Compactness of the set of trajectories of the control system described by a Urysohn type integral equation with quadratic integral constraints on the control functions

Alias, Idham; HÜSEYİN, NESİR; HÜSEYİN, ANAR

doi:10.1186/s13660-015-0908-9

Compactness of the set of trajectories of the control system described by a Urysohn type integral equation with quadratic integral constraints on the control functions

Atıf İçin Kopyala

Alias I. A., HÜSEYİN N., HÜSEYİN A.

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Basım Tarihi: 2016
Doi Numarası: 10.1186/s13660-015-0908-9
Dergi Adı: JOURNAL OF INEQUALITIES AND APPLICATIONS
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sivas Cumhuriyet Üniversitesi Adresli: Evet

Özet

In this paper the control system is considered described by a Urysohn type integral equation which is nonlinear with respect to the state vector and is affine with respect to the control vector. The functions from the space L-2([t(0),theta]; R-m) satisfying a quadratic integral constraint are chosen as admissible control functions. The set of trajectories generated by all admissible control functions is studied. The boundedness, closedness, precompactness, and hence the compactness of the set of trajectories in the space of continuous functions is proved.