Stochastic fractional optimal control of quasi-integrable Hamiltonian system with fractional derivative damping

Abstract

A stochastic fractional optimal control strategy for quasi-integrable Hamiltonian systems with fractional derivative damping is proposed. First, equations of the controlled system are reduced to a set of partially averaged It\(\hat{o}\) stochastic differential equations for the energy processes by applying the stochastic averaging method for quasi-integrable Hamiltonian systems and a stochastic fractional optimal control problem (FOCP) of the partially averaged system for quasi-integrable Hamiltonian system with fractional derivative damping is formulated. Then the dynamical programming equation for the ergodic control of the partially averaged system is established by using the stochastic dynamical programming principle and solved to yield the fractional optimal control law. Finally, an example is given to illustrate the application and effectiveness of the proposed control design procedure.