Discrete stochastic port-Hamiltonian systems

Cordoni, Francesco; Persio, Luca Di; Muradore, Riccardo

doi:10.1016/j.automatica.2021.110122

Cited by 8 publications

(11 citation statements)

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“…The present paper continues the investigation of stochastic PHS started in [Cordoni et al, 2021a, Cordoni et al, 2020, Cordoni et al, 2019, Cordoni et al, 2022, Cordoni et al, 2021b, addressing the problem of energy shaping of SPHS. Such topic has been one of the main interest in the study of deterministic PHS and consequently it has been object of deep investigation also in the stochastic case.…”

Section: Discussionmentioning

confidence: 76%

“…Such a general description of a physical system allows to a systematic investigation of the interconnection, van der Schaft, 1992, Dalsmo andVan der Schaft, 1997], integrability, [Dalsmo and Van Der Schaft, 1998] and symmetries, [Blankenstein and Van Der Schaft, 2001], and also to study physical systems with nonholonomic constraints, [Gay-Balmaz and Yoshimura, 2015]. Recently, PHSs have been extended to the stochastic case, [Cordoni et al, 2019, Cordoni et al, 2021a, Cordoni et al, 2020, Cordoni et al, 2022, Satoh, 2017, Satoh and Fujimoto, 2012, Satoh and Saeki, 2014, Satoh and Fujimoto, 2010.…”

Section: Introductionmentioning

confidence: 99%

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Weak energy shaping for stochastic controlled port-Hamiltonian systems

Cordoni¹,

Persio²,

Muradore³

2022

Preprint

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The present work address the problem of energy shaping for stochastic port-Hamiltonian system. Energy shaping is a powerful technique that allows to systematically find feedback law to shape the Hamiltonian of a controlled system so that, under a general passivity condition, it converges or tracks a desired configuration. Energy shaping has been recently generalized to consider stochastic port-Hamiltonian system. Nonetheless the resulting theory presents several limitation in the application so that relevant examples, such as the additive noise case, are immediately ruled out from the possible application of energy shaping. The current paper continues the investigation of the properties of a weak notion of passivity for a stochastic system and a consequent weak notion of convergence for the shaped system considered recently by the authors. Such weak notion of passivity is strictly related to the existence and uniqueness of an invariant measure for the system so that the theory developed has a purely probabilistic flavour. We will show how all the relevant results of energy shaping can be recover under the weak setting developed. We will also show how the weak passivity setting considered draw an insightful connection between stochastic port-Hamiltonian systems and infinite-dimensional port-Hamiltonian system.

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Section: Discussionmentioning

confidence: 76%

Section: Introductionmentioning

confidence: 99%

Weak energy shaping for stochastic controlled port-Hamiltonian systems

Cordoni¹,

Persio²,

Muradore³

2022

Preprint

Self Cite

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show abstract

“…In particular, their phase space flows (almost surely) preserve the canonical symplectic structure. We will argue that maintaining this property in model reduction is beneficial because the resulting reduced systems can then be integrated using stochastic symplectic methods (see [21], [34], [36], [38], [39], [55], [57], [59], [68], [80], [83], [84], [111], [122]), and consequently more accurate numerical solutions can be obtained. This goal can be achieved by an appropriate adaptation of the PSD method in the stochastic setting.…”

Section: Data-driven Structure-preserving Model Reduction 221mentioning

confidence: 99%

Data-driven structure-preserving model reduction for stochastic Hamiltonian systems

Tyranowski

2024

JCD

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In this work we demonstrate that SVD-based model reduction techniques known for ordinary differential equations, such as the proper orthogonal decomposition, can be extended to stochastic differential equations in order to reduce the computational cost arising from both the high dimension of the considered stochastic system and the large number of independent Monte Carlo runs. We also extend the proper symplectic decomposition method to stochastic Hamiltonian systems, both with and without external forcing, and argue that preserving the underlying symplectic or variational structures results in more accurate and stable solutions that conserve energy better than when the non-geometric approach is used. We validate our proposed techniques with numerical experiments for a semi-discretization of the stochastic nonlinear Schrödinger equation and the Kubo oscillator.

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“…However, since these models are Hamiltonian, it is advisable to integrate them using structure-preserving methods. Stochastic symplectic integrators, similar to their deterministic counterparts, preserve the symplecticity of the Hamiltonian flow and demonstrate good energy behavior in long-time simulations (see [7], [8], [9], [10], [27], [35], [37], [45], [48], [50], [51], [60], [79], [81], [83], [94], [106], [107], [111], [112], [113], [142], [153], [154], [156], [159] and the references therein). In this work we will focus on two stochastic symplectic Runge-Kutta methods, namely the stochastic midpoint method (2.10), which is symplectic when applied to a Hamiltonian system, and the stochastic Störmer-Verlet method ( [81], [94], [107]).…”

Section: Time Integrationmentioning

confidence: 99%

“…In particular, their phase space flows (almost surely) preserve the canonical symplectic structure. We will argue that maintaining this property in model reduction is beneficial because the resulting reduced systems can then be integrated using stochastic symplectic methods (see [7], [8], [9], [10], [27], [35], [37], [45], [48], [50], [51], [60], [79], [81], [83], [94], [106], [107], [111], [112], [113], [142], [153], [154], [156], [159]), and consequently more accurate numerical solutions can be obtained. This goal can be achieved by an appropriate adaptation of the PSD method in the stochastic setting.…”

Section: Introductionmentioning

confidence: 99%