Laris Université D'angers

This paper deals with controller synthesis for (max,+) linear system. It aims at comparing the performances and the robustness of two control strategies introduced in and respectively. In both strategies, the influences of the possible mismatches between the system and its model are analyzed. This work shows that the control strategy using simultaneously a precompensator and a feedback controller (introduced in ) gives better performances.

This paper deals with feedback controller synthesis for timed event graphs in dioids, 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.

In previous work it has been shown how a max-plus algebraic model can be derived for cyclically operated high-throughput screening systems and how such a model can be used to design a controller to handle unexpected deviations from the predetermined cyclic operation during run-time. In this paper, this approach is extended by modeling the system in a general dioid algebraic setting. Then a feedback controller can be computed using residuation theory. The resulting control strategy is optimal in the sense of the just-in-time criterion, which is very common in scheduling practice.

This report introduces a toolbox called ContainerMinMaxGD which handles some "container" of ultimately pseudo-periodic functions representing (min,+)-linear systems. This toolbox is a set of C++ classes where the main operations of these systems -ie. the sum, the convolution and the subadditive closure (also called the Kleene star operator) -are computed thanks to efficient algorithms of linear and quasi-linear complexity.

Pulsed flows, characterized by periodic fluctuations in flow rate, are noise-productive, but an oscillating valve positioned in the exhaust duct can attenuate the main harmonic of pulsed flow. We define a valve adaptive control in the frequency domain implemented by a digital signal processor for experimental purposes. Results show noise reduction at ground level and tracking of process unstationarity.

A ⊗ x b, where A, x and b are interval matrices with entries defined over idempotent semiring. It deals also with the computation of a pair of intervals, (x, y) which satisfies the equation A⊗x = B⊗y. It will be shown that this equation may be solved by considering the interval version of the iterative scheme proposed in [7].

In this paper semirings with an idempotent addition are considered. These algebraic structures are endowed with a partial order. This allows to consider residuated maps to solve systems of inequalities A ⊗ X B (see ). The purpose of this paper is to consider a dual product, denoted , and the dual residuation of matrices, in order to solve the following inequality A ⊗ X X B X. Sufficient conditions ensuring the existence of a non-linear projector in the solution set are proposed. The results are extended to semirings of intervals such as they were introduced in [25].

This paper introduces an adaptive feedback control strategy for (max,+)-linear systems. The feedback loop is tuned following to an estimation of the system transfer and in order to match a given reference model. An application of such an adaptive control strategy is possible for some manufacturing systems in which the feedback control corresponds to an adaptive resource allocation. keywords : discrete event systems, (max,+)-linear system, output feedback loop, adaptive control. * This work was partially supported by FAPESP under grant n.04/00848-01 2 Models of (max,+)-linear systems and control

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.

This paper deals with robust open-loop control 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 control set for uncertain systems that can be described by parametric models, the unknown parameters of which are assumed to vary between known bounds. Each control is computed in order to guarantee that the controlled system behavior is greater than the lower bound of a desired output reference 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.

Manufacturing systems are frequently adapted to changing customer demands. However, every extension with respect to the hardware requires a modification of the corresponding model and controller. In this paper we propose a dioid model of manufacturing processes in which parts may visit the same resource more than once. The proposed model can be used to determine a controller that maintains the throughput while starting activities just-in-time. Furthermore, the model can easily be adapted in case of hardware modifications. Also nested processes, i.e., processes in which some activities of part k may be executed prior to activities of part (k − 1), can be modeled with the proposed approach.