本文選題：隨機(jī)平均法 + 動(dòng)態(tài)規(guī)劃��； 參考：《廈門(mén)大學(xué)》2014年碩士論文

【摘要】：高斯白噪聲激勵(lì)下的隨機(jī)系統(tǒng)最優(yōu)有界控制問(wèn)題一直是隨機(jī)動(dòng)力學(xué)研究的熱點(diǎn)問(wèn)題,本文針對(duì)這一問(wèn)題研究了具有黏彈性阻尼的隨機(jī)系統(tǒng)的最優(yōu)有界控制問(wèn)題。 第一部分研究了高斯白噪聲激勵(lì)下具有黏彈性阻尼的擬可積非共振哈密頓系統(tǒng)的最優(yōu)有界控制問(wèn)題。首先將黏彈性阻尼的狀態(tài)變量用無(wú)黏彈性的狀態(tài)變量近似,把黏彈性阻尼力分成兩部分：一部分改變系統(tǒng)的保守力；另一部分改變系統(tǒng)的阻尼力。由此得到了無(wú)黏彈性阻尼的擬可積非共振哈密頓系統(tǒng)。再運(yùn)用隨機(jī)平均法,建立相應(yīng)的Ito方程。之后把根據(jù)動(dòng)態(tài)規(guī)劃原理求解得出的半無(wú)限時(shí)間區(qū)間上的最優(yōu)有界控制力代入平均FPK方程。在此基礎(chǔ)上研究了系統(tǒng)的最優(yōu)有界控制問(wèn)題,并研究了不同控制力的控制效果以及控制效率問(wèn)題。結(jié)果表明最優(yōu)有界控制力對(duì)具有黏彈性阻尼隨機(jī)系統(tǒng)有良好的控制作用。 第二部分在前面內(nèi)容的基礎(chǔ)上進(jìn)一步研究了高斯白噪聲激勵(lì)下具有黏彈性阻尼受控哈密頓系統(tǒng)的瞬態(tài)響應(yīng)問(wèn)題。應(yīng)用Galerkin法將瞬態(tài)概率密度近似表示為多重Laguerre正交基函數(shù)的級(jí)數(shù)和,求解得到了能量響應(yīng)的近似瞬態(tài)概率密度。在此基礎(chǔ)上研究了瞬態(tài)響應(yīng)的最優(yōu)有界控制問(wèn)題。結(jié)果表明最優(yōu)有界控制力對(duì)具有黏彈性阻尼哈密頓系統(tǒng)的瞬態(tài)響應(yīng)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.
【學(xué)位授予單位】：廈門(mén)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類(lèi)號(hào)】：TB535

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 戚魯媛;徐偉;高維廷;;色噪聲激勵(lì)Rayleigh-Duffing振子瞬態(tài)響應(yīng)及最優(yōu)有界控制[J];工程力學(xué);2013年12期

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本文編號(hào)：1947989