Outer Γ-Convexity in Vector Spaces

Phú, Hoàng Xuân

doi:10.1080/01630560802282250

Cited by 7 publications

(7 citation statements)

References 14 publications

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“…Remark 19. Informally, the concept of outer Γ-convexity, introduced in [19], is a formalisation of the concept of convexity for a class of functions which are 'roughly' convex, i.e. they possess properties similar to those of convex functions [43].…”

Section: Proposition 4 (Nonlinear Moment-based Unconstrained Np)mentioning

confidence: 99%

“…These are particularly useful for the results derived in Section IV-B. In particular, we begin by recalling the definition of outer Γ-convexity, originally proposed in [19], [43].…”

Section: Appendix a Outer γ-Convexitymentioning

confidence: 99%

“…• We propose a method to map the objective function (and system variables) to a finite-dimensional tractable nonlinear program (NP), which can be efficiently solved using state-of-the-art nonlinear programming solvers (see, for instance, [18]). • By showing that the objective function arising from the proposed moment-based strategy belongs to a family of approximately convex/concave mappings (particularly to the so-called outer Γ-convex/concave [19] functions), we guarantee the existence of a global energy-maximising solution, under mild assumptions. • In analogy to the case of convex/concave functions, where each local solution is also global, we give explicit conditions to determine whether a local energy-maximising solution is, effectively, a global maximiser for the proposed moment-based OCP, having strong practical implications when numerically solving the associated NP.…”

mentioning

confidence: 94%

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Nonlinear Energy-Maximizing Optimal Control of Wave Energy Systems: A Moment-Based Approach

Faedo

Scarciotti

Astolfi

et al. 2021

IEEE Trans. Contr. Syst. Technol.

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Linear dynamics are virtually always assumed when designing optimal controllers for wave energy converters (WECs), motivated by both their simplicity and computational convenience. Nevertheless, unlike traditional tracking control applications, the assumptions under which the linearisation of WEC models is performed are challenged by the energy-maximising controller itself, which intrinsically enhances device motion to maximise power extraction from incoming ocean waves. In this paper, we present a moment-based energy-maximising control strategy for WECs subject to nonlinear dynamics. We develop a framework under which the objective function (and system variables) can be mapped to a finite-dimensional tractable nonlinear program, which can be efficiently solved using state-of-the-art nonlinear programming solvers. Moreover, we show that the objective function belongs to a class of generalised convex functions when mapped to the moment-domain, guaranteeing the existence of a global energy-maximising solution, and giving explicit conditions for when a local solution is, effectively, a global maximiser. The performance of the strategy is demonstrated through a case study, where we consider (state and input-constrained) energymaximisation for a state-of-the-art CorPower-like WEC, subject to different hydrodynamic nonlinearities.

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Section: Proposition 4 (Nonlinear Moment-based Unconstrained Np)mentioning

confidence: 99%

“…These are particularly useful for the results derived in Section IV-B. In particular, we begin by recalling the definition of outer Γ-convexity, originally proposed in [19], [43].…”

Section: Appendix a Outer γ-Convexitymentioning

confidence: 99%

mentioning

confidence: 94%

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Nonlinear Energy-Maximizing Optimal Control of Wave Energy Systems: A Moment-Based Approach

Faedo

Scarciotti

Astolfi

et al. 2021

IEEE Trans. Contr. Syst. Technol.

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show abstract

“…This definition given in [14] is different from the original definition in [17], but they are equivalent. Next, we use this notion for describing lower level sets of the perturbed functionf .…”

mentioning

confidence: 96%

“…This kind of generalized convexity was introduced in [17], and the definition mentioned here follows [14].…”

mentioning

confidence: 99%