Composite control of non-linear singularly perturbed systems: meeting a design objective

Sharkey, P. M. (1989) Composite control of non-linear singularly perturbed systems: meeting a design objective. International Journal of Control, 50 (6). pp. 2173-2186. ISSN 1366-5820 doi: 10.1080/00207178908953492

Abstract/Summary

Using the integral manifold approach, a composite control—the sum of a fast control and a slow control—is derived for a particular class of non-linear singularly perturbed systems. The fast control is designed completely at the outset, thus ensuring the stability of the fast transients of the system and, furthermore, the existence of the integral manifold. A new method is then presented which simplifies the derivation of a slow control such that the singularly perturbed system meets a preselected design objective to within some specified order of accuracy. Though this approach is, by its very nature, ad hoc, the underlying procedure is easily extended to more general classes of singularly perturbed systems by way of three examples.