Optimal nonlinear stochastic control of hysteretic systems

A strategy for optimal nonlinear stochastic control of hysteretic systems w ith parametrically and/or externally random excitations is proposed and ill ustrated with an example of a single-degree-of-freedom system. A hysteretic system subject to random excitation is first replaced by a nonlinear nonhy steretic stochastic system, from which an Ita equation for the averaged tot al energy of the system as a 1D controlled diffusion process is derived by using the stochastic averaging method of energy envelope. For a given perfo rmance index, a Hamilton-Jacobi-Bellman equation is then established based on the stochastic dynamical programming principle and solved to yield the o ptimal control force. Finally, the statistics of the responses of uncontrol led and controlled systems and those of the optimal control force are predi cted analytically. Comparison with the modified optimal polynomial controll er indicates that the proposed strategy is more effective and efficient.