Analysis of nonlinear fractional control systems in Banach spaces

作者：Wang, JinRong; Zhou, Yong^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(17): 5929-5942.

DOI：10.1016/j.na.2011.05.059

• Fractional control systems
• Mild solutions
• Weakly singular inequality
• Optimal controls
• Weakly compactness

In this paper, we consider the nonlinear control systems of fractional order and its optimal controls in Banach spaces. Using the fractional calculus, Holder's inequality, p-mean continuity, weakly singular inequality and Leray-Schauder's fixed point theorem with compact mapping, the sufficient condition is given for the existence and uniqueness of mild solutions for a broad class of fractional nonlinear infinite dimensional control systems. Utilizing the approximately lower semicontinuity of integral functionals and weakly compactness, we extend the existence result of optimal controls for nonlinear control systems to nonlinear fractional control systems under generally mild conditions. An example is given to illustrate the effectiveness of the results obtained.

• 出版日期2011-12
• 单位贵州大学; 湘潭大学