Optimal control and maximum principle in (B)-spaces. Examples for partial differential equations in (H)-spaces and ordinary differential equations in Rn

Observation and control problems in Banach (B)-spaces are investigated. On the basis of the BUME method and the monotone mapping method, a criterion of controllability and optimal controllability is formulated. The inverse controllability problem is introduced and an abstract maximum principle is formulated in (B)-spaces. For PDE in Hilbert (H)-spaces and for ODE in Rn, the integral maximum principle is proved and the optimality system is written out.

Integral maximum principle and its applications

The integral maximum principle for the heat equation on a Riemannian manifold is improved and applied to obtain estimates of double integrals of the heat kernel.