An output sensitivity problem for a class of linear distributed systems with uncertain initial state

• Autorzy: Larrache Abdelilah , Lhous Mustapha , Rhila Soukina Ben , Rachik Mostafa , Tridane Abdessamad

Identyfikatory

DOI

10.24425/acs.2020.132589

• Języki publikacji: EN

Abstrakty

EN

In this paper,we consider an infinite dimensional linear systems. It is assumed that the initial state of system is not known throughout all the domain Ω C Rⁿ, the initial state x₀ ϵ L²(Ω) is supposed known on one part of the domain Ω and uncertain on the rest. That means Ω = ω₁ U ω₂ U... U ω_t with ω_i ∩ ω_j = ∅, ∀_i ≠ j ϵ {1,...,t}, i ≠ j where ω_i ≠ ∅ and x₀(θ) = α_i for θ ϵ ω_i, ∀_i, i.e., x₀(θ) = [wzór] (θ) where the values α₁,...,α_r are supposed known and α_r+1,...,α_t unknown and 1ω_i is the indicator function. The uncertain part (α₁,...,(α)_rof the initial state x₀ is said to be (ɛ₁,...,ɛ_r )-admissible if the sensitivity of corresponding output signal (y_i)_i≥0 relatively to uncertainties (α_k)_1≤k≤r is less to the treshold ɛ_k, i.e., ∥∂y_i)/(∂α_k∥ ≤ ɛ_k, ∀_i≥ 0, ∀_k ϵ {1,...,r]. The main goal of this paper is to determine the set of all possible gain operators that makes the system insensitive to all uncertainties. The characterization of this set is investigated and an algorithmic determination of each gain operators is presented. Some examples are given.

Słowa kluczowe

EN

linear system; distributed system; uncertain initial state; gain operators; observability; stability; linear programming

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2020
• Tom: Vol. 30, No. 1
• Strony: 139--155
• Opis fizyczny: Bibliogr. 16 poz., wzory

Twórcy

autor

Larrache Abdelilah

• Laboratory of Analysis Modelling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, B.P 7955 Sidi Othman Casablanca, Morocco

autor

Lhous Mustapha

• Laboratory of Modeling, Analysis, Control and Statistics, Department of Mathematics and Computer Science, Faculty of Sciences Ain Chock, Hassan II University of Casablanca, B.P 5366 Maarif Casablanca, Morocco

autor

Rhila Soukina Ben

• Laboratory of Analysis Modelling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, B.P 7955 Sidi Othman Casablanca, Morocco

autor

Rachik Mostafa

• Laboratory of Analysis Modelling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, B.P 7955 Sidi Othman Casablanca, Morocco.

autor

Tridane Abdessamad

• Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551, Al Ain, UAE

Bibliografia

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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).