Nonlinear feedback stabilization of incompressible flows via updated Riccati-based gains

Benner, Peter; Heiland, Jan

doi:10.1109/cdc.2017.8263813

Cited by 5 publications

(6 citation statements)

References 14 publications

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“…robustness margin . Let G (s) = M (s) −1 N (s) be another system in normalized LQG form (9), then K is guaranteed to also stabilize G if holds.…”

Section: The Normalized H ∞ Problem and Low-rank Robust Controllersmentioning

confidence: 99%

“…Theorem 1 (Sufficient a-priori conditions for stabilization of disturbed systems) Given a system G = M(s) −1 N(s) in normalized LQG form (9) and a reduced-order system Ĝ computed by HINFBT (Algorithm 1) with the robustness margin . The central controller K based on Ĝ is guaranteed to stabilize the full-order system G if where = √ 1 − −2 , and is computed from the truncated characteristic H ∞ -values (14).…”

Section: The Normalized H ∞ Problem and Low-rank Robust Controllersmentioning

confidence: 99%

“…We note that only the projected parts X ∶= X and Y = Y of the Riccati solutions X and Y contribute to the controller; see (8) and [9]; where X and Y solve the equations (22b)…”

Section: Projector-free Realization For Incompressible Flowsmentioning

confidence: 99%

“…Remark 3 (Validity of Assumption 1) The problem at hand derives from a state-space system with input operator B and output operator C that is brought into the normalized form (9). Accordingly, Assumption 1 is reduced to stability and detectability with respect to the given inputs and outputs; cf.…”

Section: Further Computational Setup For Both Test Casesmentioning

confidence: 99%

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Robust output-feedback stabilization for incompressible flows using low-dimensional $$\mathcal {H}_{\infty }$$-controllers

2022

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Output-based controllers are known to be fragile with respect to model uncertainties. The standard $$\mathcal {H}_{\infty }$$ H ∞ -control theory provides a general approach to robust controller design based on the solution of the $$\mathcal {H}_{\infty }$$ H ∞ -Riccati equations. In view of stabilizing incompressible flows in simulations, two major challenges have to be addressed: the high-dimensional nature of the spatially discretized model and the differential-algebraic structure that comes with the incompressibility constraint. This work demonstrates the synthesis of low-dimensional robust controllers with guaranteed robustness margins for the stabilization of incompressible flow problems. The performance and the robustness of the reduced-order controller with respect to linearization and model reduction errors are investigated and illustrated in numerical examples.

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“…robustness margin . Let G (s) = M (s) −1 N (s) be another system in normalized LQG form (9), then K is guaranteed to also stabilize G if holds.…”

Section: The Normalized H ∞ Problem and Low-rank Robust Controllersmentioning

confidence: 99%

Section: The Normalized H ∞ Problem and Low-rank Robust Controllersmentioning

confidence: 99%

“…We note that only the projected parts X ∶= X and Y = Y of the Riccati solutions X and Y contribute to the controller; see (8) and [9]; where X and Y solve the equations (22b)…”

Section: Projector-free Realization For Incompressible Flowsmentioning

confidence: 99%

Section: Further Computational Setup For Both Test Casesmentioning

confidence: 99%

See 2 more Smart Citations

Robust output-feedback stabilization for incompressible flows using low-dimensional $$\mathcal {H}_{\infty }$$-controllers

2022

Self Cite

View full text Add to dashboard Cite

show abstract

“…For that, we note that only the projected parts X Π := Π T XΠ and Y Π = Π T Y Π of the Riccati solutions X and Y contribute to the controller (cp. (8) and [10]) and that X Π and Y Π solve the equations…”

Section: Projector-free Realization For Incompressible Flowsmentioning

confidence: 99%

Robust output-feedback stabilization for incompressible flows using low-dimensional $\mathcal{H}_{\infty}$-controllers

Benner,

Heiland,

Werner

2021

Preprint

Self Cite

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Output-based controllers are known to be fragile with respect to model uncertainties. The standard H ∞ -control theory provides a general approach to robust controller design based on the solution of the H ∞ -Riccati equations. In view of stabilizing incompressible flows in simulations, two major challenges have to be addressed: the high-dimensional nature of the spatially discretized model and the differential-algebraic structure that comes with the incompressibility constraint. This work demonstrates the synthesis of low-dimensional robust controllers with guaranteed robustness margins for the stabilization of incompressible flow problems. The performance and the robustness of the reduced-order controller with respect to linearization and model reduction errors are investigated and illustrated in numerical examples.

show abstract

On Approximating Polynomial-Quadratic Regulator Problems

Borggaard

Zietsman

2021

IFAC-PapersOnLine

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Nonlinear feedback stabilization of incompressible flows via updated Riccati-based gains

Cited by 5 publications

References 14 publications

Robust output-feedback stabilization for incompressible flows using low-dimensional $$\mathcal {H}_{\infty }$$-controllers

Robust output-feedback stabilization for incompressible flows using low-dimensional $$\mathcal {H}_{\infty }$$-controllers

Robust output-feedback stabilization for incompressible flows using low-dimensional $\mathcal{H}_{\infty}$-controllers

On Approximating Polynomial-Quadratic Regulator Problems

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