Optimal control and synthesis of nonlinear infinite dimensional systems (Q2717291)

The systems are described by NEWLINE\[NEWLINE x'(t) = Ax(t) + f(t, x(t), u(t)), \quad x(0) = x_0, \tag{1}NEWLINE\]NEWLINE \(A\) the infinitesimal generator of a strongly continuous semigroup in a Banach space \(X.\) The controls \(u(t)\) take values in a control set \(U \subseteq Y, \) \(Y\) another Banach space. The optimal control problem is that of minimizing a functional NEWLINE\[NEWLINE J(x_0, u) = \int_0^T Q(t, x(t), u(t)) dt NEWLINE\]NEWLINE among controls taking values in \(U\) and such that (1) has a solution in the entire interval \(0 \leq t \leq T.\) The results include a proof of Pontryagin's maximum principle and a synthesis theorem based on Lipschitz continuity of the value function and differential inclusion techniques.NEWLINENEWLINEFor the entire collection see [Zbl 0959.00047].