Controllability and Optimal Control of Partial Differential Equations on Compact Manifolds

摘要

The general control problem for distributed systems is studied via the theory of vector bundles on compact manifolds. A generalization of the controllability theory and the linear quadratic regulator problem with particular reference to compact orientable surfaces of genus g is presented. Parabolic evolution equations on a compact manifold are considered. Aspects of the theory are exemplified for the case of heat flow on a spherical or toroidal surface. It is shown that numerical spectral problems frequently appear in the determination of controllability criteria.