Non-clipping optimal control of randomly excited nonlinear systems using semi-active ER/MR dampers

A stochastic optimal control strategy for randomly excited nonlinear systems using semi-active electro-rheological/magnetorheological (ER/MR) dampers is developed based on the stochastic averaging method, stochastic dynamical programming, and variational principle. The control force of ER/MR dampers is separated into passive part and controllable part. The passive part is incorporated into the uncontrollable terms and the stochastic averaging method is applied to the system with controllable damping force to yield a diffusion process of system energy along with Itô stochastic differential equations. Then the stochastic dynamical programming principle is applied to the controlled energy process to establish a dynamical programming equation. According to the variational principle, optimal control force is obtained from the dynamical programming equation under the constraint that ER/MR dampers are only able to exert dissipative forces. Because the requirement of dissipative control force is directly enforced as a constraint condition in the variational formula, the resulting control force is a generalized damping force and always implementable by ER/MR dampers without clipping. An example is given to illustrate the application and effectiveness of the proposed non-clipping semi-active control method.