Ultrashort pulses contain only a few optical cycles and exhibit broad spectra. Their carrier frequency is therefore not well defined and their description in terms of the standard slowly varying envelope approximation (SVEA) becomes questionable. Existing modeling approaches can be divided in two classes, namely generalized envelope equations, that stem from the nonlinear Schrödinger equation (...

In this study of the nonlinear H∞-optimal control design for strict-feedback nonlinear systems our objective is to construct globally stabilizing control laws to match the optimal control law up to any desired order, and to be inverse optimal with respect to some computable cost functional. Our recursive construction of a cost functional and the corresponding solution to the Hamilton-Jacobi-Isa...

For a set S of distinct points in the x-y plane and a 3-dimensional surface with the general quadratic equation f ey dx cxy by ax z + + + + + = 2 2 we study the problem of finding a locally optimal triangulation of S for the linear approximation of the surface under the Lp norm. We show that the Lp norm error is independent of the translation and rotation by 180 degrees of a single triangle in ...

• We often approximate a large number of periods, even if the horizon is known and finite, by assuming an infinite number of periods, and hope that this assumption will simplify the solution. Indeed, even if the general theory becomes more involved, the solution obtained often is simpler and has important computational and conceptual advantages: in particular, the optimal policy is often statio...

This paper characterizes the behavior of value functions in dynamic stochastic discounted programming models near fixed points of the state space. When the second derivative of the flow payoff function is bounded, the value function is proportional to a linear function plus xψδ . A specific formula for ψδ is provided, which implies ψδ continuously falls in the rate of patience. If the state var...

This work addresses the problem of non-preemptively scheduling a cyclic set of interdependent operations, representing for instance a program loop, when p identical processors are available. For p = 1 we give a simple, eecient, polynomial time algorithm producing optimum results. When p < 1 the problem becomes NP-hard and a slight modiication of our algorithm generates provably close to optimum...

A policy gradient method is a reinforcement learning approach that directly optimizes a parametrized control policy by gradient descent. It belongs to the class of policy search techniques that maximize the expected return of a policy in a fixed policy class while traditional value function approximation approaches derive policies from a value function. Policy gradient approaches have various a...

The Challenge IT organizations working with reduced budgets often delay refreshing their desktop hardware. And to avoid lump-sum hardware costs, companies often refresh only a portion of their PCs at one time. But delaying the PC refresh can lead to higher support and productivity costs, and staggered refreshes can result in higher deployment costs for companies that outsource their IT infrastr...