Exact determinantions of maximal output admissible set for a class of semilinear discrete systems

Consider the semilinear system defined by x(i+1) = Ax(i) + f(x(i)), i≥ 0 x(0) = x0 ϵ ℜn and the corresponding output signal y(i)=Cx(i), i ≥ 0, where A is a n x 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 constr...

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Bibliographic Details
Published in:Archives of control sciences 2020-01, Vol.30 (3), p.523-550
Main Authors: El Bhih, Amine, Benfatah, Youssef, Rachik, Mostafa
Format: Article
Language:English
Subjects:
Algorithms
Approximation
asymptotic stability
controlled system
delayed system
Discrete systems
discrete-time
Initial conditions
output admissible set
semilinear system
uncontrolled system
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Summary:Consider the semilinear system defined by x(i+1) = Ax(i) + f(x(i)), i≥ 0 x(0) = x0 ϵ ℜn and the corresponding output signal y(i)=Cx(i), i ≥ 0, where A is a n x 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 in ℜp if the output signal (y(i))i associated to our system satisfies the condition y(i) in 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.
ISSN:1230-2384
2300-2611
DOI:10.24425/acs.2020.134676