The concept of classical optimal feedback, optimal unclosable feedback and repeatedly closable feedbacks are introduced.
R. Gabasov, F.M. Kirillova 2015, 'On the Optimal Synthesis Problem for Control Systems', Известия Иркутского государственного университета: Серия "Математика"http://isu.ru/journal/downloadArticle?article=_b303b7ccc5c341a9b81d0df8a4656829&lang=rus. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Our approach makes use of a notion of symmetric (closable) pairs of operators.
Palle Jorgensen, Feng Tian 2016, 'Infinite-dimensional Lie Algebras, Representations, Hermitian Duality and the Operatorsof Stochastic Calculus', Axiomshttp://www.mdpi.com/2075-1680/5/2/12. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
For these, we introduce a notion of symmetric (closable) pairs of operators.
Palle Jorgensen, Feng Tian 2016, 'Infinite-dimensional Lie Algebras, Representations, Hermitian Duality and the Operatorsof Stochastic Calculus', Axiomshttp://www.mdpi.com/2075-1680/5/2/12. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We consider semibounded operators and find necessary and sufficient conditions for their quadratic forms to be closable.
Dmitri R. Yafaev 2018, 'Toeplitz versus Hankel: semibounded operators', Opuscula Mathematicahttp://www.opuscula.agh.edu.pl/vol38/4/art/opuscula_math_3826.pdf. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)