發(fā)布時(shí)間：2018-07-08 21:20

  本文選題：隨機(jī)系統(tǒng) + 統(tǒng)計(jì)特征��； 參考：《西安理工大學(xué)》2016年博士論文

【摘要】：世界充滿不確定性,從量子系統(tǒng)到一般的工業(yè)系統(tǒng),無不如此。隨機(jī)系統(tǒng)控制理論經(jīng)歷了半個(gè)多世紀(jì)的研究,在均值、方差這兩個(gè)低階統(tǒng)計(jì)特征控制方面已經(jīng)取得了一系列理論成果,并廣泛應(yīng)用于航空航天、工業(yè)生產(chǎn)等實(shí)際工程領(lǐng)域。然而,現(xiàn)有的隨機(jī)控制方法存在著兩個(gè)方面的問題:一是僅針對(duì)外部干擾噪聲或測(cè)量噪聲的不確定性進(jìn)行處理,無法同時(shí)兼顧系統(tǒng)參數(shù)本身的不確定性,而系統(tǒng)的數(shù)學(xué)模型是對(duì)實(shí)際過程的近似,一些情況下必然存在著參數(shù)的不確定性;二是受控系統(tǒng)的結(jié)構(gòu)往往限定為線性系統(tǒng),這樣僅通過均值、方差這兩個(gè)低階統(tǒng)計(jì)特征的控制就能夠?qū)崿F(xiàn)系統(tǒng)的整體性能,而對(duì)于非線性系統(tǒng)來說,僅僅均值和方差并不足以表征系統(tǒng)的完整特征。顯然,傳統(tǒng)的隨機(jī)控制理論已經(jīng)無法很好的滿足當(dāng)前的控制需求。本文針對(duì)存在不確定參數(shù)線性隨機(jī)系統(tǒng)的低階統(tǒng)計(jì)特征控制以及非線性隨機(jī)系統(tǒng)的完全統(tǒng)計(jì)特征控制進(jìn)行了深入研究,并將部分研究成果應(yīng)用于車輛懸架控制系統(tǒng)。主要研究?jī)?nèi)容如下:1、針對(duì)隨機(jī)系統(tǒng)存在多個(gè)子模型的情況,把大系統(tǒng)的分解-協(xié)調(diào)思想引入到多模型控制中,以各子模型的后驗(yàn)概率作為協(xié)調(diào)變量,將多個(gè)子模型的控制律進(jìn)行融合歸一,利用歸一后的模型對(duì)系統(tǒng)進(jìn)行控制,獲得一種新的低階統(tǒng)計(jì)特征控制策略。采用融合模型控制方法,能夠在系統(tǒng)的控制過程中減少模型切換導(dǎo)致的響應(yīng)抖動(dòng)影響,有效改善控制過程的平滑性。2、針對(duì)系統(tǒng)參數(shù)發(fā)生飄移且變化量服從高斯分布的系統(tǒng),提出一種次優(yōu)低階統(tǒng)計(jì)特征控制方法。該方法基于對(duì)性能指標(biāo)跟蹤與參數(shù)辨識(shí)的雙重考慮,把系統(tǒng)輸出的最小方差和系統(tǒng)參數(shù)的估計(jì)協(xié)方差矩陣融入到衡量控制優(yōu)劣的性能指標(biāo)中進(jìn)行綜合分析,設(shè)計(jì)出一種具有學(xué)習(xí)和控制權(quán)衡效果的次優(yōu)對(duì)偶控制策略。3、針對(duì)非線性隨機(jī)系統(tǒng),研究了矩逼近完全統(tǒng)計(jì)特征控制問題。首先假設(shè)對(duì)系統(tǒng)施行干預(yù)的控制律為狀態(tài)響應(yīng)的多項(xiàng)式反饋,同時(shí)把動(dòng)態(tài)方程中的非線性函數(shù)進(jìn)行泰勒展開。然后導(dǎo)出了隨機(jī)狀態(tài)響應(yīng)各階矩的遞推方程,該方程的解為控制增益的函數(shù)。最后,為使被控制的概率密度函數(shù)形狀具有期望的形式,構(gòu)造了一個(gè)優(yōu)化問題,并通過梯度法搜索出最優(yōu)控制增益,實(shí)現(xiàn)了完全統(tǒng)計(jì)特征的有效控制。4、進(jìn)一步研究了非線性隨機(jī)系統(tǒng)完全統(tǒng)計(jì)特征精確控制問題。通過把概率密度函數(shù)展開為多項(xiàng)式以及指數(shù)多項(xiàng)式的方法,研究了幾種分析途徑,成功推導(dǎo)出穩(wěn)態(tài)概率密度函數(shù)和隨機(jī)系統(tǒng)控制增益的關(guān)系。尤其是通過把概率密度函數(shù)展開為指數(shù)多項(xiàng)式的方法,推導(dǎo)出指數(shù)函數(shù)泰勒展開系數(shù)與待求反饋控制增益間的一一精確對(duì)應(yīng)關(guān)系。然后,根據(jù)目標(biāo)概率密度函數(shù)的不同情況,分別給出了采用本方法的跟蹤控制策略。5、針對(duì)一類具備半主動(dòng)式懸架系統(tǒng)的越野車輛,應(yīng)用本文提出的融合思想的多模型低階統(tǒng)計(jì)特征控制方法進(jìn)行懸架系統(tǒng)的控制研究。首先建立半主動(dòng)式懸架系統(tǒng)控制動(dòng)力學(xué)模型,在此基礎(chǔ)上得到其對(duì)應(yīng)的連續(xù)時(shí)間狀態(tài)方程,并對(duì)其進(jìn)行離散化處理。然后分別針對(duì)車輛重載和輕載情況建立了不同的運(yùn)行模型,設(shè)計(jì)出對(duì)應(yīng)的控制器。仿真分析展示了該方法的有效性。最后,對(duì)全文進(jìn)行了概括性總結(jié),并指出有待進(jìn)一步研究和完善的問題。
[Abstract]:The world is full of uncertainty, from quantum systems to general industrial systems. The theory of stochastic system control has gone through more than half a century of research. A series of theoretical results have been obtained in the two low order statistical characteristics control of mean and variance, and it is widely used in practical engineering fields such as aerospace, industrial production and so on. There are two problems in the existing stochastic control methods: one is to deal with the uncertainty of the external interference noise or the measurement noise, and the uncertainty of the system parameters can not be taken into account at the same time. The mathematical model of the system is similar to the actual process. In some cases, the uncertainty of the parameters is inevitable; two is the uncertainty of the parameters. The structure of a controlled system is often limited to a linear system, so that the overall performance of the system can be achieved only through the control of the two low order statistical characteristics of mean and variance, but for nonlinear systems, only the mean and variance are not sufficient to characterize the complete characteristics of the system. It is obvious that the traditional stochastic control theory is not very good. In order to meet the current control requirements, this paper studies the low order statistical characteristics control of the linear stochastic systems with uncertain parameters and