A stochastic optimal control strategy for viscoelastic systems with actuator saturation

• A new stochastic optimal control strategy for viscoelastic system with actuator saturation is proposed.
• The strategy has high control efficiency and effectiveness.
• The control strategy attenuates the chattering in the bang-bang control.
• The strategy is also applicable even for strongly nonlinear system.
• The analytical results agrees well with the MCS results.

A nonlinear stochastic optimal control strategy for single degree-of-freedom viscoelastic system with actuator saturation is proposed based on the stochastic averaging method and stochastic dynamical programing principle. First, the viscoelastic system is converted into an equivalent nonlinear non-viscoelastic system by replacing the viscoelastic force with amplitude-dependent stiffness and damping. Second, the partially averaged Itô stochastic differential equation for total system energy as one-dimensional controlled diffusion process is derived by using the stochastic averaging method of energy envelope. For the semi-infinite time-interval ergodic control, the dynamical programming equation is established by applying the stochastic dynamical programming principle to the partially averaged Itô equation with a performance index. The optimal saturated control consisting of unbounded optimal control and bang-bang control is determined by solving the dynamical programming equation. Both the analytical and simulation results verify the higher efficiency and chattering attenuation of the proposed control strategy compared with the corresponding bang-bang control.