Hopf bifurcation control for stochastic dynamical system with nonlinear random feedback method. (English) Zbl 1235.93231
Summary: Hopf bifurcation control in nonlinear stochastic dynamical system with nonlinear random feedback method is studied in this paper. Firstly, orthogonal polynomial approximation is applied to reduce the controlled stochastic nonlinear dynamical system with nonlinear random controller to the deterministic equivalent system, solvable by suitable numerical methods. Then, Hopf bifurcation control with nonlinear random feedback controller is discussed in detail. Numerical simulations show that the method provided in this paper is not only available to control the stochastic Hopf bifurcation in nonlinear stochastic dynamical system, but is also superior to the deterministic nonlinear feedback controller.
MSC:
| 93E03 | Stochastic systems in control theory (general) |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93B52 | Feedback control |
Keywords:
stochastic dynamical system; random parameter; random feedback control method; orthogonal polynomial approximationReferences:
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