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On the minimum energy compensation for linear time-varying disturbed systems

Magri El Mostafa, Amissi Chadi, Afifi Larbi, Lhous Mustapha

Archives of Control Sciences

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2022

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Vol. 32, No. 4

733--754

EN

We consider in this work a class of finite dimensional time-varying linear disturbed systems. The main objective of this work is to studied the optimal control which ensures the remediability of a disturbance of time-varying disturbed systems. The remediability concept consist to find a convenient control which bringing back the corresponding observation of disturbed system to the normal one at the final time. We give firstly some characterisations of compensation and in second party we find a control which annul the output of the system and we show also that the Hilbert Uniqueness Method can be used to solve the optimal control which ensure the remediability. A general approach was given to minimize the linear quadratic problem. Examples and numerical simulations are given.

2

Protector control: Extension to a class of nonlinear distributed systems

Qaraai Y., Bernoussi A. S.

International Journal of Applied Mathematics and Computer Science

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2010

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Vol. 20, no 3

427-443

EN

We present an extension of the protector control scheme introduced for the linear case in a previous work to a class of nonlinear systems. The systems considered are assumed to have a finite propagation velocity while the initial state is subject to a spreading disturbance. We characterize such a control first by using the remediability approach to the resulting nonlinear delay system, and then by coupling families of transformations and the delay approach. To illustrate this work, we provide a simulation example.

3

How to compensate a spreading disturbance for a class of nonlinear systems

Quaraai Y., Bernoussi A. S., El Jai A.

International Journal of Applied Mathematics and Computer Science

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2008

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Vol. 18, no 2

171-187

EN

We consider a system which is assumed to be affected by an expanding disturbance which occurs at the initial time. The compensation of the disturbance is accomplished by extending the concept of remediability to a class of nonlinear systems. The results are implemented and illustrated with a nonlinear distributed model.

4

Enlarged Exact Compensation in Distributed Systems

Afifi L., Chafiai A., Bel Fekih A.

International Journal of Applied Mathematics and Computer Science

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2002

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Vol. 12, no 4

467-477

EN

In this work, we examine, through the observation of a class of linear distributed systems, the possibility of reducing the effect of disturbances (pollution, etc.), by making observations within a given margin of tolerance using a control term. This problem is called enlarged exact remediability. We show that with a convenient choice of input and output operators (actuators and sensors, respectively), the considered control problem has a unique optimal solution, which will be given. We also study the relationship between the notion of remediability, introduced in previous works, and that of enlarged exact remediability.

5

Spatial Compensation of Boundary Disturbances by Boundary Actuators

Afifi L., Chafiai A., El Jai A.

International Journal of Applied Mathematics and Computer Science

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2001

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Vol. 11, no 4

899-920

EN

In this paper we show how to find convenient boundary actuators, termed boundary efficient actuators, ensuring finite-time space compensation of any boundary disturbance. This is the so-called remediability problem. Then we study the relationship between this remediability notion and controllability by boundary actuators, and hence the relationship between boundary strategic and boundary efficient actuators. We also determine the set of boundary remediable disturbances, and for a boundary disturbance, we give the optimal control ensuring its compensation.