Data-driven method for response control of nonlinear random dynamical systems

The response control of nonlinear random dynamical systems is an important but also difficult subject in scientific and industrial fields. This work merges the decomposition technique of feedback control and the data-driven identification method of stationary response probability density, converts the constrained functional extreme value problem associated with optimal control to an unconstrained optimization problem of multivariable function, and determines the optimal coefficients of preselected control terms by an optimization algorithm. This data-driven method avoids the difficulty of solving the stochastic dynamic programming equation or forward-backward stochastic differential equations encountered in classical control theories, the miss of the conservative mechanism in the nonlinear stochastic optimal control strategy, and the difficulty of judging the integrability and resonance of the controlled Hamiltonian systems encountered in the direct-control method. The application and efficacy of the data-driven method are illustrated by the random response control problems of the Duffing oscillator, van der Pol system, and a two degrees-of-freedom nonlinear system.