Christophe Prieur

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This article deals with the regulation of water 6ow in open-channels modelled by Saint-Venant equations. By means of a Riemann invariants approach, we deduce stabilizing control laws for a single horizontal reach without friction. The stability condition is extended to a general class of hyperbolic systems which can describe canal networks with more general(More)
The problem of the stabilization of the flow in a reach is investigated. To study this problem, we consider the nonlinear Saint-Venant equations, written as a system of two conservation laws perturbed by non-homogeneous terms. The non-homogeneous terms are due to the effects of the bottom slope, the slope’s friction, and also the lateral supply. The(More)
Finite automata with weights in the max-plus semiring are considered. The main result is: it is decidable in an effective way whether a series that is recognized by a finitely ambiguous max-plus automaton is unambiguous, or is sequential. A collection of examples is given to illustrate the hierarchy of max-plus series with respect to ambiguity.
This note addresses the problems of stability analysis and stabilization of systems presenting nested saturations. Depending on the open-loop stability assumption, the global stability analysis and stabilization problems are considered. In the (local) analysis problem, the objective is the determination of estimates of the basin of attraction of the system.(More)
We described here a construction on transducers that give a new conceptual proof for two classical decidability results on transducers: it is decidable whether a nite transducer realizes a functional relation, and whether a nite transducer realizes a sequential relation. A better complexity follows then for the two decision procedures.
We consider the class of nonlinear optimal control problems (OCP) with polynomial data, i.e., the differential equation, state and control constraints and cost are all described by polynomials, and more generally for OCPs with smooth data. In addition, state constraints as well as state and/or action constraints are allowed. We provide a simple hierarchy of(More)
A new model-based controller for the magnetic flux profile in a Tokamak plasma was developed using a simplified model of the magnetic flux dynamics. This simplified model is based on physically relevant dynamics that take into account the distributed nature of the system. Shape constraints on the controlled inputs are introduced, representing the(More)
The stability problem of a system of conservation laws perturbed by non-homogeneous terms is investigated. These non-homogeneous terms are assumed to have a small C1-norm. By a Riemann coordinates approach a sufficient stability criterion is established in terms of the boundary conditions. This criterion can be interpreted as a robust stabilization(More)