Monotone RLC circuits

Chaffey, Thomas; Sepulchre, Rodolphe

doi:10.23919/ecc54610.2021.9654912

Cited by 7 publications

(8 citation statements)

References 35 publications

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“…Of course, the assumption of a quadratic-affine Hamiltonian H(x) = 1 2 x T Qx + Ax+c in order to let the monotone port-Hamiltonian system be incrementally passive and differentially passive is restrictive. On the other hand, it is known from the literature [3,30] that for 'unconditional' incremental properties such an assumption may be necessary as well. For example we can formulate the following simple result.…”

Section: Steady State Analysis Of Incrementally Port-hamiltonian Systemsmentioning

confidence: 99%

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Port-Hamiltonian systems and monotonicity

Camlibel¹,

Schaft²

2022

Preprint

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The relationships between port-Hamiltonian systems modeling and the notion of monotonicity are explored. The earlier introduced notion of incrementally port-Hamiltonian systems is extended to maximal cyclically monotone relations, together with their generating functions. This gives rise to new classes of incrementally port-Hamiltonian systems, with examples stemming from physical systems modeling as well as from convex optimization. An in-depth treatment is given of the composition of maximal monotone and maximal cyclically monotone relations, where in the latter case the resulting maximal cyclically monotone relation is shown to be computable through the use of generating functions. Furthermore, connections are discussed with incremental versions of passivity, and it is shown how incrementally port-Hamiltonian systems with strictly convex Hamiltonians are (maximal) equilibrium independent passive. Finally, the results on compositionality of monotone relations are employed for a convex optimization approach to the computation of the equilibrium of interconnected incrementally port-Hamiltonian systems.

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Section: Steady State Analysis Of Incrementally Port-hamiltonian Systemsmentioning

confidence: 99%

“…First, monotonicity has been a key notion in the study of nonlinear electrical circuits and general nonlinear network dynamics; see e.g. the recent paper [3] for a historical context and references. From a systems and control point of view this view on monotonicity is strongly related to notions of incremental passivity [4] and contraction [5].…”

mentioning

confidence: 99%

Port-Hamiltonian systems and monotonicity

Camlibel¹,

Schaft²

2022

Preprint

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“…Here, we consider one-port circuits formed by the series and parallel interconnection of resistors, capacitors and inductors. This is the class of circuits considered in the conference version of this paper [40].…”

Section: Rlc Circuitsmentioning

confidence: 99%

“…In this paper, we revisit the classical study of nonlinear electrical networks in light of recent developments in the theory of maximal monotone operators. Preliminary results in this direction were presented at ECC2021 [40]. We study the problem of computing the periodic output of a system described by a series/parallel interconnection of basic elements, which is forced by a periodic input.…”

Section: Introductionmentioning

confidence: 99%

Monotone one-port circuits

Chaffey¹,

Sepulchre²

2021

Preprint

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Maximal monotonicity is explored as a generalization of the linear theory of passivity, aiming at an algorithmic input/output analysis of physical models. The theory is developed for maximal monotone one-port circuits, formed by the series and parallel interconnection of basic elements. An algorithmic method is presented for solving the periodic output of a periodically driven circuit using a maximal monotone splitting algorithm, which allows computation to be separated for each circuit component. A new splitting algorithm is presented, which applies to any monotone circuit defined as a port interconnection of monotone elements.The research leading to these results has received funding from the European Research Council under the Advanced ERC Grant Agreement Switchlet n. 670645.

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“…The main contribution of this paper is to reunite the algorithmic framework of maximal monotonicity with nonlinear circuit analysis. A preliminary version of this work has been submitted for presentation at ECC2021 [37]. We consider nonlinear circuits obtained as port interconnections of the four fundamental 1-port circuit elements: the resistor, the inductor, the capacitor, and the memristor.…”

Section: Introductionmentioning

confidence: 99%