Rafael Santos-Mendes

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.

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.

Generalized multivariable control of discrete event systems in dioids

Dioids are algebraic structures suitable to represent a timed event graph by means of a linear state-space or transfer function model, where synchronization of events can be described. This paper proposes a model reference control strategy under partial observation and control of internal system transitions, where a controller is obtained by matching the closed-loop transfer function to a given transfer function (control specification). The problem formulation is quite general, allowing to deal studied cases in the literature as particular cases and to generalize some of them.

A super-eigenvector approach to control constrained max-plus linear systems

The control of timed Petri nets subject to synchronization and time delay phenomena is addressed in this paper. This class of timed Petri nets can be described by using the max-plus algebra. The objective is to design a feedback controller for a max-plus linear system to ensure that the system evolution respects time constraints imposed to the state that can be expressed by a semimodule. In order to achieve this goal, an approach based on the definition of the super-eigenvector of a matrix is proposed. Under some conditions, it ensures the existence of a feedback and allows us to compute it. The contribution is illustrated by a transportation control problem taken from literature.

Adaptive feedback control for (max,+)-linear systems

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

The Max-Plus Algebra and the Network Calculus

Discrete event dynamic systems (DEDS) are systems whose state transitions are triggered by events that occur at discrete instants of time. The communication networks are examples of this kind of systems. The mathematical constraints of some DEDS can be described more adequately using the max-plus algebra. Previous works show that the problem of determining performance bounds for communication networks is simplified if modeled using this algebra. The compilation of existing rules and results on this field is called network calculus. The goal of this article is to improve a systematic use of the max-plus algebra in the formulation and derivation of results on network calculus. To illustrate the introduced methodology, we analyze a window flow controller, a system that controls the traffic admitted by a network in order to limit its backlog in a specified manner

Dioid of formal power series for the determination of performance parameters of communication networks

Discrete event dynamic systems (DEDS) are systems whose state transitions are triggered by events that occur at discrete instants. The communication networks are examples of this kind of systems. The mathematical constraints of some DEDS can be described more adequately using the dioid algebra. Previous works show that the problem of determining performance bounds for communication networks is simplified if modeled using this algebra. The compilation of existing rules and results on this field is called network calculus (NC). The goal of this article is to propose a dioid of formal power series for the treatment of NC problems. To illustrate the adequacy of the proposed dioid, we analyze a FIFO multiplexer. The results obtained for this particular system represent an extension of previous results.

Control and robustness analysis for (max,+)-linear systems

Abstract 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 (Cottenceau et al. , 2001) and (Maia et al. , 2003) 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 (Maia et al. , 2003)) gives better performances.

Multivariable control of discrete event systems in dioids

Abstract Timed event graphs are described in dioids by a linear state-space or transfer function model. This paper proposes a state feedback control under complete control and observation of the states. By using a model reference control approach, the closed-loop transfer function matches the control specification expressed as a given transfer function. It is shown that under certain conditions an optimal controller exists, although two sub-optimal controllers can always be obtained.

Transitory Control in Cyclic Job Shop Scheduling

Consider a cyclic job shop scheduling and a corresponding steady state solution. Typical perturbations of this kind of system, like machine failures, lack of raw material etc., can affect the implementation of the steady state solution. This work is concerned with the determination of a control law i.e. the determination of the starting time of each operation in the subsequent cycles such that the steady state solution (reference solution) be reestablished and maintained.