Optimal Bounded Control of Hysteretic Systems under External and Parametrical Random Excitations

Abstract

A method for designing optimal bounded control of nonlinear hysteretic systems under externally and parametrically random excitations is presented and illustrated with a numerical example on hysteretic column. The hysteretic system subjected to random excitations is firstly replaced by an equivalent nonlinear non-hysteretic stochastic system. Then, the Itô stochastic differential equation for the total energy of the system as a controlled diffusion process is derived by using the stochastic averaging method of energy envelope. For the semi-infinite time interval ergodic control, the dynamic programming equation is established based on the stochastic dynamical programming principle, and the optimal bounded control law is obtained from this equation under the control constraint. The responses of uncontrolled and controlled hysteretic systems are predicted and used for evaluating control efficacy. The robustness of the optimal bounded control for the hysteretic system with uncertain parameters is further analyzed. Numerical results show that the proposed control method has high efficacy and good robustness.