Maximum principle for a control problem governed by an evolution equation
The control problem is that of minimizing the functional \[ \int_0^T L(t, y(t), u(t)) dt + g(y(0), y(T)) \] over the trajectories of the system \[ y'(t) + A(t)y(t)= f(t, y(t), u(t)), \quad 0 \leq t \leq T, \] \[ (y(0), y(T)) \in C, \qquad u(t) \in U(t). \] Here, \(A(t)\) is a family of unbounded operators generating an evolution system \(U(t, s)\) in a Hilbert space. The author proves Pontryagin's maximum principle for optimal controls under three different sets of assumptions involving the set \(C\) and properties of the evolution system.
scientific article; zbMATH DE number 1523627