Optimal Bounded Control for Stationary Response of Strongly Nonlinear Oscillators under Combined Harmonic and Wide-Band Noise Excitations

YongjunWu; ChangshuiFeng; RonghuaHuan

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Optimal Bounded Control for Stationary Response of Strongly Nonlinear Oscillators under Combined Harmonic and Wide-Band Noise Excitations

机译：谐波和宽带噪声激励作用下强非线性振荡器平稳响应的最优有界控制

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We study the stochastic optimal bounded control for minimizing the stationary response of strongly nonlinear oscillators under combined harmonic and wide-band noise excitations. The stochastic averaging method and the dynamical programming principle are combined to obtain the fully averaged Itô stochastic differential equations which describe the original controlled strongly nonlinear system approximately. The stationary joint probability density of the amplitude and phase difference of the optimally controlled systems is obtained from solving the corresponding reduced Fokker-Planck-Kolmogorov (FPK) equation. An example is given to illustrate the proposed procedure, and the theoretical results are verified by Monte Carlo simulation.

机译：我们研究随机最优有界控制，以使谐波和宽带噪声激励下的强非线性振荡器的平稳响应最小。将随机平均方法和动态规划原理相结合，以获得完全平均的Itô随机微分方程，该方程近似描述了原始受控强非线性系统。通过求解相应的简化Fokker-Planck-Kolmogorov（FPK）方程，可以获得最优控制系统的幅值和相位差的平稳联合概率密度。给出了一个实例来说明所提出的过程，并通过蒙特卡洛仿真验证了理论结果。

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《Mathematical Problems in Engineering: Theory, Methods and Applications》 |2011年第2期|共21页
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YongjunWu; ChangshuiFeng; RonghuaHuan;
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1. Optimal Bounded Control for Stationary Response of Strongly Nonlinear Oscillators under Combined Harmonic and Wide-Band Noise Excitations [J] . Yongjun Wu, Changshui Feng, Ronghua Huan Mathematical Problems in Engineering . 2011,第PTa3期

机译：谐波和宽带噪声激励作用下强非线性振荡器平稳响应的最优有界控制
2. Stochastic optimal bounded control for MDOF nonlinear systems under combined harmonic and wide-band noise excitations with actuator saturation [J] . R.C. Hu, W.Q. Zhu Probabilistic engineering mechanics . 2015,第jana期

机译：具有执行器饱和的谐波和宽带噪声组合激励下的MDOF非线性系统的随机最优有界控制
3. Stochastic optimal control of MDOF nonlinear systems under combined harmonic and wide-band noise excitations [J] . Hu R. C., Zhu W. Q. Nonlinear dynamics . 2015,第2期

机译：谐波和宽带噪声激励共同作用下的MDOF非线性系统的随机最优控制
4. Stationary Response of Duffing-van der Pol Oscillator with Delayed Feedback Control under Wide-Band Noise Excitation [C] . Peng Lin, Chang Shui Feng, Qiao Yi Wang ICAM 2012 . 2013

机译：Duffing-Van der POL振荡器在宽带噪声激励下具有延迟反馈控制的静止响应
5. Some Interesting Effects of High-Frequency Non-Resonant Harmonic Excitations on the Slow Response of Duffing Oscillators [D] . Abusoua, Abdraouf. 2018

机译：高频非谐振谐波激发对Duffing振荡器慢响应的一些有趣影响
6. Robust synchronization control scheme of a population of nonlinear stochastic synthetic genetic oscillators under intrinsic and extrinsic molecular noise via quorum sensing [O] . Bor-Sen Chen, Chih-Yuan Hsu 2012

机译：固有和外在分子噪声下的群体感应下的非线性随机合成遗传振荡器的鲁棒同步控制方案
7. Optimal Bounded Control for Stationary Response of Strongly Nonlinear Oscillators under Combined Harmonic and Wide-Band Noise Excitations [O] . Yongjun Wu, Changshui Feng, Ronghua Huan 2011

机译：谐波和宽带噪声激励下强非线性振荡器静止响应的最佳界限控制
8. Response of Multidegree-of-Freedom Systems with Quadratic and Cubic Nonlinearities to Harmonic Excitation, with Application to a Shallow Arch. 2. Multifrequency Excitation [R] . Plaut, R. H. , Mook, D. T. , HaQuang, N. 1984

机译：具有二次和三次非线性的多自由度系统对谐波激励的响应及其在浅拱中的应用。 2.多频激励

Optimal Bounded Control for Stationary Response of Strongly Nonlinear Oscillators under Combined Harmonic and Wide-Band Noise Excitations

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