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Time minimal control of batch reactors

B. Bonnard, G. Launay (2010)

ESAIM: Control, Optimisation and Calculus of Variations


In this article we consider a control system modelling a batch reactor in which three species X1, X2, X3 are reacting according to the scheme X1 → X2 → X3, each reaction being irreversible. The control is the temperature T of the reactions or the derivative of this temperature with respect to time. The terminal constraint is to obtain a given concentration of the product X2 at the end of the batch. The objective of our study is to introduce and to apply all the mathematical tools to compute the...

Timed Petri-net based formulation and an algorithm for the optimal scheduling of batch plants

Tianlong Gu, Parisa Bahri, Guoyong Cai (2003)

International Journal of Applied Mathematics and Computer Science

The effective scheduling of operations in batch plants has a great potential for high economic returns, in which the formulation and an optimal solution algorithm are the main issues of study. Petri nets have proven to be a promising technique for solving many difficult problems associated with the modelling, formal analysis, design and coordination control of discrete-event systems. One of the major advantages of using a Petri-net model is that the same model can be used for the analysis of behavioural...

Topologies, Continuity and Bisimulations

J. M. Davoren (2010)

RAIRO - Theoretical Informatics and Applications

The notion of a bisimulation relation is of basic importance in many areas of computation theory and logic. Of late, it has come to take a particular significance in work on the formal analysis and verification of hybrid control systems, where system properties are expressible by formulas of the modal μ-calculus or weaker temporal logics. Our purpose here is to give an analysis of the concept of bisimulation, starting with the observation that the zig-zag conditions are suggestive of some...

Topology design for group consensus in directed multi-agent systems

Onur Cihan (2020)

Kybernetika

In this paper, we investigate the grouping behavior of multi-agent systems by exploiting the graph structure. We propose a novel algorithm for designing a network from scratch which yields the desired grouping in a network of agents utilizing a consensus-based algorithm. The proposed algorithm is shown to be optimal in the sense that it consists of the minimum number of links. Furthermore, we examine the effect of adding new vertices and edges to the network on the number of groups formed in the...

Towards a framework for continuous and discrete multidimensional systems

Rudolf Rabenstein, Lutz Trautmann (2003)

International Journal of Applied Mathematics and Computer Science

Continuous multidimensional systems described by partial differential equations can be represented by discrete systems in a number of ways. However, the relations between the various forms of continuous, semi-continuous, and discrete multidimensional systems do not fit into an established framework like in the case of one-dimensional systems. This paper contributes to the development of such a framework in the case of multidimensional systems. First, different forms of partial differential equations...

Towards robustness in neural network based fault diagnosis

Krzysztof Patan, Marcin Witczak, Józef Korbicz (2008)

International Journal of Applied Mathematics and Computer Science

Challenging design problems arise regularly in modern fault diagnosis systems. Unfortunately, classical analytical techniques often cannot provide acceptable solutions to such difficult tasks. This explains why soft computing techniques such as neural networks become more and more popular in industrial applications of fault diagnosis. Taking into account the two crucial aspects, i.e., the nonlinear behaviour of the system being diagnosed as well as the robustness of a fault diagnosis scheme with...

Tracking control algorithms for a laboratory aerodynamical system

Przemysław Gorczyca, Krystyn Hajduk (2004)

International Journal of Applied Mathematics and Computer Science

The tracking control problem of a strongly nonlinear MIMO system is presented. The system shares some features with a helicopter, such as important interactions between the vertical and horizontal motions. The dedicated IO board allows for control, measurements and communication with a PC. The RTWT toolbox in the MATLAB environment is used to perform real-time experiments. The control task is to track a predefined reference trajectory. A mathematical model of the system, containing experimental...

Tracking control design for nonlinear polynomial systems via augmented error system approach and block pulse functions technique

Bassem Iben Warrad, Mohamed Karim Bouafoura, Naceur Benhadj Braiek (2019)

Kybernetika

In this paper, tracking control design for a class of nonlinear polynomial systems is investigated by augmented error system approach and block pulse functions technique. The proposed method is based on the projection of the close loop augmented system and the associated linear reference model that it should follow over a basis of block pulse functions. The main advantage of using this tool is that it allows to transform the analytical differential calculus into an algebraic one relatively easy...

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