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    Wyświetlanie 1-4 z 4
    Tytuł:
    Exact determinantions of maximal output admissible set for a class of semilinear discrete systems
    Autorzy:
    El Bhih, Amine
    Benfatah, Youssef
    Rachik, Mostafa
    Powiązania:
    https://bibliotekanauki.pl/articles/229674.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    discrete-time
    output admissible set
    semilinear system
    asymptotic stability
    uncontrolled system
    controlled system
    delayed system
    Opis:
    Consider the semilinear system defined by {x(i+1)=Ax(i)+f(x(i)), i≥0 x(0)=x0∈Rn and the corresponding output signal y(i)=C x(i), i≥0, where A is a n×n matrix, C is a p x n matrix and f is a nonlinear function. An initial state x(0) is output admissible with respect to A, f, C and a constraint set Ω ⊂ Rp, if the output signal (y(i)i associated to our system satisfies the condition y(i) ∈ Ω, for every integer i≥0. The set of all possible such initial conditions is the maximal output admissible set Γ(Ω). In this paper we will define a new set that characterizes the maximal output set in various systems(controlled and uncontrolled systems) .Therefore, we propose an algorithmic approach that permits to verify if such set is finitely determined or not. The case of discrete delayed systems is taken into consideration as well. To illustrate our work, we give various numerical simulations.
    Źródło:
    Archives of Control Sciences; 2020, 30, 3; 523-552
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An output sensitivity problem for a class of fractional order discrete-time linear systems
    Autorzy:
    Benfatah, Youssef
    El-Bhih, Amine
    Rachik, Mostafa
    Lafif, Marouane
    Powiązania:
    https://bibliotekanauki.pl/articles/2106242.pdf
    Data publikacji:
    2021
    Wydawca:
    Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
    Tematy:
    fractional order systems
    output sensitivity
    discrete time systems
    maximal output set admissible uncertainty
    Opis:
    Consider the linear discrete-time fractional order systems with uncertainty on the initial state {Δαxi+1=Axi+Bui, i≥0x0=τ0+τ̂0∈Rn, τ̂0∈Ωyi=Cxi, i≥0}, where A,B and C are appropriate matrices, x0 is the initial state, yi is the signal output, α the order of the derivative, τ0 and τ̂0 are the known and unknown part of x0, respectively, ui=Kxi is feedback control and Ω⊂Rn is a polytope convex of vertices w1,w2,...,wp. According to the Krein–Milman theorem, we suppose that τ̂0=Σ pj=1αjwj for some unknown coefficients α1≥0,...,αp≥0 such that Σ pj=1αj=1. In this paper, the fractional derivative is defined in the Grünwald–Letnikov sense. We investigate the charac-terisation of the set χ(τ̂0,ϵ) of all possible gain matrix K that makes the system insensitive to the unknown part τ̂0, which means χ(τ̂0,ϵ)={K∈Rm×n / ∥∂yi∂αj∥≤ϵ, ∀j=1,...,p,∀i≥0}, where the inequality ∥∂yi∂αj∥≤ϵ showing the sensitivity of yi relative-ly to uncertainties {αj}j=1p will not achieve the specified threshold ϵ>0. We establish, under certain hypothesis, the finite determination of χ(τ̂0,ϵ) and we propose an algorithmic approach to made explicit characterisation of such set.
    Źródło:
    Acta Mechanica et Automatica; 2021, 15, 4; 227--235
    1898-4088
    2300-5319
    Pojawia się w:
    Acta Mechanica et Automatica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the control of the final speed for a class of finite-dimensional linear systems: controllability and regulation
    Autorzy:
    Rachik, Mostafa
    Khaloufi, Issam
    Benfatah, Youssef
    Boutayeb, Hamza
    Laarabi, Hassan
    Powiązania:
    https://bibliotekanauki.pl/articles/29432204.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    speed-controllability
    controllability
    continuous systems
    regulation
    Kalman’s condition
    Opis:
    In this article, we extended the concept of controllability, traditionally used to control the final state of a system, to the exact control of its final speed. Inspired by Kalman’s theory, we have established some conditions to characterize the control that allows the system to reach a desired final speed exactly. When the assumptions ensuring speed-controllability are not met, we adopt a regulation strategy that involves determining the control law to make the system’s final speed approach as closely as possible to the predefined final speed, and this at a lower cost. The theoretical results obtained are illustrated through three examples.
    Źródło:
    Archives of Control Sciences; 2023, 33, 3; 497--525
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    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
    Powiązania:
    https://bibliotekanauki.pl/articles/229238.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    linear system
    distributed system
    uncertain initial state
    gain operators
    observability
    stability
    linear programming
    Opis:
    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 ωt with ωi ∩ ωj = ∅, ∀i ≠ j ϵ {1,...,t}, i ≠ j where ωi ≠ ∅ and x0(θ) = αi for θ ϵ ωi, ∀i, i.e., x0(θ) = [wzór] (θ) where the values α1,...,αr are supposed known and αr+1,...,αt unknown and 1ωi is the indicator function. The uncertain part (α1,...,(α)rof the initial state x0 is said to be (ɛ1,...,ɛr )-admissible if the sensitivity of corresponding output signal (yi)i≥0 relatively to uncertainties (αk)1≤k≤r is less to the treshold ɛk, i.e., ∥∂yi)/(∂αk∥ ≤ ɛk, ∀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.
    Źródło:
    Archives of Control Sciences; 2020, 30, 1; 139-155
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-4 z 4

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