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A bounded optimal control strategy for strongly non-linear systems under non-white wide-band random excitation with actuator saturation is proposed.First,the stochastic averag- ing method is introduced for controlled strongly non-linear systems under wide-band random excitation using generalized harmonic functions.Then,the dynamical programming equation for the saturated control problem is formulated from the partially averaged It equation based on the dynamical programming principle.The optimal control consisting of the unbounded optimal control and the bounded bang-bang control is determined by solving the dynamical programming equation.Finally,the response of the optimally controlled system is predicted by solving the re- duced Fokker-Planck-Kolmogorov (FPK) equation associated with the completed averaged It(?) equation.An example is given to illustrate the proposed control strategy.Numerical results show that the proposed control strategy has high control effectiveness and efficiency and the chattering is reduced significantly comparing with the bang-bang control strategy.
A bounded optimal control strategy for strongly non-linear systems under non-white wide-band random excitation with actuator saturation is proposed. First, the stochastic averag-ing method is introduced for strongly strongly non-linear systems under wide-band random excitation using generalized harmonic functions.Then, the dynamical programming equation for the saturated control problem is formulated from the partially averaged It equation based on the dynamical programming principle.The optimal control consisting of the unbounded optimal control and the bounded bang-bang control is determined by solving the dynamical programming equation .Finally, the response of the optimally controlled system is predicted by solving the re- duced Fokker-Planck-Kolmogorov (FPK) equation associated with the completed averaged It (?) equation. An example is given to illustrate the proposed control strategy.Numerical results show that the proposed control strategy has high control effectiveness and effic iency and the chattering is reduced significantly comparing with the bang-bang control strategy.