Optimal Bounded Control And Transient Response For Stochastic Systems With Viscoelastic Damping

The studies on optimal bounded control of stochastic systems subject to Gaussian white noise excitations are attracting many researchers in stochastic dynamics. This paper studies the problem of optimal bounded control of stochastic systems with viscoelastic damping.The first part is mainly about the optimal bounded control of quasi integrable and non resonant Hamiltonian systems with viscoelastic damping subject to Gaussian white noise excitations. Firstly, the original system are transformed into differential equations without viscoelastic damping, The viscoelastic damping force is divided into two parts:one part change conservative force; another part change damping force. Then, the corresponding Ito equation is established by using stochastic averaging method. Bring the optimal bounded control algorithm in semi infinite time interval built by dynamical programming principle to FPK equation. Based on the averaged equations, the ptimal bounded control of the system are investigated. The control effect and control efficiency of the viscoelastic systems are also investigated. The results show that the optimal bounded control has a good effect on the stochastic system with viscoelastic damping.In the second part, based on the previous content the transient response of controlled Hamiltonian systems with viscoelastic damping subject to Gaussian white noise excitations is investigated. By applying the Galerkin method, the transient probability density can be expressed as a series expansion in terms of a set of orthogonal base Laguerre. Then, the approximate transient probability density for energy response can be obtained. Based on the approximate transient probability density for energy response, the optimal bounded control of transient response are investigated. The results show that the optimal bounded control forces on the transient response of a viscoelastic damping Hamiltonian system has a good control effect.