Probability-Weighted Optimal Control for Nonlinear Stochastic Vibrating Systems with Random Time Delay - R. C. Hu; Q. F. Lü; X. F. Wang; Z. G. Ying; R. H. Huan (Shock and Vibration)
A probability-weighted optimal control strategy for nonlinear stochastic vibrating systems with random time delay is proposed. First, by modeling the random delay as a finite state Markov process, the optimal control problem is converted into the one of Markov jump systems with finite mode. Then, upon limiting averaging principle, the optimal control force is approximately expressed as probability-weighted summation of the control force associated with different modes of the system. Then, by using the stochastic averaging method and the dynamical programming principle, the control force for each mode can be readily obtained. To illustrate the effectiveness of the proposed control, the stochastic optimal control of a two degree-of-freedom nonlinear stochastic system with random time delay is worked out as an example.