Time optimal control to a partial stochastic differential system with pseudo almost periodic coefficients

Abstract

In this paper, we study the time optimal control of a class of partial stochastic impulsive functional differential systems with pseudo almost periodic coefficients in the α-norm functional spaces. Firstly, the existence of p-mean piecewise pseudo almost periodic mild solutions for the impulsive stochastic control systems is investigated by utilising stochastic analysis, analytic semigroup, the fixed-point techniques with fractional power arguments. Secondly, the existence of time optimal pairs of a system governed by partial stochastic impulsive functional differential equations is also obtained. Finally, two examples are provided to illustrate the time optimal control problems of parabolic control system with pseudo almost periodic coefficients and impulses.

Keywords:

• Time optimal control
• partial stochastic impulsive differential systems
• piecewise pseudo almost periodic functions
• fractional powers operators
• fixed point

2010 MR Subject Classifications:

• 34A37
• 60H10
• 35B15
• 34F05
• 93E20

Acknowledgements

The author would like to thank the editor and the reviewer for their constructive comments and suggestions. This work is supported by the National Natural Science Foundation of China (11461019).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (11461019).