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1

On some ways to implement state-multiplicative fault detection in discrete-time linear systems

Krokavec Dušan, Filasová Anna

International Journal of Applied Mathematics and Computer Science

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2022

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Vol. 32, no. 2

229--240

EN

New design conditions on the observer based residual filter design for the linear discrete-time linear systems with zoned system parameter faults are presented. With respect to time evolution of residual signals and with a guarantee of their robustness, the design task is stated in terms of linear matrix inequalities, while the recursive implementation of algorithms is motivated by the platform existence for real-time processing. A major objective is to analyze the configuration required and, in particular, a new characterization of the norm boundaries of the multiplicative zonal parametric faults to be projected onto the structure of the set of linear matrix inequalities.

2

Decentralized multi-agent formation control with pole-region placement via cone-complementarity linearization

González Antonio, Sala Antonio, Armesto Leopoldo

International Journal of Applied Mathematics and Computer Science

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2022

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Vol. 32, no. 3

415--428

EN

An output-feedback decentralised formation control strategy is pursued under pole-region constraints, assuming that the agents have access to relative position measurements with respect to a set of neighbors in a graph describing the sensing topology. No communication between the agents is assumed; however, a shared one-way communication channel with a pilot is needed for steering tasks. Each agent has a separate copy of the same controller. A virtual structure approach is presented for the formation steering as a whole; actual formation control is established via cone-complementarity linearization algorithms for the appropriate matrix inequalities. In contrast to other research where only stable consensus is pursued, the proposed method allows us to specify settling-time, damping and bandwidth limitations via pole regions. In addition, a full methodology for the decoupled handling of steering and formation control is provided. Simulation results in the example section illustrate the approach.

3

T–S fuzzy BIBO stabilisation of non-linear systems under persistent perturbations using fuzzy Lyapunov functions and non-PDC control laws

Salcedo José V., Martínez Miguel, García-Nieto Sergio, Hilario Adolfo

International Journal of Applied Mathematics and Computer Science

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2020

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Vol. 30, no. 3

529--550

EN

This paper develops an innovative approach for designing non-parallel distributed fuzzy controllers for continuous-time non-linear systems under persistent perturbations. Non-linear systems are represented using Takagi–Sugeno fuzzy models. These non-PDC controllers guarantee bounded input bounded output stabilisation in closed-loop throughout the computation of generalised inescapable ellipsoids. These controllers are computed with linear matrix inequalities using fuzzy Lyapunov functions and integral delayed Lyapunov functions. LMI conditions developed in this paper provide non-PDC controllers with a minimum ⋆-norm (upper bound of the 1-norm) for the T–S fuzzy system under persistent perturbations. The results presented in this paper can be classified into two categories: local methods based on fuzzy Lyapunov functions with guaranteed bounds on the first derivatives of membership functions and global methods based on integral-delayed Lyapunov functions which are independent of the first derivatives of membership functions. The benefits of the proposed results are shown through some illustrative examples.

4

Distributed fault estimation of multi-agent systems using a proportional-integral observer: A leader-following application

Farrera Beltrán, López-Estrada Francisco-Ronay, Chadli Mohammed, Valencia-Palomo Guillermo, Gómez-Peñate Samuel

International Journal of Applied Mathematics and Computer Science

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2020

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Vol. 30, no. 3

551--560

EN

This paper proposes a methodology for observer-based fault estimation of leader-following linear multi-agent systems subject to actuator faults. First, a proportional-integral distributed fault estimation observer is developed to estimate both actuator faults and states of each follower agent by considering directed and undirected graph topologies. Second, based on the proposed quadratic Lyapunov equation, sufficient conditions for the asymptotic convergence of the observer are obtained as a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the proposed approach.

5

BIBO stabilisation of continuous-time Takagi–Sugeno systems under persistent perturbations and input saturation

Salcedo J. V., Martínez M., García-Nieto S., Hilario A.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 3

457--472

EN

This paper presents a novel approach to the design of fuzzy state feedback controllers for continuous-time non-linear systems with input saturation under persistent perturbations. It is assumed that all the states of the Takagi–Sugeno (TS) fuzzy model representing a non-linear system are measurable. Such controllers achieve bounded input bounded output (BIBO) stabilisation in closed loop based on the computation of inescapable ellipsoids. These ellipsoids are computed with linear matrix inequalities (LMIs) that guarantee stabilisation with input saturation and persistent perturbations. In particular, two kinds of inescapable ellipsoids are computed when solving a multiobjective optimization problem: the maximum volume inescapable ellipsoids contained inside the validity domain of the TS fuzzy model and the smallest inescapable ellipsoids which guarantee a minimum *-norm (upper bound of the 1-norm) of the perturbed system. For every initial point contained in the maximum volume ellipsoid, the closed loop will enter the minimum *-norm ellipsoid after a finite time, and it will remain inside afterwards. Consequently, the designed controllers have a large domain of validity and ensure a small value for the 1-norm of closed loop.

