Funnel control has also been considered in several aplications.…”

Section: Introductionmentioning

confidence: 99%

Adaptive output error feedback for a class of nonlinear infinite-dimensional systems

Hastir¹,

Winkin²,

Dochain³

2021

Preprint

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An adaptive funnel control method is considered for the regulation of the output for a class of nonlinear infinitedimensional systems on real Hilbert spaces. After a decomposition of the state space and some change of variables related to the Byrnes-Isidori form, it is shown that the funnel controller presented in (Berger et al., 2020b) achieves the control objective under that some assumptions on the system dynamics are considered, like well-posedness and BIBO stability assumptions of the nonlinear system. The theory is applied to the regulation of the temperature in a chemical plug-flow tubular reactor whose reaction kinetics are modeled by the Arrhenius nonlinearity. Furthermore a damped sine-Gordon model is shown to fit the required assumptions as well. The theoretical results are illustrated by means of numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Adaptive output error feedback for a class of nonlinear infinite-dimensional systems

Hastir¹,

Winkin²,

Dochain³

2021

Preprint

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“…which becomes exactly the blended dynamics introduced in [2] when e i ≡ 0 for all i ∈ N . Therefore, if synchronization with prescribed performance as in (7) is achieved (similar to (3) in the case of node-wise funnel coupling), then e i also evolves within a prespecified error margin, as we have…”

Section: Assumption 5 (Design Parameters For Coupling)mentioning

confidence: 99%

“…The idea of an edge-wise funnel coupling law was first proposed in [3] and the specific use of this design to solve distributed consensus optimization can be found in [4]. Both this novel coupling law and the node-wise funnel coupling law (2) are inspired by the funnel control introduced in [5]; see also the recent works [6,7] and the literature review therein. We note that the problem of dynamic average consensus, where its goal is for each agent to follow the average of the given time-varying signals, which is known only to each agent, has been solved in a similar manner in [8] using the prescribed performance control methodology (which is related to the funnel control).…”

Section: Contribution Of the Present Papermentioning

confidence: 99%

“…where d G is the diameter of the communication graph G = (N , E) and Ψ(t) := max p∈M max (j,i)∈E ψ p ij (t) ≤ ψ. 3 The synchronization objective (7) is obtained under the additional assumption that solutions of (8) do not exhibit a finite escape time.…”

Section: Assumption 5 (Design Parameters For Coupling)mentioning

confidence: 99%

“…. , x N ) : [t 0 , ∞) → R n1+...+n N of (4) and (6) which satisfies the synchronization objective (7).…”

Section: Assumption 5 (Design Parameters For Coupling)mentioning

confidence: 99%

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Edge-wise funnel output synchronization of heterogeneous agents with relative degree one

Lee¹,

Berger²,

Trenn³

et al. 2021

Preprint

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In a recent work by three of the authors, in order to enforce synchronization for scalar heterogeneous multi-agent systems with some useful characteristics, a node-wise funnel coupling law was proposed. The emergent dynamics, to which each of the agents synchronizes, was characterized and it was studied how networks can be synthesized which exhibit these emergent dynamics. The advantage of this synthesis is its suitability for plug-and-play operation. However, the aforementioned emergent dynamics under node-wise funnel coupling are determined by an algebraic equation which does not admit an explicit solution in general, and even its pointwise solution proves rather difficult. Furthermore, the contractivity assumption on the emergent dynamics, required to establish the synchronization, is hard to be checked without solving the algebraic equation. To resolve these drawbacks, in the present paper we present a new funnel coupling law that uses edge-wise output differences. Under this novel coupling the benign properties of node-wise funnel coupling are retained, but the emergent dynamics are given explicitly by the blended dynamics of the multi-agent system, which already proved an advantageous tool in the analysis and design of such networks. Additionally, our results are not restricted to scalar systems and treat the case that neighboring agents only communicate their output information, and not their complete state.

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Introduction

Gao,

2023

Spacecraft Maneuver With Performance Guaranteed

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Funnel control of nonlinear systems

Cited by 56 publications

References 54 publications

Adaptive output error feedback for a class of nonlinear infinite-dimensional systems

Adaptive output error feedback for a class of nonlinear infinite-dimensional systems

Edge-wise funnel output synchronization of heterogeneous agents with relative degree one

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