This paper studies several solution paths of sparse quadratic minimization problems as a function of the weighing parameter of the biobjective of estimation loss versus solution sparsity. Three such paths are considered: the “
Minimumgain Pole Placement with Sparse Static Feedback
The minimumgain 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 equalityconstrained optimization problem and present an analytical characterization of its locally optimal 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 obtain local solutions for 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 local solutions to the MGEAP. Finally, numerical studies are presented to compare the properties of the algorithms, which suggest that the proposed projec
 Award ID(s):
 1631112
 Publication Date:
 NSFPAR ID:
 10196090
 Journal Name:
 IEEE Transactions on Automatic Control
 Page Range or eLocationID:
 1 to 1
 ISSN:
 00189286
 Sponsoring Org:
 National Science Foundation
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