Optimal control problem governed by an infinite dimensional two-nilpotent bilinear systems

Aziza Aib; Naceurdine Bensalem

doi:10.3934/naco.2022018

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2023, Volume 13, Issue 2: 314-327. Doi: 10.3934/naco.2022018

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Optimal control problem governed by an infinite dimensional two-nilpotent bilinear systems

Aziza Aib^, and
Naceurdine Bensalem

Numerical and Fundamental Mathematics Laboratory, Ferhat Abbas University Setif 1. Setif 19000, Algeria

^*Corresponding author: Aziza Aib
^*Corresponding author: Aziza Aib

Received: June 2021

Revised: June 2022

Early access: July 2022

Published: January 2023

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Abstract

The object of this work is to construct an explicit linear operators $ A $ and $ B $ which generate a nilpotent Lie algebra for the bracket $ \left[A,B\right] = AB-BA $ of degree 2 in infinite dimensional spaces. This construction can be applied to give an exact optimal solution for a class of infinite dimensional bilinear systems.

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Mathematics Subject Classification: 49J15, 47A07, 22E27.

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References

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