Bertrand Cottenceau

Brief Model reference control for timed event graphs in dioids

This paper deals with feedback controller synthesis for timed event graphs in dioids. We discuss here the existence and the computation of a controller which leads to a closed-loop system whose behavior is as close as possible to the one of a given reference model and which delays as much as possible the input of tokens inside the (controlled) system. The synthesis presented here is mainly based on residuation theory results and some Kleene star properties.

Optimal closed-loop control of timed EventGraphs in dioids

This note deals with the model-reference control of timed event graphs using the dioid algebra and the residuation theory. It proposes a control structure based on a precompensator and a feedback controller to improve the controlled system performance. It is shown that this approach always leads to an optimal behavior of the closed-loop system. An example is given to illustrate the proposed approach.

Interval analysis and dioid: application to robust controller design for timed event graphs

This paper deals with feedback controller synthesis for timed event graphs, where the number of initial tokens and time delays are only known to belong to intervals. We discuss here the existence and the computation of a robust controller set for uncertain systems that can be described by parametric models, the unknown parameters of which are assumed to vary between known bounds. Each controller is computed in order to guarantee that the closed-loop system behavior is greater than the lower bound of a reference model set and is lower than the upper bound of this set. The synthesis presented here is mainly based on dioid, interval analysis and residuation theory.

Synthesis of greatest linear feedback for timed-event graphs in dioid

This paper deals with the synthesis of greatest linear causal feedback for discrete-event systems whose behavior is described in dioid. Such a feedback delays as far as possible the input of the system while keeping the same transfer relation between the input and the output. When a feedback exists in the system, the authors show how to compute a greater one without decreasing the systems performance.

On the Model Reference Control for Max-Plus Linear Systems

This paper deals with the model-reference control of max-plus linear systems. The main contribution of this work is a general control structure that encompasses the previous one found in the literature. It is based on the RST-structure for conventional differentiable system. In addition it provides a comparison among some sub-structures and simulation results are presented.

Observer Design for

This technical note deals with the state estimation for max-plus linear systems. This estimation is carried out following the ideas of the observer method for classical linear systems. The system matrices are assumed to be known, and the observation of the input and of the output is used to compute the estimated state. The observer design is based on the residuation theory which is suitable to deal with linear mapping inversion in idempotent semiring.

(\max, +)

Abstract This paper presents a design method for a state observer of max-plus linear systems based on the observation of the input and the output, by assuming the knowledge of the system matrices. The observer design is done in an analogous way to the observer method for classical linear system. The paper will be concluded by an illustration.

Linear Systems

In this paper, we give a numerical algorithm able to prove whether a set S described by nonlinear inequalities is path-connected or not. To our knowledge, no other algorithm (numerical or symbolic) is able to deal with this type of problem. The proposed approach uses interval arithmetic to build a graph which has exactly the same number of connected components as S. Examples illustrate the principle of the approach.

OBSERVER DESIGN FOR MAX-PLUS-LINEAR SYSTEMS

This paper deals with solution of inequality A x b, where A; x and b are interval matrices with entries dened over idempotent semiring. It deals also with the computation of a pair of intervals, (x; y) which satises the equation

Using interval arithmetic to prove that a set is path-connected

This paper deals with control of (max,+)-linear systems when a disturbance acts on system state. In a first part we synthesize the greatest control which allows to match the disturbance action. Then, we look for an output feedback which makes the disturbance matching. Formally, this problem is very close to the disturbance decoupling problem for continuous linear systems.