Some properties of boundedly perturbed strictly convex quadratic functions

Phú, Hoàng Xuân; Pho, V.M.

doi:10.1080/02331931003746114

Cited by 5 publications

(11 citation statements)

References 23 publications

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“…Finally, given that the mappingJ QP has a unique global maximiserȲ opt l (see Remark 18), and the set Γ ∩ R 1×(ν+ι) is closed, the NP defined by the objective functionJ always admits a global optimal solutionȲ opt (see [43,Lemma 4.3] and Property 3 in Appendix A). Proposition 5 makes explicit use of the strictly outer Γconvexity of the function −J to ensure existence of a global solution to the moment-based energy-maximising OCP proposed in this study.…”

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

confidence: 99%

“…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]. The reader is referred to Definition 5 in Appendix A for a formal treatment of this concept.…”

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

confidence: 99%

“…The reader is referred to Definition 5 in Appendix A for a formal treatment of this concept. Moreover, recalling key theoretical results from [43], we can use the following property of strictly outer convex functions (see Property 4 in Appendix A), which establishes a direct relationship between local and global maximisers forJ , having strong practical implications.…”

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

confidence: 99%

“…To keep the paper self-contained, we recall some facts from [43]. These are particularly useful for the results derived in Section IV-B.…”

Section: Appendix a Outer γ-Convexitymentioning

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%

See 4 more Smart Citations

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%

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

confidence: 99%

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

confidence: 99%

“…To keep the paper self-contained, we recall some facts from [43]. These are particularly useful for the results derived in Section IV-B.…”

Section: Appendix a Outer γ-Convexitymentioning

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%

See 3 more Smart Citations

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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Maximizing Strictly Convex Quadratic Functions with Bounded Perturbations

Phú

Pho

2011

J Optim Theory Appl

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Optimal control of wave energy systems considering nonlinear Froude–Krylov effects: control-oriented modelling and moment-based control

et al. 2022

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Motivated by the relevance of so-called nonlinear Froude–Krylov (FK) hydrodynamic effects in the accurate dynamical description of wave energy converters (WECs) under controlled conditions, and the apparent lack of a suitable control framework effectively capable of optimally harvesting ocean wave energy in such circumstances, we present, in this paper, an integrated framework to achieve such a control objective, by means of two main contributions. We first propose a data-based, control-oriented, modelling procedure, able to compute a suitable mathematical representation for nonlinear FK effects, fully compatible with state-of-the-art control procedures. Secondly, we propose a moment-based optimal control solution, capable of transcribing the energy-maximising optimal control problem for WECs subject to nonlinear FK effects, by incorporating the corresponding data-based FK model via moment-based theory, with real-time capabilities. We illustrate the application of the proposed framework, including energy absorption performance, by means of a comprehensive case study, comprising both the data-based modelling, and the optimal moment-based control of a heaving point absorber WEC subject to nonlinear FK forces.

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Some properties of boundedly perturbed strictly convex quadratic functions

Cited by 5 publications

References 23 publications

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

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

Maximizing Strictly Convex Quadratic Functions with Bounded Perturbations

Optimal control of wave energy systems considering nonlinear Froude–Krylov effects: control-oriented modelling and moment-based control

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