Feedback norm minimisation with regional pole placement

Datta, Subashish; Chakraborty, Debraj

doi:10.1080/00207179.2014.908476

Cited by 9 publications

(3 citation statements)

References 24 publications

(42 reference statements)

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“…= 1 2 f T f is given by dJ=f T df . Using (23) and P.12, we get (19). To derive the Hessian, we compute the second-order differentials of the involved variables.…”

Section: A Algorithms For Non-sparse Mgeapmentioning

confidence: 99%

“…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. While all these studies have provided useful insights on REAP/MGEAP, they do not consider sparsity constraints on the feedback matrix.…”

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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“…= 1 2 f T f is given by dJ=f T df . Using (23) and P.12, we get (19). To derive the Hessian, we compute the second-order differentials of the involved variables.…”

Section: A Algorithms For Non-sparse Mgeapmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Minimum-gain Pole Placement with Sparse Static Feedback

Katewa¹,

Pasqualetti²

2018

Preprint

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“…below (n − 1) in the SISO case). This pole placement scenario is more relevant in practice (Datta & Chakraborty, 2013, 2014Datta, Chakraborty, & Belur, 2012;Datta, Chakraborty, & Chaudhuri, 2012) since the performance specifications usually mention time domain characteristics like settling time/damping ratio. Hence, it would be enough if a designed controller guarantees that all the closed-loop poles are placed within some desirable region in the complex plane.…”

Section: Introductionmentioning

confidence: 98%

Reduced-order controller synthesis with regional pole constraint

Datta

Chakraborty

Belur

2015

International Journal of Control

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A reduced order output feedback controller is designed for a linear time invariant system, which guarantees that the closed-loop poles are placed within some pre-specified stability region in the complex plane. A convex approximation of the non-convex constraints is used to pose a sequence of semi-definite programs, which provide the lowest order proper controller satisfying the approximate constraints. The proposed method is demonstrated on two practical controller design applications.

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