Data-driven stochastic optimal control of nonlinear randomly vibrating systems

Abstract

Effective control of randomly vibrating systems plays a critical role in enhancing the safety and performance of structures in various engineering applications. This paper proposes a data-driven stochastic optimal control methodology in which control laws are derived directly from random state data without requiring knowledge of the governing equations. The proposed approach consists of two stages. In the first stage, starting from random state data, the stochastic system is identified by estimating the drift and diffusion coefficients using the Kramers–Moyal expansion combined with sparse regression. In the second stage, the optimal control forces are determined by integrating genetic algorithms with sparse optimization, thereby reducing the control problem to a multidimensional optimization task. To compute the statistical moments involved in the control optimization, two complementary strategies are employed. When the chosen control-force structures render the controlled system analytically solvable, the statistical moments are obtained in closed form. Otherwise, they are estimated numerically using Monte Carlo simulations. While the analytical-based method is more efficient, the MCS-based method serves as a fallback when analytical solutions are not feasible. Representative examples demonstrate that the proposed method achieves effective control performance with good efficiency, particularly in handling strongly nonlinear regimes. Moreover, the control law derived from the analytical-based formulation remains effective despite structural restrictions on the control force.