Perturbation theory for nonlinear feedback control systems and Spencer- Goldschmidt integrability of linear partial differential equations (Q917503)

The paper aims in the first place at extending the tools and methods of standard theory for dynamical systems to the situation where control mechanisms are added. The main results, besides developing the formalism in some detail, are concerned with finding approximate solutions to the linearized feedback control equation in terms of perturbation theory (the operator is assumed to depend in a polynomial manner on some perturbation parameter). At a more theoretic level, Spencer-Goldschmidt integrability criteria for overdetermined systems of linear partial differential equations enter the discussion in the paper. Essentially it is demonstrated that nonlinear feedback control has a natural formulation in terms of the standard concepts of nonlinear partial differential equation theory as developed in the works of e.g. Spencer, Kumpera, Goldschmidt and Vinogradov.