Model Reduction by Moment Matching: Beyond Linearity A Review of the Last 10 Years

Astolfi, Alessandro; Scarciotti, Giordano; Simard, Joel D.; Faedo, Nicolás; Ringwood, John V.

doi:10.1109/cdc42340.2020.9304389

Cited by 12 publications

(12 citation statements)

References 41 publications

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“…This section recalls standard results in moment-based model reduction. The reader is referred to [6], [7], for a thorough treatment of the topic. Let Σ be a nonlinear, single-input single-output (SISO) system, given by the set of equations 1…”

Section: Preliminaries On Moment-matchingmentioning

confidence: 99%

“…[6], [7] Suppose Assumptions 1 and 2 hold. Let the zero equilibrium of system (1) be locally exponentially stable.…”

Section: Preliminaries On Moment-matchingmentioning

confidence: 99%

“…[6], [7] Suppose the assumptions of Lemma 1 are fulfilled. We call the mapping h • π the moment of system (1) at the signal generator (2), i.e.…”

Section: Preliminaries On Moment-matchingmentioning

confidence: 99%

“…A particularly well-developed WEC system is the so-called ISWEC device [4], originally proposed by the Politecnico di Torino (see Figure 1). Motivated by the intrinsic nonlinear behavior of this device [5], and the underlying necessity of reduced models for optimal control design, the objective of this paper is to produce reliable and computationally efficient reduced models by moment-matching [6], [7] for the ISWEC system, under a variety of input conditions.…”

Section: Introductionmentioning

confidence: 99%

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Data-driven nonlinear model reduction by moment-matching for the ISWEC system

Faedo

Piuma

Giorgi

et al. 2021

2021 International Conference on Electrical, Computer, Communications and Mechatronics Engineering (ICECCME)

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Given the relevance of control-oriented models in optimal control design for wave energy converters (WECs), this paper presents a data-driven approach to nonlinear model reduction by moment-matching for the ISWEC device, a device originally developed at the Politecnico di Torino. The presented model reduction technique is capable of providing simple WEC models, which inherently preserve steady-state response characteristics from the target nonlinear system, by merely using information on the system outputs, defined for a specific class of operating conditions. We demonstrate that the proposed model reduction by moment-matching procedure is well-posed for the ISWEC, and illustrate the efficacy of this reduction technique under a variety of sea conditions.

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Section: Preliminaries On Moment-matchingmentioning

confidence: 99%

“…[6], [7] Suppose Assumptions 1 and 2 hold. Let the zero equilibrium of system (1) be locally exponentially stable.…”

Section: Preliminaries On Moment-matchingmentioning

confidence: 99%

“…[6], [7] Suppose the assumptions of Lemma 1 are fulfilled. We call the mapping h • π the moment of system (1) at the signal generator (2), i.e.…”

Section: Preliminaries On Moment-matchingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Data-driven nonlinear model reduction by moment-matching for the ISWEC system

Faedo

Piuma

Giorgi

et al. 2021

2021 International Conference on Electrical, Computer, Communications and Mechatronics Engineering (ICECCME)

Self Cite

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show abstract

“…In any case, such modifications only address the symptoms of the problem, but do not directly undertake on the source of the conflict, that is, the ill-conditioning of the observability gramian. In this direction, better conditioning may be achieved by implementing a proper model order reduction [7], [8], [18], [19], which only retains the most observable modes. Nonetheless, this approach may eliminate weakly-observable modes that may be of interest for the application.…”

Section: A State Reconstruction In Weakly-observable Systemsmentioning

confidence: 99%

On state-estimation in weakly-observable scenarios and implicitly regularized observers

Cecilia

Costa‐Castelló

2021

2021 60th IEEE Conference on Decision and Control (CDC)

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This work proposes a framework to design observers for systems that present low observability. It is shown that, in these scenarios, the estimation problem becomes illposed, which drastically limits the performance of standard observers, specially in the presence of noise. Consequently, this paper presents a method to design an observer that optimizes some potential function to be defined by the designer. This allows to implicitly regularize the estimation and recover a wellposed problem. The proposed technique is validated in a set of weakly-observable systems and the performance is compared with a common Kalman filter-like observer.

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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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Model Reduction by Moment Matching: Beyond Linearity A Review of the Last 10 Years

Cited by 12 publications

References 41 publications

Data-driven nonlinear model reduction by moment-matching for the ISWEC system

Data-driven nonlinear model reduction by moment-matching for the ISWEC system

On state-estimation in weakly-observable scenarios and implicitly regularized observers

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

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