Catastrophes in Optimal Control

Abstract

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.