Physical Sciences and Mathematics Commons^™

Optimal Stochastic Scheduling Of Power Generation Systems With Scheduling Delays And Large Cost Differentials, G. L. Blankenship, J.-L. Menaldi

Mathematics Faculty Research Publications

The optimal scheduling or unit commitment of power generation systems to meet a random demand involves the solution of a class of dynamic programming inequalities for the optimal cost and control law. We study the behavior of this optimality system in terms of two parameters: (i) a scheduling delay, e.g., the startup time of a generation unit; and (ii) the relative magnitudes of the costs (operating or starting) of different units. In the first case we show that under reasonable assumptions the optimality system has a solution for all values of the delay, and, as the delay approaches zero, that …

Optimal Control Of Stochastic Integrals And Hamilton-Jacobi-Bellman Equations, Ii, Pierre-Louis Lions, José-Luis Menaldi

Mathematics Faculty Research Publications

We consider the solution of a stochastic integral control problem, and we study its regularity. In particular, we characterize the optimal cost as the maximum solution of ∀v ∈ V, A(v)u ≤ ƒ(v) in D'(Ο), u = 0 on ∂Ο, u ∈ W^1,∞(Ο),

where A(v) is a uniformly elliptic second order operator and V is the set of the values of the control.

Optimal Control Of Stochastic Integrals And Hamilton-Jacobi-Bellman Equations, I, Pierre-Louis Lions, José-Luis Menaldi

Mathematics Faculty Research Publications

We consider the solution of a stochastic integral control problem and we study its regularity. In particular, we characterize the optimal cost as the maximum solution of ∀v ∈ V, A(v)u ≤ ƒ(v) in D'(Ο), u = 0 on ∂Ο, u ∈ W^1,∞(Ο),

where A(v) is a uniformly elliptic second order operator and V is the set of the values of the control.

On The Optimal Impulse Control Problem For Degenerate Diffusions, J. L. Menaldi

Mathematics Faculty Research Publications

In this paper, we give a characterization of the optimal cost of an impulse control problem as the maximum solution of a quasi-variational inequality without assuming nondegeneracy. An estimate of the velocity of uniform convergence of the sequence of stopping time problems associated with the impulse control problem is given.