6

Zastosowanie liniowych nierówności macierzowych do syntezy sterowania poziomem wody w układzie kaskadowym dwóch zbiorników

Rybczak M., Tomera M.

Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej

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2017

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Nr 57

109--116

PL

Referat zawiera metodykę doboru parametrów regulatora stanu z wykorzystaniem liniowych nierówności macierzowych (ang. LMI - Linear Matrix Inequalities) metodą lokowania biegunów. W pracy zdefiniowano warunki rozmieszczenia biegunów w lewej półpłaszczyźnie zmiennej zespolonej s i wyznaczono obszary dopuszczalnych położeń biegunów. Na potrzeby rozważanej, liniowej metody projektowania dokonano linearyzacji modelu matematycznego obiektu w wybranym punkcie pracy. Zaprojektowany regulator stanu zastosowany został do sterowania obiektem rzeczywistym, którym był układ kaskadowy dwóch zbiorników. W referacie przedstawione zostały zarówno wyniki badań symulacyjnych jak i badań eksperymentalnych przeprowadzonych na obiekcie rzeczywistym.

EN

The paper describes a state feedback controller design by pole placement method using Linear Matrix Inequalities (LMI) approach. Conditions of pole placement constraints in a left half plane of the complex plane s are defined and allowable region for poles of the closed-loop control system are determined. For the purpose of using the linear design method, the mathematical model of controlled plant was linearized at a selected operating point. The designed state feedback controller was used for controlling the water level in a two-tank cascade system. The paper presents results of both computer simulations and real-time experiments.

7

Zastosowanie liniowych nierówności macierzowych do syntezy okrętowych układów sterowania

Rybczak M.

Zeszyty Naukowe Akademii Morskiej w Gdyni

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2017

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nr 98

217--221

PL

Artykuł opiera się na kilku znaczących pozycjach w literaturze przedmiotu związanych z liniowymi nierównościami macierzowymi i ich zastosowaniem do syntezy okrętowych układów sterowania. Pierwsza część artykułu nawiązuje do liniowych nierówności macierzowych. Druga część poświęcona jest opisowi dwóch publikacji, zawierających zastosowanie liniowych nierówności macierzowych wdrożonych do zastosowań morskich na rzeczywistych obiektach. W podsumowaniu przedstawiono zalety i wady proponowanej metody numerycznej.

EN

The paper is a short review of publications about the use of linear matrix inequalities for synthesis of marine controlled object models. The first part is a short description of linear matrix inequalities. The second part presents two publications where linear matrix inequalities were implemented in marine industry. The summary describes advantages and disadvantages of the proposed numerical method.

8

Robust quasi-LPV model reference FTC of a quadrotor UAV subject to actuator faults

Rotondo D., Nejjari F., Puig V.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 1

7--22

EN

A solution for fault tolerant control (FTC) of a quadrotor unmanned aerial vehicle (UAV) is proposed. It relies on model reference-based control, where a reference model generates the desired trajectory. Depending on the type of reference model used for generating the reference trajectory, and on the assumptions about the availability and uncertainty of fault estimation, different error models are obtained. These error models are suitable for passive FTC, active FTC and hybrid FTC, the latter being able to merge the benefits of active and passive FTC while reducing their respective drawbacks. The controller is generated using results from the robust linear parameter varying (LPV) polytopic framework, where the vector of varying parameters is used to schedule between uncertain linear time invariant (LTI) systems. The design procedure relies on solving a set of linear matrix inequalities (LMIs) in order to achieve regional pole placement and H∞ norm bounding constraints. Simulation results are used to compare the different FTC strategies.