the complete statistical characteristics control of the nonlinear stochastic systems. Some research results are applied to the vehicle suspension control system. The main contents are as follows: 1, there are many random systems. In the case of the sub model, the decomposition coordination idea of large system is introduced into the multi model control, and the posterior probability of each sub model is used as the coordination variable. The control law of the multiple sub models is fused, and the system is controlled by the model after the normalization, and a new low order statistical characteristic control strategy is obtained. The fusion model control is adopted. The method can reduce the effect of response jitter caused by model switching in the process of system control and effectively improve the smoothness of the control process. A suboptimal low order statistical feature control method is proposed for the system with which the system parameters are floating and the change quantity obeys Gauss distribution. This method is based on the performance index tracking and parameter identification. In the double consideration, the minimum variance of the system output and the estimated covariance matrix of the system parameters are integrated into the performance index of the control and control. A suboptimal dual control strategy,.3, which has the effect of learning and control, is designed. The moment approximation complete statistical feature control is studied for the nonlinear stochastic system. First, it is assumed that the control law for the intervention of the system is a polynomial feedback of the state response, and the nonlinear function in the dynamic equation is carried out by Taylor expansion. Then the recursive equation of the random state response of each order moment is derived, and the solution of the equation is a function of controlling the gain. Finally, the shape of the controlled probability density function is made to have the shape of the controlled probability density function. In the form of expectation, an optimization problem is constructed, and the optimal control gain is searched by the gradient method. The effective control.4 for complete statistical characteristics is realized. The exact control problem of the complete statistical characteristics of a nonlinear stochastic system is further studied. By expanding the probability density function into a polynomial and an exponential polynomial, a few studies are made. The relationship between the steady-state probability density function and the control gain of the stochastic system is derived successfully. In particular, the exact relation between the exponential function Taylor expansion coefficient and the feedback control gain is derived by expanding the probability density function as an exponential polynomial. Then, the probability density function of the target is based on the probability density function of the target. The tracking control strategy.5 using this method is given in different situations. For a class of off-road vehicles with semi-active suspension system, the multi model low order statistical feature control method proposed in this paper is used to control the control of suspension system. First, a semi-active suspension system control dynamic model is established. On the basis of it, the corresponding continuous time state equation is obtained and discretized. Then different running models are established for heavy load and light load, and the corresponding controller is designed. The simulation analysis shows the effectiveness of the method. Finally, a general summary of the full text is summarized, and it is pointed out that it needs to be further studied. Study and improve the problem.
【學(xué)位授予單位】：西安理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：TP273

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