Optimal control for fractional stochastic impulsive damped switched systems

This paper addresses the optimal control problem for a class of fractional stochastic impulsive switched systems with damping in Hilbert spaces. The considered systems jump at the switching times. On each time interval, only one subsystem is active. Our initial step is to establish the existence of mild solutions for the proposed system using the theory of (α,μ)-regularised families of operators, a fixed point theorem, stochastic analysis theory and fractional calculus. Next, we derive the existence of optimal control pairs for the stochastic evolution equations by the minimising sequence technique. Finally, two examples are given to illustrate the theory.