Carlos Andrey Maia

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.

Brief paper: On the control of max-plus linear system subject to state restriction

This paper deals with the control of discrete event systems subject to synchronization and time delay phenomena, which can be described by using the max-plus algebra. The objective is to design a feedback controller to guarantee that the system evolves without violating time restrictions imposed on the state. To this end an equation is derived, which involves the system, the feedback and the restriction matrices. Conditions concerning the existence of a feedback are discussed and sufficient conditions that ensure the computation of a causal feedback are presented. To illustrate the results of this paper, a workshop control problem is presented.

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

Uncertainties are commonly present in optimization systems, and when they are considered in the design stage, the problem usually is called a robust optimization problem. Robust optimization problems can be treated as noisy optimization problems, as worst case minimization problems, or by considering the mean and standard deviation values of the objective and constraint functions. The worst case scenario is preferred when the effects of the uncertainties on the nominal solution are critical to the application under consideration. Based on this worst case scenario, we developed the [I]RMOEA (Interval Robust Multi-Objective Evolutionary Algorithm), a hybrid method that combines interval analysis techniques to deal with the uncertainties in a deterministic way and a multi-objective evolutionary algorithm. We introduce [I]RMOEA and illustrate it on three robust test functions based on the ZDT problems. The results show that [I]RMOEA is an adequate way of tackling robust optimization problems with evolutionary techniques taking advantage of the interval analysis framework.

OBSERVER DESIGN FOR MAX-PLUS-LINEAR SYSTEMS

In this paper we propose a methodology for short-term electric load forecasting, which is adaptive and based on signal processing theory. The main interest here is to construct a next day predictor for the peak and hourly load. To this end the load data are organized into profiles according to day type and temperature interval. For each load profile, we use a specialized adaptive recursive digital filter, for which parameters are estimated on-line by using a recursive algorithm. As a result, the complete forecasting system is nonlinear and the prediction is computed based on the type and on the temperature interval of the next day. The effectiveness of the proposed methodology is illustrated by a numerical example, in which we compare performance of the proposed approach to a non-specialized and a naive predictors, by using the Mean Absolute Percentage Error (MAPE) of the forecasting errors.

Interval Robust Multi-Objective Evolutionary Algorithm

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.

A methodology for short-term electric load forecasting based on specialized recursive digital filters

Abstract This paper deals with the observer design for max-plus linear systems. The approach is based on the residuation theory which is suitable to deal with linear mapping inversion in idempotent semiring. An illustrative example allows to discuss about a practical implementation.

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

The aim of this paper is to study a control problem for a class of restriction, which appears in design of feedback controllers for timed discrete event systems, taking performance (eigenvalue of the closed loop matrix) and realization issues into account. The obtained results are based on properties of the system and the restriction matrices. For a given class of theses matrices, it is shown that a causal feedback can be computed by solving linear equations. In order to illustrate the applicability of the results, we solve a small traffic light problem.