Stochastic optimal bounded control for MDOF nonlinear systems under combined harmonic and wide-band noise excitations with actuator saturation

Abstract

A stochastic optimal bounded control strategy for multi-degrees-of-freedom (MDOF) strongly nonlinear systems under combined harmonic and wide-band noise excitations with actuator saturation is proposed. First, a stochastic averaging procedure is introduced for controlled strongly nonlinear systems under combined harmonic and wide-band noise excitations using generalized harmonic functions. Then, the dynamical programming equation for the stochastic bounded control problem is derived from the partially averaged Itô equations and solved to yield the optimal control law. Finally, the responses of optimally controlled MDOF nonlinear systems are predicted by solving the Fokker–Planck–Kolmogorov (FPK) equation associated with the fully averaged Itô equations. An example is given to illustrate the proposed control strategy and comparing is made with the bang–bang control. The effectiveness of the proposed control strategy is verified by using the results from Monte Carlo simulation.