A nonlinear stochastic optimal time-delay control strategy for quasi-integrable Hamiltonian systems is proposed. First, a stochastic optimal control problem of quasi-integrable Hamiltonian system with time-delay in feedback control subjected to Gaussian white noise is formulated. Then, the time-delayed feedback control forces are approximated by the control forces without time-delay and the original problem is converted into a stochastic optimal control problem without time-delay. After that, the converted stochastic optimal control problem is solved by applying the stochastic averaging method and the stochastic dynamical programming principle. As an example, the stochastic time-delay optimal control of two coupled van der Pol oscillators under stochastic excitation is worked out in detail to illustrate the procedure and effectiveness of the proposed control strategy.
|Journal||Communications in Nonlinear Science and Numerical Simulation|
|Publication status||Published - 2011|
- Stochastic optimal control
- Quasi-integrable Hamiltonian system
- Stochastic averaging
Feng, J., Zhu, W-Q., & Liu, Z-H. (2011). Stochastic optimal time-delay control of quasi-integrable Hamiltonian systems. Communications in Nonlinear Science and Numerical Simulation, 16(8), 2978-2984. https://doi.org/10.1016/j.cnsns.2010.11.020