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Robustness with Parametric and Dynamic Uncertainty


Young, Peter Michael (1993) Robustness with Parametric and Dynamic Uncertainty. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/HJF8-J281.


In many disciplines of engineering it is often convenient, for analysis and design purposes, to approximate the real behavior of physical systems by mathematical models. For some applications however, and in particular when one wishes to design a high performance controller, the differences between the behavior of the mathematical model and the physical system can be crucial to the performance of the final design. The theory of robust control attempts to take into account these inherent inaccuracies in the model, and provide systematic analysis and design techniques in the face of this "uncertainty."

These goals can be restated as formal mathematical problems. In order to handle more realistic descriptions of physical systems, one has to allow more sophisticated models, and this leads to more difficult mathematical problems. In this thesis we will consider both the theoretical and computational aspects of such problems. In particular we will consider robustness in the presence of both real (e. g., parametric) and complex (e. g., dynamic) structured uncertainty.

This leads to a consideration of the general mixed µ analysis and synthesis problems. Some special cases of the analysis problem can be solved exactly, but the general problem is in fact NP hard, so that in order to develop solutions for large problems with reasonable computational requirements, we will adopt a scheme of computing and refining upper and lower bounds. By exploiting the theoretical properties of the problem, we are able to develop practical algorithms, capable of handling mixed µ analysis problems with tens of parameters, in computation times that are typically of the order of minutes. This is despite the fact that the mixed µ problem appears to have inherently combinatoric worst-case behavior.

For the synthesis problem a new "D,G-K iteration" procedure is developed to design a stabilizing controller which attempts to minimize the peak value across frequency of mixed µ. The scheme utilizes a combination of some new results from the mixed µ upper bound problem with the H optimal control solution. The theoretical results developed here have already been successfully applied to a number of real engineering problems, and some of these applications are briefly reviewed, to illustrate the advantages offered by the new analysis and synthesis techniques.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Electrical Engineering)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Electrical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Doyle, John Comstock
Thesis Committee:
  • Doyle, John Comstock (chair)
  • Franklin, Joel N.
  • Morari, Manfred
  • Dahleh, Munther A.
  • Murray, Richard M.
Defense Date:10 May 1993
Record Number:CaltechETD:etd-11302007-075425
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4695
Deposited By: Imported from ETD-db
Deposited On:06 Dec 2007
Last Modified:30 Aug 2022 21:34

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