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A Direct Approach to Robustness Optimization


You, Seungil (2016) A Direct Approach to Robustness Optimization. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9X34VDV.


This dissertation reformulates and streamlines the core tools of robustness analysis for linear time invariant systems using now-standard methods in convex optimization. In particular, robust performance analysis can be formulated as a primal convex optimization in the form of a semidefinite program using a semidefinite representation of a set of Gramians. The same approach with semidefinite programming duality is applied to develop a linear matrix inequality test for well-connectedness analysis, and many existing results such as the Kalman-Yakubovich--Popov lemma and various scaled small gain tests are derived in an elegant fashion. More importantly, unlike the classical approach, a decision variable in this novel optimization framework contains all inner products of signals in a system, and an algorithm for constructing an input and state pair of a system corresponding to the optimal solution of robustness optimization is presented based on this information. This insight may open up new research directions, and as one such example, this dissertation proposes a semidefinite programming relaxation of a cardinality constrained variant of the H ∞ norm, which we term sparse H ∞ analysis, where an adversarial disturbance can use only a limited number of channels. Finally, sparse H ∞ analysis is applied to the linearized swing dynamics in order to detect potential vulnerable spots in power networks.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Robust control theory; Semidefinite program; Robustness analysis
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Control and Dynamical Systems
Minor Option:Applied And Computational Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Doyle, John Comstock
Thesis Committee:
  • Doyle, John Comstock (chair)
  • Murray, Richard M.
  • Hassibi, Babak
  • Chandrasekaran, Venkat
Defense Date:12 August 2015
Funding AgencyGrant Number
Kwanjeong Educational FoundationUNSPECIFIED
Record Number:CaltechTHESIS:08122015-172710296
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9101
Deposited By: Seungil You
Deposited On:02 Sep 2015 16:42
Last Modified:04 Oct 2019 00:09

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