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 averaging method is introduced for controlled ...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 averaging 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 Itō 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 reduced Fokker-Planck-Kolmogorov （FPK） equation associated with the completed averaged Itō 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.展开更多
The nonlinear planar mean square response and the random stability of a viscoelastic cable that has a small curvature and subjects to planar narrow band random excitation is studied. The Kelvin viscoelastic constituti...The nonlinear planar mean square response and the random stability of a viscoelastic cable that has a small curvature and subjects to planar narrow band random excitation is studied. The Kelvin viscoelastic constitutive model is chosen to describe the viscoelastic property of the cable material. A mathematical model that describes the nonlinear planar response of a viscoelastic cable with small equilibrium curvature is presented first. And then a method of investigating the mean square response and the almost sure asymptotic stability of the response solution is presented and regions of instability are charted. Finally , the almost sure asymptotic stability condition of a viscoelastic cable with small curvature under narrow band excitation is obtained.展开更多
基金the National Natural Science Foundation of China(Nos.10332030 and 10772159)Research Fund for Doctoral Program of Higher Education of China(No.20060335125).
文摘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 averaging 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 Itō 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 reduced Fokker-Planck-Kolmogorov （FPK） equation associated with the completed averaged Itō 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.
文摘The nonlinear planar mean square response and the random stability of a viscoelastic cable that has a small curvature and subjects to planar narrow band random excitation is studied. The Kelvin viscoelastic constitutive model is chosen to describe the viscoelastic property of the cable material. A mathematical model that describes the nonlinear planar response of a viscoelastic cable with small equilibrium curvature is presented first. And then a method of investigating the mean square response and the almost sure asymptotic stability of the response solution is presented and regions of instability are charted. Finally , the almost sure asymptotic stability condition of a viscoelastic cable with small curvature under narrow band excitation is obtained.
