## Abstract and Applied Analysis

### On the Continuity Properties of the Attainable Sets of Nonlinear Control Systems with Integral Constraint on Controls

#### Abstract

The attainable sets of the nonlinear control systems with integral constraint on the control functions are considered. It is assumed that the behavior of control system is described by differential equation which is nonlinear with respect to phase-state vector and control vector. The admissible control functions are chosen from the closed ball centered at the origin with radius ${{\mu{}}}_{0}$ in ${L}_{p}([{t}_{0},{\theta{}}];{{\mathbb{R}}}^{m})\,(p\in{}(1,+{\infty{}}))$. Precompactness of the solutions set is specified, and dependence of the attainable sets on the initial conditions and on the parameters of the control system is studied.

#### Article information

Source
Abstr. Appl. Anal., Volume 2008 (2008), Article ID 295817, 14 pages.

Dates
First available in Project Euclid: 9 September 2008

https://projecteuclid.org/euclid.aaa/1220969149

Digital Object Identifier
doi:10.1155/2008/295817

Mathematical Reviews number (MathSciNet)
MR2393114

Zentralblatt MATH identifier
05313167

#### Citation

Guseinov, Khalik G.; Nazlipinar, Ali S. On the Continuity Properties of the Attainable Sets of Nonlinear Control Systems with Integral Constraint on Controls. Abstr. Appl. Anal. 2008 (2008), Article ID 295817, 14 pages. doi:10.1155/2008/295817. https://projecteuclid.org/euclid.aaa/1220969149

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