Existence of slow solutions for a class of differential inclusions

Optimality conditions for reflecting boundary control problems

“…Moreover, in this approximated control problem, the dynamics F n is Lipshitz while the dynamics F of (3) is only usc. Hence, optimality conditions for (13) can be derived in a standard way see [12]. Let us introduce the Hamiltonian function associated to problem (13) H :…”

“…Theorem 4.8. Let (ȳū n n (·),ū n (·)) be an optimal pair for the control problem (13). There exists an absolutely continuous function…”

Minimax control of nonlinear evolution equations

“…Hausdorff metric), and so K(t, λ n ) M −→ K(t, λ), which by Mosco [11] Evolution equations of the form (4) arise in mathematical economics in the study of resource allocation problems (see Cornet [6]) and in theoretical mechanics in the analysis of elastoplastic systems (see Moreau [10]). Furthermore, if H = R N and K(t, λ) = K(λ) (i.e.…”

On Parametric Evolution Inclusions of the Subdifferential Type with Applications to Optimal Control Problems

“…Furthermore, if K(t, X) = K(X) (i.e. the set K is independent of time) and H = RN , then Cornet [8] proved that inclusion (11) above is in fact equivalent to the following projected differential inclusion:…”

“…Cornet [8] and Henry [14] indicated that differential inclusions like (12) above arise naturally in mathematical economics in the study of planning procedures. More generally, if a dynamic system has state constraints, in describing the effect of the constraints on the dynamic equation, it can be assumed in many cases that the velocity x(t) is projected at each time instant on the set of allowed directions towards the constraint set at the point x(l).…”