Optimal Parametric Control of Nonlinear Random Vibrating Systems

Abstract

Due to the great progresses in the fields of smart structures, especially smart soft materials and structures, the parametric control of nonlinear systems attracts extensive attentions in scientific and industrial communities. This paper devotes to the derivation of the optimal parametric control strategy for nonlinear random vibrating systems, in which the excitations are confined to Gaussian white noises. For a prescribed performance index balancing the control performance and control cost, the stochastic dynamic programming equation with respect to the value function is first derived by the principle of dynamic programming. The optimal feedback control law is established according to the extremum condition. The explicit expression of the value function is determined by approximately expressing as a quadratic function of state variables and by solving the final dynamic programming equation. The application and efficacy of the optimal parametric control are illustrated by a random-excited Duffing oscillator and a dielectric elastomer balloon with random pressure. The numerical results show that the optimal parameter control possesses good effectiveness, high efficiency, and high robustness to excitation intensity, and is superior than the associated optimal bounded parametric control.