A unified theory of necessary conditions for nonlinear nonconvex control systems

We consider optimal problems for a general nonlinear nonconvex input-output relation for Banach space valued functions. A maximum principle is obtained using Ekeland's variational principle. The formulation applies to systems described by ordinary differential equations, functional differential equations, and partial differential equations (both for distributed and boundary control systems).This work was supported in part by the National Science Foundation under Grant No. DMS-8200645.