Accounting for Nonlinearities in Open Loop Protocols for Symmetry Fault Compensation

Abstract

In this paper, we consider model examples of dynamical systems with only a few degrees of freedom, and with desirable symmetry properties, and explore compensating control strategies for retaining robust symmetric system response even under symmetrybreaking defects. The analysis demonstrates the distinct differences between linear versions of these models, in which faultcompensating strategies are always found, and weakly nonlinear counterparts with varying degrees of asymmetry, for which a multitude of locally optimal solutions may coexist. We further formulate a candidate optimization protocol for fault compensation applied to selfhealing systems, which respond to symmetrybreaking defects by a continuous process of fault correction. The analysis shows that such a protocol may exhibit discontinuous changes in the control strategy as the selfhealing system successively regains its original symmetry properties. In addition, it is argued that upon return to a symmetric configuration, such a protocol may result in a different control strategy from that applied prior to the occurrence of a fault.