On the control by interconnection and exponential stabilisation of infinite dimensional port-Hamiltonian systems

Macchelli, Alessandro

doi:10.1109/cdc.2016.7798739

Cited by 8 publications

(5 citation statements)

References 19 publications

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“…. Lemma 1 then implies the bound on the exponential decay of H(t) in (19). Lemma 2: Consider the matrices A s (x) and B(x) defined in ( 16) and (15), respectively.…”

Section: Exponential Stabilitymentioning

confidence: 98%

Exponential decay rate bound of one-dimensional distributed port-Hamiltonian systems with boundary dissipation

Mora

Morris

2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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In this work, the multiplier method is extended to obtain a general lower bound of the exponential decay rate in terms of the physical parameters for port-Hamiltonian systems in one space dimension with boundary dissipation. The physical parameters of the system may be spatially varying. It is shown that under assumptions of boundary or internal dissipation the system is exponentially stable. This is established through a Lyapunov function defined through a general multiplier function. Furthermore, an explicit bound on the decay rate in terms of the physical parameters is obtained. The method is applied to a number of examples.

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“…. Lemma 1 then implies the bound on the exponential decay of H(t) in (19). Lemma 2: Consider the matrices A s (x) and B(x) defined in ( 16) and (15), respectively.…”

Section: Exponential Stabilitymentioning

confidence: 98%

Exponential decay rate bound of one-dimensional distributed port-Hamiltonian systems with boundary dissipation

Mora

Morris

2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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“…The methodology is applied to a nanotweezer DNA-manipulation device. In Macchelli (2016b) the control by interconnection paradigm is augmented with an output feedback control loop providing exponential stability of the closed-loop system of the internally shaped equilibrium. An important contribution summarizing the ideas about boundary control laws for (4.1) is Macchelli et al (2017b), where Casimir generation, state feedback control laws able to overcome dissipation obstacle, and asymptotic stabilization with damping injection are extensively addressed.…”

Section: Control Of Dph Systems As Bcsmentioning

confidence: 99%

Twenty years of distributed port-Hamiltonian systems: a literature review

Rashad

Califano

Schaft

2020

IMA Journal of Mathematical Control and Information

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The port-Hamiltonian (pH) theory for distributed parameter systems has developed greatly in the past two decades. The theory has been successfully extended from finite-dimensional to infinite-dimensional systems through a lot of research efforts. This article collects the different research studies carried out for distributed pH systems. We classify over a hundred and fifty studies based on different research focuses ranging from modeling, discretization, control and theoretical foundations. This literature review highlights the wide applicability of the pH systems theory to complex systems with multi-physical domains using the same tools and language. We also supplement this article with a bibliographical database including all papers reviewed in this paper classified in their respective groups.

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“…and H a (ξ) that can be selected as in (17). The energy-shaping control β(x 1 , x 2 ) and the damping injection term u (x 1 , x 2 ) are the same as in (18).…”

Section: A Energy-shaping and Damping Injectionmentioning

confidence: 99%

“…via energy-balancing. This fact is exploited in the so-called energy-Casimir method that shows that all the energy-balancing control laws can be generated by a properly initialised port-Hamiltonian system with a lowerbounded Hamiltonian, [13], [17]. However, the requirements for having exponential stability in closed-loop stated in Proposition 3.2 and, in particular, condition (23), are not met.…”

Section: B Exponential Stabilisation Of Bcs In Port-hamiltonian Formmentioning

confidence: 99%

Exponential Stabilization of Port-Hamiltonian Boundary Control Systems via Energy Shaping

Macchelli

Gorrec

Ramírez

2020

IEEE Trans. Automat. Contr.

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This paper is concerned with the exponential stabilisation of a class of linear boundary control systems (BCS) in port-Hamiltonian form through energy-shaping. Starting from a first feedback loop that is in charge of modifying the Hamiltonian function of the plant, a second control loop that guarantees exponential convergence to the equilibrium is designed. In this way, a major limitation of standard energy-shaping plus damping injection control laws applied to linear port-Hamiltonian BCS, namely the fact that only asymptotic convergence is assured, has been removed.

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On the control by interconnection and exponential stabilisation of infinite dimensional port-Hamiltonian systems

Cited by 8 publications

References 19 publications

Exponential decay rate bound of one-dimensional distributed port-Hamiltonian systems with boundary dissipation

Exponential decay rate bound of one-dimensional distributed port-Hamiltonian systems with boundary dissipation

Twenty years of distributed port-Hamiltonian systems: a literature review

Exponential Stabilization of Port-Hamiltonian Boundary Control Systems via Energy Shaping

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