Performance survey of minimum gain exact pole placement methods

Pandey, Amit; Schmid, Robert; Nguyen, Thang

doi:10.1109/ecc.2015.7330800

Cited by 7 publications

(8 citation statements)

References 17 publications

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“…Proof. Any feedback f which satisfies the sparsity constraint (2c) can be written as f = PFf ns where f ns ∈ R mn is a non-sparse vector 3 . Vectorizing (2a) using P.3 and P.4, and substituting f = PFf ns , we get…”

Section: B Algorithms For Sparse Eapmentioning

confidence: 99%

“…This is known as Minimum Gain Eigenvalue Assignment Problem (MGEAP). Both of these problems have been studied extensively [2]- [3].…”

Section: Introductionmentioning

confidence: 99%

“…Simultaneous robust and minimum gain pole placement were studied in [11], [19]- [21]. For a survey and performance comparison of these MGEAP studies, see [3] and the references therein. The regional pole placement problem was studied in [22], [23], where the eigenvalues were assigned inside a specified region.…”

Section: Introductionmentioning

confidence: 99%

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Minimum-gain Pole Placement with Sparse Static Feedback

Katewa¹,

Pasqualetti²

2018

Preprint

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The minimum-gain eigenvalue assignment/pole placement problem (MGEAP) is a classical problem in LTI systems with static state feedback. In this paper, we study the MGEAP when the state feedback has arbitrary sparsity constraints. We formulate the sparse MGEAP problem as an equality-constrained optimization problem and present an analytical characterization of its solution in terms of eigenvector matrices of the closed loop system. This result is used to provide a geometric interpretation of the solution of the nonsparse MGEAP, thereby providing additional insights for this classical problem. Further, we develop an iterative projected gradient descent algorithm to solve the sparse MGEAP using a parametrization based on the Sylvester equation. We present a heuristic algorithm to compute the projections, which also provides a novel method to solve the sparse EAP. Also, a relaxed version of the sparse MGEAP is presented and an algorithm is developed to obtain approximately sparse solutions to the MGEAP. Finally, numerical studies are presented to compare the properties of the algorithms, which suggest that the proposed projection algorithm converges in almost all instances.

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Section: B Algorithms For Sparse Eapmentioning

confidence: 99%

“…This is known as Minimum Gain Eigenvalue Assignment Problem (MGEAP). Both of these problems have been studied extensively [2]- [3].…”

Section: Introductionmentioning

confidence: 99%

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Minimum-gain Pole Placement with Sparse Static Feedback

Katewa¹,

Pasqualetti²

2018

Preprint

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“…Both problems have an extensive literature; see (Schmid et al, 2014a) for a recent survey. Numerical experiments offering performance comparisons of several methods for these two problems appeared in (Pandey et al, 2014) and (Pandey et al, 2015).…”

Section: Optimal Pole Placement Problemsmentioning

confidence: 99%

Arbitrary pole placement with the extended Kautsky–Nichols–van Dooren parametric form

Schmid

Ntogramatzidis

Nguyen

2016

International Journal of Control

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“…The model-based exact pole placement problem has a long history; a non-exhaustive list of references includes [15]- [18]. However, all these classical methods construct on a model-based description of the system to control; in contrast with these methods, our focus here is to derive formulas for pole placement that can be applied directly on data.…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Synthesis of Optimization-Based Controllers for Regulation of Unknown Linear Systems

Bianchin¹,

Vaquero²,

Cortés³

et al. 2021

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

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The exact pole placement problem concerns computing a feedback gain that will assign the poles of a system, controlled via static state feedback, at a set of pre-specified locations. This is a classic problem in feedback control and numerous methodologies have been proposed in the literature for cases where a model of the system to control is available.In this paper, we study the problem of computing feedback gains for pole placement (and, more generally, eigenstructure assignment) directly from experimental data. Interestingly, we show that the closed-loop poles can be placed exactly at arbitrary locations without relying on any model description but by using only finite-length trajectories generated by the open-loop system. In turn, these findings imply that classical control objectives, such as feedback stabilization or meeting transient performance specifications, can be achieved without first identifying a system model. Numerical experiments demonstrate the benefits of the data-driven pole-placement approach as compared to its model-based counterpart.

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Performance survey of minimum gain exact pole placement methods

Cited by 7 publications

References 17 publications

Minimum-gain Pole Placement with Sparse Static Feedback

Minimum-gain Pole Placement with Sparse Static Feedback

Arbitrary pole placement with the extended Kautsky–Nichols–van Dooren parametric form

Data-Driven Synthesis of Optimization-Based Controllers for Regulation of Unknown Linear Systems

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