Joël Blot

New approach for weighted pseudo-almost periodic functions under the light of measure theory, basic results and applications

The aim of this work is to present new approach to study weighted pseudo almost periodic functions using the measure theory. We present a new concept of weighted ergodic functions which is more general than the classical one. Then we establish many interesting results on the functional space of such functions like completeness and composition theorems. The theory of this work generalizes the classical results on weighted pseudo almost periodic functions. For illustration, we provide some applications for evolution equations which include reaction diffusion systems and partial functional differential equations.

Infinite-horizon optimal control in the discrete-time framework

1. Presentation of the problems and tools of the finite horizon.- 2. Infinite horizon theorems.- 3. The special case of the bounded processes.- Related topics. Appendix A : Sequences.- Appendix B: Static optimization.- References.

First-order necessary conditions for infinite-horizon variational problems

AbstractWe establish rigorously several pointwise or asymptotic firstorder necessary conditions for infinite-horizon variational problems in general form, in the framework of continuous time. We obtain several new results, and we extend to general differentiable Lagrangians

Existence and Structure Eesults on Almost Periodic Solutions of Difference Equations

L(t,x,\dot x)

Infinite Horizon Discrete Time Control Problems for Bounded Processes

some results known only in special cases. To realize this aim, we justify two different ways to associate a family of finite-horizon problems to an infinite-horizon problem.

Technical Communique: Conjugate points in infinite-horizon control problems

We give new proofs of first-order and second-order necessary conditions for the infinite-horizon variational problems in the framework of the continuous time. We study the notion of conjugate points and we build new second-order necessary conditions. We also translate all of our results into the Hamiltonian formalism. Moreover, we apply these general results to the special Lagrangians in the form

Spaces of Quasi-Periodic Functions and Oscillations in Differential Equations

e^{-\delta i} lx, \dot x

Average case analysis of greedy algorithms for optimisation problems on set systems

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