使用神經(jīng)網(wǎng)絡(luò)的非線性隨機(jī)系統(tǒng)雙效適應(yīng)控制畢業(yè)論文文獻(xiàn)翻譯

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1、 自 動(dòng) 化 專(zhuān) 業(yè) 英 語(yǔ) 論 文 學(xué)號(hào)： 姓名： 班級(jí)：自動(dòng)化09-02 Dual Adaptive Control of Nonlinear Stochastic Systems Using Neural Networks Introduction The use of neural networks for adaptive control of the affined class of nonlinear systems in discrete time has been recently investigated.

2、The neural networks are included for modeling the system functions which are assumed to be unknown. Adaptive laws are used to adjust the network parameters so as to obtain a good control performance. The approaches taken so far in neural adaptive control typically adopt a heuristic certainty equiva

3、lence procedure. This implies that the network approximations are used in a control law as if they were the true system functions, completely ignoring their uncertainty. When the uncertainty is large, for example during start-up, this can lead to an inadequate transient response. To take the uncerta

4、inty of unknowns into consideration, a stochastic adaptive approach can be taken. This leads to the so-called dual control principle introduced by Fel’dbaum in the 1960’s. Dual adaptive control has been analyzed mainly for adaptive control of linear systems with unknown parameters or for nonlinear s

5、ystems having known functions but whose state must be estimated. Because of the advantages associated with it, there has been a recent resurgence of research on dual control. However, none of these addresses the problem when the system is nonlinear and the functions are unknown. Hence, in this work

6、 we investigate the use of adaptive control for the affined class of nonlinear, discrete-time systems when the nonlinear functions are unknown and a stochastic additive disturbance is present at the output. Two types of neural work are considered for modeling the unknown functions. In Section 2 a br

7、ief overview of dual control is given. Section 3 develops a conclusion. Dual Control The advantages of dual control follow because the resulting system will possess the dual features of (i) taking the system state optimally along a desired trajectory, with due consideration given to the uncertain

8、ty of the parameter estimates and (ii) eliciting further information so as to reduce future parameter uncertainty, thereby improving the estimation process. Effect (i) is called caution because, in providing the tracking function, the controller does not use the estimated parameters blindly as if th

9、ey are true. Effect (ii) is called probing because the controller generates signals that encourage faster parameter convergence. Such a controller is said to be actively adaptive. Dual control can offer improvement over other adaptive schemes, particularly when the control horizon is short, the init

10、ial parameter uncertainty is large or the parameters are changing rapidly. It has exhibited improved performance in practical applications such as economic system optimization and chip refiner control in the pulp industry. Technically, a dual controller aims at finding a control input u(t) which mi

11、nimizes the N-stage criterion: J=E{} 　　(44.1) Where y(t) is the system reference input, y(t) is the controlled output, E{ } denotes mathematical expectation taken over all random variables, including the parameters, and Y is the information state at time t defined as: Y={y(t

12、)…y(0)u(t-1)…u(0)}. In principle, this control input can be found by solution of the so-called Bellman equation, via dynamic programming. However, in most practical situations, this is impossible to implement because it involves operations that highly computationally and memory intensive. For this

13、reason, most practical adaptive controllers disregard completely the dual features proposed by Fel’dbaum and are referred to as nondual controllers. Two such examples often result in an inadequate transient response; the former exhibiting large overshoot and the latter, slow response time. Some of

14、the neural network control schemes proposed in literature, being of the HCE type, avoid the serious overshoot and stability problems that might arise from neglecting caution by the first performing intensive, open-loop, off-line training to identify the plant and reduce the prior uncertainty of the

15、parameters. Then a control and identification phase is started, with the neural network parameters set to these pre-trained values, which are substantially close to the actual values. In our case, this pre- training phase is avoided and parameter uncertainty is taken into consideration and influence

16、d by a control law derived from dual adaptive principles. This is more efficient and economical in practical applications because the off-line training scheme can be time consuming and hence expensive. The approach to solve the problem of complexity associated with Bellman’s equation is to derive c

17、ontrol laws that are practically implementable but which, to a certain extent, retain the desirable properties of the ideal dual controller, i.e. caution and probing. This approach does not lead an exact solution of Bellman’s equation and so, such controllers are called suboptimal dual. They can be

18、broadly into the implicit and explicit type. This investigation will use an explicit type suboptimal dual approach based on that described by Milito et al. for suboptimal control of linear stochastic systems, but extended to the case of stochastic, discrete-time, affined nonlinear systems. Gaussian

19、 radial basis function and sigmoidal multilayer perception neural networks are both considered for modeling the unknown nonlinear system functions. Conclusions The main contribution of the paper is to show how dual control concepts can be applied to neural adaptive control of unknown nonlinear sys

