Jean Jacques Loiseau

Exponential stability analysis of the drilling system described by a switched neutral type delay equation with nonlinear perturbations

This paper deals with the exponential stability analysis of switched neutral systems under certain state-dependent switching rules with nonlinear perturbations bounded in magnitude. The proposal of an energy functional allow us to investigate the asymptotic and exponential stability of switched neutral systems through the solution of linear matrix inequalities. The results are illustrated with the exponential stability analysis of an oilwell drilling system allowing a significant reduction of the stick slip behavior.

Control of Linear Min-plus Systems under Temporal Constraints

We consider a class of controlled timed event graphs subject to strict temporal constraints. Such a graph is deterministic, in the sense that its behaviour only depends on the initial marking and on the control that is applied. This behaviour can be modelled by a system of difference equations that are linear in the Min-Plus algebra. The temporal constraint is represented by an inequality that is also linear in the min-plus algebra. Then, a method for the synthesis of a control law ensuring the respect of constraints is described. We give explicit formulas characterizing a control law, which, if two conditions are satisfied, ensures the validity of the temporal constraints. It is a causal state feedback, involving delays. The method is illustrated on an example.

Applied Interval Computation: A New Approach for Time-Delays Systems Analysis

This paper deals with interval analysis applied to linear time-delays systems. With basic examples, we describe some applications to solve various control problems, and to show that interval computation is an effective tool for time-delays systems analysis.

Reducing stick-slip oscillations in oilwell drillstrings

Torsional drillstring vibrations, also known as stick-slip oscillations appearing in oilwell drillstrings are a source of failures which reduce penetration rates and increase drilling operation costs. An important problem to solve is the determination of control laws that reduce stick-slip phenomenon. A distributed model for the drilling system is given, this model is reduced to a neutral type retarded model through two different approaches: the dAlembert transformation and Laplace transforms techniques. Some experience-based control strategies are evaluated in order to reduce stick-slip oscillations. The use of the angular velocity at the drillstring upper part, the torque on the bit and the weight on the bit is shown to have a key effect in the reduction of drillstring torsional vibrations.

Feedback realization of non-singular precompensators for linear systems over a polynomial ring

For linear systems defined over a polynomial ring, the problem of realization of dynamic precompensators by static or dynamic state feedback or output feedback is considered. Necessary and sufficient conditions for the solutions are given.

Finite Eigenstructure Assignment for Input Delay Systems

The problem of invariant factors assignment of input delay systems with classical finite spectrum assigment control laws wit h distributed delays is adressed. The multiplicities of the invanant factors are shown to be restricted by specified Rosenbrock type inequalities. The results are proved with the help of an equivalent linear assignment problem with no delay, and within the Bezout domain ξ. Two different algorithms are hence provided. A bidimensional illustrative example is given.

Supervisory control of Petri nets using polyhedral regions

Abstract We propose to use polyhedral computations to check the reachability and co-reachability of Petri nets, and design supervisors enforcing polyhedral invariance. To this aim, we first state a semi-algebraic behavioral model for Petri nets, derived from the marking equation. From it, we derive explicit characterizations of the sets of k-reachable marking vectors, in terms of polyhedral regions of a real vector space. This permits to calculate the region of reachable marking vectors, when the considered Petri net is bounded, as the projection of an integral polyhedron. The polyhedron is computed using the Γ-algorithm, in polynomial time. We propose an algorithm to this computation. We adapt the method to further compute the polytope of reachable, co-reachable and safe marking vectors, meeting a given set of polyhedral constraints, and finally apply it to design a supervising controller. We illustrate the method on the supervisor design of a simple AGV system.

Some Remarks on Matrix Completion Problems

Abstract The matrix completion problem introduced in (Loiseau et al., 1998) is reconsidered and the latest results achieved in that field are discussed.