Stability and solvability for a class of optimal control problems described by non-instantaneous impulsive differential equations

• Main Authors: Yi Chen, Kaixuan Meng
• Format: Article
• Language: English
• Published: SpringerOpen 2020-09-01
• Series: Advances in Difference Equations
• Subjects: Optimal control; Non-instantaneous impulse; Stability analysis
• Online Access: http://link.springer.com/article/10.1186/s13662-020-02919-z

Abstract In this paper, we investigate the existence and stability of solutions for a class of optimal control problems with 1-mean equicontinuous controls, and the corresponding state equation is described by non-instantaneous impulsive differential equations. The existence theorem is obtained by the method of minimizing sequence, and the stability results are established by using the related conclusions of set-valued mappings in a suitable metric space. An example with the measurable admissible control set, in which the controls are not continuous, is given in the end.