A variable stochastic admittance control framework with energy tank

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

doi:10.1016/j.ifacol.2020.12.2716

Cited by 4 publications

(11 citation statements)

References 18 publications

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“…The present section is devoted to introducing a weak notion of stochastic passivity and a consequently related notion of stability, that appears to be tailor-made for tackling the problem of energy shaping for SPHS. Such a notion has been first introduced in [Fang and Gao, 2016] and already used in the SPHS in [Cordoni et al, 2021a, Cordoni et al, 2020.…”

Section: On the Passivity For Controlled Sdementioning

confidence: 99%

“…The definition of ultimately stochastic passivity for a stochastic port-Hamiltonian system, [Cordoni et al, 2020] is recalled. Definition 3.1.…”

Section: On the Passivity For Controlled Sdementioning

confidence: 99%

“…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%

“…As noted by the authors, their approach is only valid for short time, whereas to look at the long-time behaviour the invariant measure of the stochastic system must be considered. In [Fang and Gao, 2016, Cordoni et al, 2021a, Cordoni et al, 2020 a weak notion of stochastic stability is considered, showing that such notion is in turn strictly related to the invariant measure of the SPHS. Broadly speaking, the weak notion of passivity introduced in [Fang and Gao, 2016, Cordoni et al, 2021a, Cordoni et al, 2020 is not defined on the whole state-space but only outside a ball centred at a specified state.…”

Section: Introductionmentioning

confidence: 99%

“…In [Fang and Gao, 2016, Cordoni et al, 2021a, Cordoni et al, 2020 a weak notion of stochastic stability is considered, showing that such notion is in turn strictly related to the invariant measure of the SPHS. Broadly speaking, the weak notion of passivity introduced in [Fang and Gao, 2016, Cordoni et al, 2021a, Cordoni et al, 2020 is not defined on the whole state-space but only outside a ball centred at a specified state. This definition has several desirable implications regarding the limiting distribution of the system.…”

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: On the Passivity For Controlled Sdementioning

confidence: 99%

“…The definition of ultimately stochastic passivity for a stochastic port-Hamiltonian system, [Cordoni et al, 2020] is recalled. Definition 3.1.…”

Section: On the Passivity For Controlled Sdementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Weak energy shaping for stochastic controlled port-Hamiltonian systems

Cordoni¹,

Persio²,

Muradore³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

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Stochastic Port-Hamiltonian Systems

2022

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In the present work we formally extend the theory of port-Hamiltonian systems to include random perturbations. In particular, suitably choosing the space of flow and effort variables we will show how several elements coming from possibly different physical domains can be interconnected in order to describe a dynamic system perturbed by general continuous semimartingale. Relevant enough, the noise does not enter into the system solely as an external random perturbation, since each port is itself intrinsically stochastic. Coherently to the classical deterministic setting, we will show how such an approach extends existing literature of stochastic Hamiltonian systems on pseudo-Poisson and pre-symplectic manifolds. Moreover, we will prove that a power-preserving interconnection of stochastic port-Hamiltonian systems is a stochastic port-Hamiltonian system as well.

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