The variational principle for the uniform acceleration and quasi-spin in two dimensional space-time.
Tightly proper efficiency in vector optimization with nearly cone-subconvexlike set-valued maps.
Time minimal control of batch reactors
Time minimal control of batch reactors
In this article we consider a control system modelling a batch reactor in which three species X1, X2, X3 are reacting according to the scheme X1 → X2 → X3, each reaction being irreversible. The control is the temperature T of the reactions or the derivative of this temperature with respect to time. The terminal constraint is to obtain a given concentration of the product X2 at the end of the batch. The objective of our study is to introduce and to apply all the mathematical tools to compute the...
Time minimal synthesis with target of codimension one under generic conditions
We consider the problem of constructing the optimal closed loop control in the time minimal control problem, with terminal constraint belonging to a manifold of codimension one, for systems of the form , and or , under generic assumptions. The analysis is localized near the terminal manifold and is developed to control a class of chemical systems.
Time-optimal control of plants whose transfer functions contain zeros
Topological dual of with application to stochastic systems on Hilbert space
In this paper, we prove that the topological dual of the Banach space of bounded measurable functions with values in the space of nuclear operators, furnished with the natural topology, is isometrically isomorphic to the space of finitely additive linear operator-valued measures having bounded variation in a Banach space containing the space of bounded linear operators. This is then applied to a stochastic structural control problem. An optimal operator-valued measure, considered as the structural...
Topology optimization - broadening the areas of application
Tracking an omnidirectional evader with a differential drive robot at a bounded variable distance
Transfer function equivalence of feedback/feedforward compensators
Equivalence of several feedback and/or feedforward compensation schemes in linear systems is investigated. The classes of compensators that are realizable using static or dynamic, state or output feedback are characterized. Stability of the compensated system is studied. Applications to model matching are included.
Transportation flow problems with Radon measure variables
For a multidimensional control problem involving controls , we construct a dual problem in which the variables ν to be paired with u are taken from the measure space rca (Ω,) instead of . For this purpose, we add to a Baire class restriction for the representatives of the controls u. As main results, we prove a strong duality theorem and saddle-point conditions.
Two functionals for which minimizers are also minimizers.
Un algorithme d'identification de frontières soumises à des conditions aux limites de Signorini
Un algorithme d'identification de frontières soumises à des conditions aux limites de Signorini
This work deals with a non linear inverse problem of reconstructing an unknown boundary γ, the boundary conditions prescribed on γ being of Signorini type, by using boundary measurements. The problem is turned into an optimal shape design one, by constructing a Kohn & Vogelius-like cost function, the only minimum of which is proved to be the unknown boundary. Furthermore, we prove that the derivative of this cost function with respect to a direction θ depends only on the state u0, and not...
Une approche géométrique du contrôle optimal de l’arc atmosphérique de la navette spatiale
L’objectif de ce travail est de faire quelques remarques géométriques et des calculs préliminaires pour construire l’arc atmosphérique optimal d’une navette spatiale (problème de rentrée sur Terre ou programme d’exploration de Mars). Le système décrivant les trajectoires est de dimension 6, le contrôle est l’angle de gîte cinématique et le coût est l’intégrale du flux thermique. Par ailleurs il y a des contraintes sur l’état (flux thermique, accélération normale et pression dynamique). Notre étude...
Une approche géométrique du contrôle optimal de l'arc atmosphérique de la navette spatiale
The aim of this article is to make some geometric remarks and some preliminary calculations in order to construct the optimal atmospheric arc of a spatial shuttle (problem of reentry on Earth or Mars Sample Return project). The system describing the trajectories is in dimension 6, the control is the bank angle and the cost is the total thermal flux. Moreover there are state constraints (thermal flux, normal acceleration and dynamic pressure). Our study is mainly geometric and is founded on the...
Unification of the abstract duality scheme
Upper and lower bounds for minimal norm problems under linear constraints
Upper bounds on the solution of coupled algebraic Riccati equation.
Use of semidefinite programming for solving the LQR problem subject to rectangular descriptor systems
This paper deals with the Linear Quadratic Regulator (LQR) problem subject to descriptor systems for which the semidefinite programming approach is used as a solution. We propose a new sufficient condition in terms of primal dual semidefinite programming for the existence of the optimal state-control pair of the problem considered. The results show that semidefinite programming is an elegant method to solve the problem under consideration. Numerical examples are given to illustrate the results.