Time minimal control of batch reactors
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.
Generic properties of singular trajectories
On the role of abnormal minimizers in sub-riemannian geometry
Time minimal control of batch reactors
In this article we consider a control system modelling a batch reactor in which three species X, X, X are reacting according to the scheme X → X → X, 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...
Classification générique de synthèses temps minimales avec cible de codimension un et applications
Sub-riemannian sphere in Martinet flat case
Sub-Riemannian sphere in Martinet flat case
This article deals with the local sub-Riemannian geometry on ℜ, () where is the distribution ker being the Martinet one-form : and is a Riemannian metric on . We prove that we can take as a sum of squares . Then we analyze the flat case where 1. We parametrize the set of geodesics using elliptic integrals. This allows to compute the exponential mapping, the wave front, the conjugate and cut loci and the sub-Riemannian sphere. A direct consequence of our computations is to show that...
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