9

A fault tolerant direct control allocation scheme with integral sliding modes

Hamayun M. T., Edwards C., Alwi H., Bajodah A.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 1

93--102

EN

In this paper, integral sliding mode control ideas are combined with direct control allocation in order to create a fault tolerant control scheme. Traditional integral sliding mode control can directly handle actuator faults; however, it cannot do so with actuator failures. Therefore, a mechanism needs to be adopted to distribute the control effort amongst the remaining functioning actuators in cases of faults or failures, so that an acceptable level of closed-loop performance can be retained. This paper considers the possibility of introducing fault tolerance even if fault or failure information is not provided to the control strategy. To demonstrate the efficacy of the proposed scheme, a high fidelity nonlinear model of a large civil aircraft is considered in the simulations in the presence of wind, gusts and sensor noise.

10

A new fuzzy Lyapunov approach to non-quadratic stabilization of Takagi-Sugeno fuzzy models

Abdelmalek I., Goléa N., Hadjili M. L.

International Journal of Applied Mathematics and Computer Science

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2007

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Vol. 17, no 1

39-51

EN

In this paper, new non-quadratic stability conditions are derived based on the parallel distributed compensation scheme to stabilize Takagi-Sugeno (T-S) fuzzy systems. We use a non-quadratic Lyapunov function as a fuzzy mixture of multiple quadratic Lyapunov functions. The quadratic Lyapunov functions share the same membership functions with the T-S fuzzy model. The stability conditions we propose are less conservative and stabilize also fuzzy systems which do not admit a quadratic stabilization. The proposed approach is based on two assumptions. The first one relates to a proportional relation between multiple Lyapunov functions and the second one considers an upper bound to the time derivative of the premise membership functions. To illustrate the advantages of our proposal, four examples are given.

11

Liniowe nierówności macierzowe, regulacja predykcyjna i kompensator zjawiska windup

Horla D.

Studia z Automatyki i Informatyki

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2005

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T. 30

57--64

PL

W artykule przedstawiono zagadnienia teorii liniowych nierówności macierzowych, optymalizacji wypukłej, regulacji predykcyjnej i zjawiska windup dla liniowego obiektu dyskretnego. Problem programowania kwadratowego został przedstawiony w postaci zadania optymalizacji wypukłej z przekształceniem ograniczeń do postaci liniowych nierówności macierzowych. Zamieszczono przykładowe symulacje oraz wnioski.

EN

Predictive control, windup phenomenon, convex optimisation and theory of linear matrix inequalities issues have been presented in the paper for a discrete-time plant. A QP problem has been transformed into a convex optimisation problem with simultaneous translation of constraints into a linear matrix inequality form. Results of performed simulations have been included with conclusions.

12

Zastosowanie metody elipsoidalnej i metody punktu wewnętrznego do rozwiązywania liniowych nierówności macierzowych

Markowski K.A.

Przegląd Elektrotechniczny

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2004

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R. 80, nr 1

65-71

PL

Wiele zagadnień występujących w teorii sterowania może być przedstawionych jako zagadnienie optymalizacji wypukłej, które wymaga liniowych nierówności macierzowych (LMI). Rozwiązanie kilku szczególnych zadań można łatwo wyznaczyć w sposób analityczny (na przykład nierówność Lyapunova). Natomiast istnieje wiele zagadnień, dla których wyznaczenie rozwiązania w sposób analityczny jest wręcz niemożliwe. W takiej sytuacji możemy posłużyć się obliczeniami numerycznymi - algorytm elipsoidalny i punktu wewnętrznego.

EN

A lot of problems arising in control theory we can submit as a convex optimization problem which involves linear matrix inequality (LMI). The solution to some special problems we can easily assign in the analytical method (for example Lyapunov inequality). There exist many problems for which assign solution in analytical method is impossible. In this situation we can use numerical method - ellipsoidal algorithm and interior point algorithm.

13

A LMI approach to design controller for an induction motor

Koziński W.

Przegląd Elektrotechniczny

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2004

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R. 80, nr 4

380-384

EN

The paper presents Linear Matrix Inequality (LMI) approach to design one of vital parts of controller for an induction motor. From widely accepted induction motor model subplant describing stator current behavior is selected. It forms polytope model with rotor speed as parameter. The parameter should be measurable. The optimization approach with shaping filters is used to design linear parameter varying controllers. At the end of the paper an example is presented.

PL

W artykule przedstawiono zastosowanie liniowych nierówności macierzowych (LMI) do zaprojektowania jednej składowej części regulatora dla silnika indukcyjnego. Z modelu silnika indukcyjnego wydzielono podsystem opisujący zachowanie się prądów stojana. Używając optymalizacyjnej procedury projektowania otrzymano regulator prądu, zmienny w czasie, z prędkością obrotową wirnika jako wielkością sterującą.