On observers and compensators for infinite dimensional semilinear systems

Achhab, M.E.

doi:10.3934/eect.2015.4.131

Cited by 5 publications

(7 citation statements)

References 20 publications

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“…Definition 6. A forward complete system ( 1) is called practically stabilizable if there exists a continuous feedback control 𝑢 : [𝑡 0 , ∞) → 𝑈, such that the solution of the system (1) with 𝑢(𝑡) is globally practically uniformly exponentially stable.…”

Section: Remarkmentioning

confidence: 99%

“…Let assumptions (H 1 ), (H 2 ) and (H 4 ) be satisfied. Then, the system ( 16) is a practical exponential Luenberger observer for the system (1).…”

Section: Practical Luenberger Observer Designmentioning

confidence: 99%

“…For extensions to systems with unbounded input and output operators (see [8][9][10]), and for a comparison of various finite-dimensional control designs (see [11]). On the other hand, the problem of compensator design for autonomous infinite-dimensional linear systems can be solved in [12], but if the system contains some nonlinearities, This problem has been used as a starting point in many control designs for semilinear evolution equations whose autonomous linear nominal system, and the nonlinearities satisfies conditions, see [1,14,15,17]. In [1], the stabilization problem around a desired equilibrium profile of a class of infinite-dimensional semilinear systems is resolved, yielding a compensator based on a Luenberger-like observer.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, the problem of compensator design for autonomous infinite-dimensional linear systems can be solved in [12], but if the system contains some nonlinearities, This problem has been used as a starting point in many control designs for semilinear evolution equations whose autonomous linear nominal system, and the nonlinearities satisfies conditions, see [1,14,15,17]. In [1], the stabilization problem around a desired equilibrium profile of a class of infinite-dimensional semilinear systems is resolved, yielding a compensator based on a Luenberger-like observer. Designing observer-based controllers has investigated a certain class of dynamical systems, see, for instance, [3,20,21,26].…”

Section: Introductionmentioning

confidence: 99%

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On observer compensator design for non-autonomous control semi-linear evolution equations

Badri,

Damak,

Hammami

2024

Archives of Control Sciences

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This paper investigates the Luenberger observer design problem for non-autonomous control semilinear evolution equations with disturbances in Banach spaces. Then, the practicalstabilization problem of the system is solved, yielding a compensator based on the Luenberger observer by using integral inequalities of the Gronwall type. Sufficient conditions of the controller and observer problem are satisfied, we show that the proposed controller with estimatedstate feedback from the proposed practical Luenberger observer will achieve global practical stabilization. We develop novel ideas and techniques, which present the further development of mathematical control theory. Furthermore, an example is given to show the applicability of our theoretical results.

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Section: Remarkmentioning

confidence: 99%

“…Let assumptions (H 1 ), (H 2 ) and (H 4 ) be satisfied. Then, the system ( 16) is a practical exponential Luenberger observer for the system (1).…”

Section: Practical Luenberger Observer Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On observer compensator design for non-autonomous control semi-linear evolution equations

Badri,

Damak,

Hammami

2024

Archives of Control Sciences

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“…The important issue in connection with detecting notion for usual case in linear or nonlinear DPSS has received a lot of consideration, see [1][2] and references therein. Therefore, the regional case of detectability notion in this systems has been developed through an extension to previous works as in [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Boundary Exponential Gradient Reduced Order Detectability in Neumann Conditions

Al-Bayati,

Al-Shaya,

Al-Saphory

2024

Iraqi Journal of Science

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This work, aims to study and examine the description f the gradient reduced order-strategic sensors of type boundary exponential (-strategic sensors) for completion gradient order-detectability of type boundary exponential (-detectability). Thus, this concept is linked to an estimator in distributed parameter systems (DPSS) in Neumann problem. So,we present numerous consequences regarding to diverse kinds of information, region and conditions of boundary region to allow existence of -detectable systems. In addition,we have estimated at the junction interface that the interior solution isharmonizedwith the exterior solution for -detectable and, we give the relationship between this concept and sensors structures. Finally,we demonstrate some applications with many circumstances f sensor positions.

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Observers Based Control for Stabilization of Non-autonomous Evolution Equations in Banach Spaces

Hammami

Maaloul

2023

Complex Anal. Oper. Theory

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On observers and compensators for infinite dimensional semilinear systems

Cited by 5 publications

References 20 publications

On observer compensator design for non-autonomous control semi-linear evolution equations

On observer compensator design for non-autonomous control semi-linear evolution equations

Boundary Exponential Gradient Reduced Order Detectability in Neumann Conditions

Observers Based Control for Stabilization of Non-autonomous Evolution Equations in Banach Spaces

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