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Discrete-time Takagi-Sugeno singular systems with unmeasurable decision variables: state and fault fuzzy observer design

Aitdaraou Khaoula, Essabre Mohamed, El Assoudi Abdellatif, El Yaagoubi El Hassane

Archives of Control Sciences

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2023

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Vol. 33, No. 2

321--338

EN

The studied problem in this paper, treat the issue of state and fault estimation using a fuzzy observer in the case of unmeasurable decision variable for Discrete-Time Takagi-Sugeno Singular Sytems (DTSSS). First, an augmented system is introduced to gather state and fault into a single vector, then on the basis of Singular Value Decomposition (SVD) approach, this observer is designed in explicit form to estimate both of state and fault of a nonlinear singular system. The exponential stability of this observer is studied using Lyapunov theory and the convergence conditions are solved with Linear Matrix Inequalities (LMIs). Finally a numerical example is simulated, and results are given to validate the offered approach.

2

Fuzzy state feedback with double integrator and anti-windup for the Van de Vusse reaction

Márquez-Vera C. A., Màrquez-Vera M. A., Yakoub Z., Ma’arif A., Castro-Montoya A. J., Cázarez-Castro N. R.

Archives of Control Sciences

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2022

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Vol. 32, No. 2

383--408

EN

Chemical processes use to be non-minimum phase systems. Thereby, they are a challenge for control applications. In this paper, fuzzy state feedback is applied in the Van de Vusse reaction that has an inverse response. The control design has an integrator to enhance the control performance by eliminating the steady-state error when a step reference is applied. An anti-windup action is used to reduce the undershoot in the system response. In practice, it is not possible to have always access to all the state variables. Thus, a fuzzy state observer is implemented via LMIs. Frequently, the papers that show similar applications present some comments about disturbance rejection. To eliminate the steady-state error when a ramp reference is used, in this work, a second integrator is aggregated. Now, the anti-windup also reduces the overshoot generated due to the usage of two integrators in the final application.

3

A fault estimation and fault-tolerant control based sliding mode observer for LPV descriptor systems with time delay

Hamdi Habib, Rodrigues Mickael, Rabaoui Bouali, Benhadj Braiek Naceur

International Journal of Applied Mathematics and Computer Science

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2021

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Vol. 31, no. 2

247--258

EN

This paper considers the problem of fault-tolerant control (FTC) and fault reconstruction of actuator faults for linear parameter varying (LPV) descriptor systems with time delay. A polytopic sliding mode observer (PSMO) is synthesized to achieve simultaneous reconstruction of LPV polytopic descriptor system states and actuator faults. Exploiting the reconstructed actuator faults and state estimates, a fault-tolerant controller is designed to compensate the impact of actuator faults on system performance by stabilizing the closed-loop LPV delayed descriptor system. Besides, the controller and PSMO gains are obtained throughout the resolution of linear matrix inequalities (LMIs) using convex optimization techniques. The developed PSMO could force the output estimation error to converge to zero in a finite time when the actuators faults are bounded through the reinjection of the output estimation error via a nonlinear switching term. Simulation results applied to a given numerical system are presented to highlight the superiority and effectiveness of the proposed approach.

4

Decentralized static output tracking control of interconnected and disturbed Takagi–Sugeno systems

Jabri Dalel, Guelton Kevin, Belkhiat Djamel E.C., Manamanni Noureddine

International Journal of Applied Mathematics and Computer Science

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2020

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Vol. 30, no. 2

225--238

EN

This article describes a new procedure for the design of decentralized output-feedback tracking controllers for a class of interconnected Takagi–Sugeno (TS) fuzzy systems with external bounded disturbances and measurement noise. The main idea consists in transforming the decentralized tracking control problem, by using the descriptor redundancy formulation, to a robust decentralized stabilization one. The non-parallel distributed compensation (non-PDC) controllers proposed here are synthesized to satisfy robust H∞ tracking performance with disturbance attenuation. The decentralized controllers design conditions are given in terms of LMIs via extended quadratic Lyapunov functions. Finally, simulations are presented: two numerical examples are dedicated to compare the conservatism of the proposed approach regarding the previous results available in the literature; then, the effectiveness of the decentralized controller design methodology is illustrated with a closed-loop simulation of two inverted pendulums connected by a spring.

5

LMI-based robust control of uncertain nonlinear systems via polytopes of polynomials

Sánchez Marcelino, Bernal Miguel

International Journal of Applied Mathematics and Computer Science

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2019

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Vol. 29, no. 2

275--283

EN

This investigation is concerned with robust analysis and control of uncertain nonlinear systems with parametric uncertainties. In contrast to the methodologies from the field of linear parameter varying systems, which employ convex structures of the state space representation in order to perform analysis and design, the proposed approach makes use of a polytopic form of a generalisation of the characteristic polynomial, which proves to outperform former results on the subject. Moreover, the derived conditions have the advantage of being cast as linear matrix inequalities under mild assumptions.

