Catastrophes in Optimal Control

[+] Author and Article Information
Osita D. I. Nwokah, E. Borzova, Gemunu S. Happawana

Department of Mechanical Engineering, Southern Methodist University, Dallas, TX 75275-0337

Daré Afolabi

Department of Mechanical Engineering, I.U.P.U.L., 248 West Michigan Avenue, Indianapolis, IN 46202

J. Dyn. Sys., Meas., Control 121(4), 577-582 (Dec 01, 1999) (6 pages) doi:10.1115/1.2802518 History: Received May 03, 1996; Online December 03, 2007


System optimization over a parameter space produces optimal solutions which lie on the bifurcation set of the ambient space. As such, the optimality (quality) metric (as a function of the parameters) is highly sensitive to the parameters, to the point of inducing instability for differential parameter variations. Singularities in this function diffeomorphically induce corresponding degenerate singularities in the optimal closed-loop characteristic polynomials, which serves as a signature for potential catastrophic loss of quality that is most easily exhibited by the resulting dynamic instability. In this paper, we examine the loss of quality in H∞ and related optimal systems via these diffeomorphic degenerate closed-loop poles.

Copyright © 1999 by The American Society of Mechanical Engineers
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