Convex-valued Lipschitzian differential inclusions and the Pontryagin maximum principle (Q5948392)

The author derives necessary optimality conditions for an optimal-control problem of the Mayer type over a prescribed time interval: \[ \text{ minimize } J(x(0), x(T)) \text{ subject to } \phi(x(0), x(T)) \leq 0,\;g(x(0),x(T))=0,\;\dot x \in F(x). \] The mapping \(F\) is convex-valued and satisfies a certain Lipschitz condition. The proof technique combines an approximation scheme for the differential inclusion \( \dot x \in F(x)\) and the classical Pontryagin principle.