6

Robust controlled positive delayed systems with interval parameter uncertainties: A delay uniform decomposition approach

Elloumi W., Mehdi D., Chaabane M.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 3

441--450

EN

This paper is concerned with robust stabilization of continuous linear positive time-delay systems with parametric uncertainties. The delay considered in this work is a bounded time-varying function. Previously, we have demonstrated that the equidistant delay-decomposition technique is less conservative when it is applied to linear positive time-delay systems. Thus, we use simply a delay bi-decomposition in an appropriate Lyapunov–Krasovskii functional. By using classical and partitioned control gains, the state-feedback controllers developed in our work are formulated in terms of linear matrix inequalities. The efficiency of the proposed robust control laws is illustrated with via an example.

7

Finite-time stability and stabilization of singular state-delay systems using improved estimation of a lower bound on a Lyapunov-like functional

Stojanovic S. B., Debeljkovic D. Lj., Antic D. S.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2015

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Vol. 63, nr 2

479--487

EN

In this paper, the problems of finite-time stability and stabilization for a class of singular time-delay systems are studied. Using the Lyapunov-like functional (LLF) with (exponential or power) weighting function and a new estimation method for the lower bound on LLF, some sufficient stability conditions are introduced. It is shown that the weighting function significantly reduces the conservatism of the stability criteria in comparison to estimation of the lower bound on LLF without this function. To solve the finite-time stabilization problem, a stabilizing linear state controller is designed by exploiting the cone complementarity linearization algorithm. Two numerical examples are given to illustrate the effectiveness of the proposed method.

8

Robust Dynamic Output Feedback H[infinity] Control for Uncertain Switched Singular Systems

Fu Z., Liu L., Gao A., Pu J.

Przegląd Elektrotechniczny

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2012

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R. 88, nr 3b

34-38

EN

This paper considers the problems of dynamic output feedback H[infinity] control for uncertain switched singular system with parametric uncertainties. A switching rule and a switched dynamic output feedback controller are designed to guarantee that the closed-loop system is asymptotically stable with a prescribed H[infinity] disturbance attenuation level [gamma]. Such sufficient conditions are derived via a series of strict linear matrix inequalities (LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

PL

W artykule analizuje się problem dynamiki system sterowania H[nieskończoność] dla systemu pojedynczego z niepewnymi przełączeniami. Badano zasady przełączania i dynamikę przełączania gwarantującą stabilną prace systemu. Przedstawiono przykład numeryczny ilustrujący skuteczność proponowanej metody.

9

A multi-model approach to Saint-Venant equations: A stability study by LMIs

Dos Santos Martins V., Rodrigues M., Diagne M.

International Journal of Applied Mathematics and Computer Science

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2012

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Vol. 22, no. 3

539-550

EN

This paper deals with the stability study of the nonlinear Saint-Venant Partial Differential Equation (PDE). The proposed approach is based on the multi-model concept which takes into account some Linear Time Invariant (LTI) models defined around a set of operating points. This method allows describing the dynamics of this nonlinear system in an infinite dimensional space over a wide operating range. A stability analysis of the nonlinear Saint-Venant PDE is proposed both by using Linear Matrix Inequalities (LMIs) and an Internal Model Boundary Control (IMBC) structure. The method is applied both in simulations and real experiments through a microchannel, illustrating thus the theoretical results developed in the paper.

10

Non-quadratic performance design for Takagi-Sugeno fuzzy systems

Bernal M., Husek P.

International Journal of Applied Mathematics and Computer Science

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2005

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Vol. 15, no 3

383-391

EN

This paper improves controller synthesis of discrete Takagi-Sugeno fuzzy systems based on non-quadratic Lyapunov functions, making it possible to accomplish various kinds of control performance specifications such as decay rate conditions, requirements on control input and output and disturbance rejection. These extensions can be implemented via linear matrix inequalities, which are numerically solvable with commercially available software. The controller design is illustrated with an example.

11

Linear Repetitive Process Control Theory Applied to a Physical Example

Gałkowski K., Rogers E., Paszke W., Owens D. H.

International Journal of Applied Mathematics and Computer Science

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2003

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Vol. 13, no 1

87-99

EN

In the case of linear dynamics, repetitive processes are a distinct class of 2D linear systems with uses in areas ranging from long-wall coal cutting and metal rolling operations to iterative learning control schemes. The main feature which makes them distinct from other classes of 2D linear systems is that information propagation in one of the two independent directions only occurs over a finite duration. This, in turn, means that a distinct systems theory must be developed for them for onward translation into efficient routinely applicable controller design algorithms for applications domains. In this paper, we introduce the dynamics of these processes by outlining the development of models for various metal rolling operations. These models are then used to illustrate some recent results on the development of a comprehensive control theory for these processes.