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Optimizing the linear quadratic minimum-time problem for discrete distributed systems

100%
Rachik M., Abdelhak A.
International Journal of Applied Mathematics and Computer Science
|
2002
|
tom 12
|
nr 2
153-160
EN
With reference to the work of Verriest and Lewis (1991) on continuous finite-dimensional systems, the linear quadratic minimum-time problem is considered for discrete distributed systems and discrete distributed time delay systems. We treat the problem in two variants, with fixed and free end points. We consider a cost functional J which includes time, energy and precision terms, and then we investigate the optimal pair (N, u) which minimizes J.
2
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A quadratic optimal control problem for a class of linear discrete distributed systems

81%
Rachik M., Lhous M., Kahlaoui O. E.
International Journal of Applied Mathematics and Computer Science
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2006
|
tom 16
|
nr 4
431-440
EN
A linear quadratic optimal control problem for a class of discrete distributed systems is analyzed. To solve this problem, we introduce an adequate topology and establish that optimal control can be determined though an inversion of the appropriate isomorphism. An example and a numerical approach are given.
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Admissible disturbance sets for discrete perturbed systems

81%
Bouyaghroumni J., Jai A. E., Rachik M.
International Journal of Applied Mathematics and Computer Science
|
2001
|
tom 11
|
nr 2
349-367
EN
We consider a discrete disturbed system given by the difference bilinear equation where are disturbances which excite the system in a linear and a bilinear form. We assume that the system is augmented with the output function. Let be a tolerance index on the output. The disturbance is said to be -admissible if, where is the output signal associated with the case of an uninfected system. The set of all -admissible disturbances is the admissible set. The characterization of is investigated and numerical simulations are given.
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