黏弹性阻尼随机系统最优有界控制及瞬态响应

发布时间：2018-05-28 20:00

本文选题：随机平均法 + 动态规划　；参考：《厦门大学》2014年硕士论文

【摘要】：高斯白噪声激励下的随机系统最优有界控制问题一直是随机动力学研究的热点问题,本文针对这一问题研究了具有黏弹性阻尼的随机系统的最优有界控制问题。第一部分研究了高斯白噪声激励下具有黏弹性阻尼的拟可积非共振哈密顿系统的最优有界控制问题。首先将黏弹性阻尼的状态变量用无黏弹性的状态变量近似,把黏弹性阻尼力分成两部分：一部分改变系统的保守力；另一部分改变系统的阻尼力。由此得到了无黏弹性阻尼的拟可积非共振哈密顿系统。再运用随机平均法,建立相应的Ito方程。之后把根据动态规划原理求解得出的半无限时间区间上的最优有界控制力代入平均FPK方程。在此基础上研究了系统的最优有界控制问题,并研究了不同控制力的控制效果以及控制效率问题。结果表明最优有界控制力对具有黏弹性阻尼随机系统有良好的控制作用。第二部分在前面内容的基础上进一步研究了高斯白噪声激励下具有黏弹性阻尼受控哈密顿系统的瞬态响应问题。应用Galerkin法将瞬态概率密度近似表示为多重Laguerre正交基函数的级数和,求解得到了能量响应的近似瞬态概率密度。在此基础上研究了瞬态响应的最优有界控制问题。结果表明最优有界控制力对具有黏弹性阻尼哈密顿系统的瞬态响应有良好的控制作用。
[Abstract]:The optimal bounded control problem for stochastic systems excited by Gao Si white noise has always been a hot topic in stochastic dynamics. In this paper, the optimal bounded control problem for stochastic systems with viscoelastic damping is studied. In the first part, the optimal bounded control problem for quasi-integrable non-resonant Hamiltonian systems with viscoelastic damping under Gao Si white noise excitation is studied. Firstly, the state variable of viscoelastic damping is approximated to that of non-viscoelastic state, and the viscoelastic damping force is divided into two parts: one is to change the conservative force of the system and the other is to change the damping force of the system. The quasi-integrable nonresonant Hamiltonian systems with non-viscoelastic damping are obtained. Then the Ito equation is established by using the stochastic average method. Then the optimal bounded control force on the semi-infinite time interval obtained by the dynamic programming principle is replaced by the average FPK equation. On this basis, the optimal bounded control problem of the system is studied, and the control effect and control efficiency of different control forces are studied. The results show that the optimal bounded control force has a good control effect on the stochastic system with viscoelastic damping. In the second part, the transient response of Gao Si white noise controlled Hamiltonian systems with viscoelastic damping is studied. The transient probability density is approximately expressed as the series sum of multiple Laguerre orthogonal basis functions by using the Galerkin method, and the approximate transient probability density of the energy response is obtained. On this basis, the optimal bounded control problem of transient response is studied. The results show that the optimal bounded control force has a good control effect on the transient response of the Hamiltonian system with viscoelastic damping.
【学位授予单位】：厦门大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TB535

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