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1

A multivariable multiobjective predictive controller

Ben Aicha F., Bouani F., Ksouri M.

International Journal of Applied Mathematics and Computer Science

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2013

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Vol. 23, no. 1

35--45

EN

Predictive control of MIMO processes is a challenging problem which requires the specification of a large number of tuning parameters (the prediction horizon, the control horizon and the cost weighting factor). In this context, the present paper compares two strategies to design a supervisor of the Multivariable Generalized Predictive Controller (MGPC), based on multiobjective optimization. Thus, the purpose of this work is the automatic adjustment of the MGPC synthesis by simultaneously minimizing a set of closed loop performances (the overshoot and the settling time for each output of the MIMO system). First, we adopt the Weighted Sum Method (WSM), which is an aggregative method combined with a Genetic Algorithm (GA) used to minimize a single criterion generated by the WSM. Second, we use the Non- Dominated Sorting Genetic Algorithm II (NSGA-II) as a Pareto method and we compare the results of both the methods. The performance of the two strategies in the adjustment of multivariable predictive control is illustrated by a simulation example. The simulation results confirm that a multiobjective, Pareto-based GA search yields a better performance than a single objective GA.

2

A study on new right/left inverses of nonsquare polynomial matrices

Hunek W. P., Latawiec K. J.

International Journal of Applied Mathematics and Computer Science

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2011

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Vol. 21, no 2

331-348

EN

This paper presents several new results on the inversion of full normal rank nonsquare polynomial matrices. New analytical right/left inverses of polynomial matrices are introduced, including the so-called [...]-inverses, [...]-inverses and, in particular, S-inverses, the latter providing the most general tool for the design of various polynomial matrix inverses. The application-oriented problem of selecting stable inverses is also solved. Applications in inverse-model control, in particular robust minimum variance control, are exploited, and possible applications in signal transmission/recovery in various types of MIMO channels are indicated.

3

On directional change and anti-windup compensation in multivariable control systems

Horla D.

International Journal of Applied Mathematics and Computer Science

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2009

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Vol. 19, no 2

281-289

EN

The paper presents a novel description of the interplay between the windup phenomenon and directional change in controls for multivariable systems (including plants with an uneven number of inputs and outputs), usually omitted in the literature. The paper also proposes a new classification of anti-windup compensators with respect to the method of generating the constrained control signal.

4

Control zeros and maximum-accuracy / maximum-speed control of LTI MIMO discrete-time systems

Latawiec K. J.

Control and Cybernetics

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2005

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Vol. 34, no 2

453-475

EN

Based on new definitions of "control zeros" and minimum phase property for possibly nonsquare LTI MIMO discrete-time systems, generalizations of perfect regulation and perfect filtering are presented both for polynomial matrix and state space models. Consequently, general equivalence results are announced for multi-step and single-step optimal controls as well as for maximum-accuracy and maximum-speed controls for LTI MIMO discrete-time systems. The latter is made visible after the introduction of a new-category of time-optimal control, namely infimum-time control. The equivalence conditions refer to the system's right-invertibility and the (newly-defined) minimum phase behavior, which demonstrates the usefulness of the new approach to zeros of multi variable systems.

5

Towards a Framework for Continuous and Discrete Multidimensional Systems

Rabenstein R., Trautmann L.

International Journal of Applied Mathematics and Computer Science

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2003

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Vol. 13, no 1

73-85

EN

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 of physics-based systems are presented. Secondly, it is shown how the different forms of continuous multidimensional systems lead to certain discrete models in current use (finite-difference models, multidimensional wave digital filters, transfer function models). The links between these discrete models are established on the basis of the respective continuous descriptions. The presentation is based on three examples of physical systems (heat flow, transmission of electrical signals, acoustic wave propagation).

6

A Functorial Approach to the Behaviour of Multidimensional Control Systems

Pommaret J. F., Quadrat A.

International Journal of Applied Mathematics and Computer Science

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2003

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Vol. 13, no 1

7-13

EN

We show how to use the extension and torsion functors in order to compute the torsion submodule of a differential module associated with a multidimensional control system. In particular, we show that the concept of the weak primeness of matrices corresponds to the torsion-freeness of a certain module.

7

Some Algorithmic Aspects of Subspace Identification With Inputs

Chiuso A., Picci G.

International Journal of Applied Mathematics and Computer Science

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2001

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Vol. 11, no 1

55-75

EN

It has been experimentally verified that most commonly used subspace methods for identification of linear state-space systems with exogenous inputs may, in certain experimental conditions, run into ill-conditioning and lead to ambiguous results. An analysis of the critical situations has lead us to propose a new algorithmic structure which could be used either to test difficult cases and/or to implement a suitable combination of new and old algorithms presented in the literature to help fixing the problem.

8

Stability of Multi-Dimensional Discrete Systems With Varying Structure

Dymkov M., Gaishun I.

International Journal of Applied Mathematics and Computer Science

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1999

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Vol. 9, no 4

789-799

EN

A new class of multi-dimensional discrete systems with varying structureis introduced. The notions of total solvability, p_t-boundedness, p_t-stability and asymptotic stability are defined. For studying properties of the solutions for the considered systems a curvilinear composition of mappings along discrete curves is used. Total solvability conditions similar to the Frobenius ones are obtained. Sufficient conditions for p_t-stability and asymptotic stability based on the Lyapunov functional method are also established. A two-dimensional system of Volterra equations is presented as an example of equations with varying structure.

9

Generating a self-organizing fuzzy controller from human skill performance for multivariable systems

Lekova A., Boyadjiev D.

Applied Mathematics and Computer Science

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1998

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Vol. 8, no 3

633-645

EN

The paper presents a learning concept for creating of a self-organizing fuzzy controller for multivariable systems by explicit use of human skill performance during the control of a complex technological process. When such processes cannot be entirely controlled automatically, a natural way to achieve flexible and adaptive control is a combination of human resources and information technologies. The main idea is the decomposition of a multivariable control system into several subsystems with two inputs and multiple outputs. The number of sub-systems corresponds to the number of all orthogonal projections of an N-dimensional input vector in the two-dimensional pIane. Thus the method for generating fuzzy if-then rules from numerical data in the two-dimensional pIane which is already available, can be used. Fuzzy rules with variable fuzzy regions are generated automatically. An aggregation operator for calculating the connectivity degree of membership functions which connects the whole set of the generated fuzzy rules in all decomposed subsystems is found.