Minimal realization of averaging approximations by averaging approximations

摘要

For the averaging approximating systems Sigma /sup N/ of the controlled linear retarded oscillator in the state space R/sup 2/*L/sup 2/, minimal realizations are constructed that can be interpreted as averaging approximations of another delay control system, again in a state space with structure R/sup 2/*L/sup 2/. A state transformation from Sigma /sup N/ to its minimized realizations is derived, which allows the application of the latter to approximating optimal control problems posed subject to Sigma /sup N/, making it possible to economize on time and storage without loss of accuracy.