Feedback Robustness in Structured Closed-loop System

This paper addresses the robustness of large-scale closed-loop structured systems in the sense of arbitrary pole placement when subject to failure of feedback links. Given a structured system with input, output, and feedback matrices, we first aim to verify whether the closed-loop structured system...

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Bibliographic Details
Published in:European journal of control Vol. 57; pp. 95 - 108
Main Authors: Gundeti, RaviTeja, Moothedath, Shana, Chaporkar, Prasanna
Format: Journal Article
Language:English
Published: Philadelphia Elsevier Ltd 01.01.2021
Elsevier Limited
Subjects:
Algorithms
arbitrary pole-placement
Closed loop systems
Closed loops
Communication
complex networks
Control theory
Failure
Feedback control
Links
optimal feedback design
Pole placement
Polynomials
Robust systems
Robustness
Sensors
Sparsity
structural perturbations in networks
Verification
arbitrary pole-placement
complex networks
Robust systems
structural perturbations in networks
optimal feedback design
ISSN:0947-3580, 1435-5671
Online Access:Get full text
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Summary:This paper addresses the robustness of large-scale closed-loop structured systems in the sense of arbitrary pole placement when subject to failure of feedback links. Given a structured system with input, output, and feedback matrices, we first aim to verify whether the closed-loop structured system is robust to the simultaneous failure of any subset of feedback links of cardinality at most γ. Subsequently, we address the associated design problem in which given a structured system with input and output matrices, we need to design a sparsest feedback matrix that ensures the robustness of the resulting closed-loop structured system to simultaneous failure of at most any γ feedback links. We first prove that the verification problem is NP-complete even for irreducible systems and the design problem is NP-hard even for so-called structurally cyclic systems. We also show that the design problem is inapproximable to factor (1−o(1))logn, where n denotes the system dimension. Then we propose algorithms to solve both the problems: a pseudo-polynomial algorithm to address the verification problem of irreducible systems and a polynomial-time O(log n)-optimal approximation algorithm to solve the design problem for a special feedback structure, so-called back-edge feedback structure.
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ISSN:0947-3580
1435-5671
DOI:10.1016/j.ejcon.2020.05.009