20、tems that are subjected to stochastic disturbances. This method has the advantage of improving the transient response of the system, especially during start-up when the uncertainty of the parameter estimates is high. The system developed is based on the innovations of dual controller as originally p

21、roposed by Milito et al. for linear systems. It was shown that the advantages of this design, namely superior performance over nondual controllers and a relatively simple control law, also hold for the more complex case of neural adaptive control of affined nonlinear systems. In particular, the subo

22、ptimal dual controller takes into consideration parameter uncertainty by introducing caution-like effects. Hence control and estimation are performed simultaneously from the outset; eliminating the necessity of preceding the control phase with an off-line, open-loop system identification phase, as i

23、s typically the case with indirect-adaptive HCE neural network control schemes. At the same time, the level of caution can be varied so as to reduce unacceptably slow responses. Both Gaussian RBF and sigmoidal MLP networks have been used for learning for the unknown nonlinearities. The network trai

24、n algorithms were based on Kalman filters for the RBF case and extended Kalman filter theory for the MLP case. Simulation results have been presented and the advantage of utilizing a suboptimal dual approach has been confirmed by Monte Carlo analysis. Issues for further research include evaluation o

25、f the conditions under which the assumptions taken in the derivation of the MLP control law are justified and analysis of the stability properties of the closed loop system. Translation 使用神經(jīng)網(wǎng)絡(luò)的非線性隨機(jī)系統(tǒng)雙效適應(yīng)控制 引言 關(guān)于一類(lèi)離散時(shí)間的非線性系統(tǒng)自適應(yīng)控制中神經(jīng)網(wǎng)絡(luò)應(yīng)用問(wèn)題，近來(lái)已有了很多研究。神經(jīng)網(wǎng)絡(luò)用在對(duì)系統(tǒng)的建模工作中，而該模型的系統(tǒng)函數(shù)假定是未知的。自適應(yīng)規(guī)律用來(lái)調(diào)整網(wǎng)絡(luò)

26、參數(shù)以便獲得良好的控制性能。 至今以來(lái)，用于神經(jīng)自適應(yīng)控制中具有代表性的方法都用到了啟發(fā)性的可靠性等效過(guò)程。這就意味著，完全忽略了網(wǎng)絡(luò)的不確定性，而將網(wǎng)絡(luò)近似值當(dāng)作真實(shí)系統(tǒng)用在控制規(guī)律中。當(dāng)不確定性很大時(shí)，例如在啟動(dòng)過(guò)程中，這種做法會(huì)導(dǎo)致不恰當(dāng)?shù)貢簯B(tài)響應(yīng)。為了考慮未知當(dāng)中的不確定性，可以采用隨即自適應(yīng)的方法。這就導(dǎo)致了20世紀(jì)60年代由Fel’dbaum引入的所謂雙效控制原理。至今已經(jīng)研究過(guò)的雙效自適應(yīng)控制主要用于含有未知參數(shù)的線性系統(tǒng)和含有已知函數(shù)但其狀態(tài)必須被估計(jì)的非線性系統(tǒng)的自適應(yīng)控制中。由于其相關(guān)的優(yōu)越性，雙效控制的研究近來(lái)已經(jīng)有了復(fù)蘇。然而，沒(méi)有人致力于解決系統(tǒng)為非線性及系統(tǒng)函數(shù)為

27、未知的問(wèn)題。 因此，本文我們將研究雙效自適應(yīng)控制在一類(lèi)非線性、離散時(shí)間系統(tǒng)中的應(yīng)用，并且系統(tǒng)的非線性函數(shù)是未知的以及在系統(tǒng)輸出上加上隨機(jī)干擾。第二節(jié)給出雙效控制的簡(jiǎn)短概述。第三節(jié)是結(jié)論。 雙效控制 雙效控制系統(tǒng)的優(yōu)越性來(lái)源于最終系統(tǒng)具有雙重特征：（i）使系統(tǒng)沿最優(yōu)的軌跡變化，并對(duì)參數(shù)估計(jì)的不確定性予以考慮，以及（ii）得出進(jìn)一步的信息而降低以后參數(shù)的不確定性，因此改善了估計(jì)過(guò)程。效應(yīng)（i）被稱(chēng)之為警戒效應(yīng)，這是因?yàn)樵谔峁└櫣δ軙r(shí)，控制器并不會(huì)盲目地將估計(jì)的參數(shù)當(dāng)作真實(shí)值來(lái)加以利用。效應(yīng)（ii）稱(chēng)為試探效應(yīng)，原因是控制器能產(chǎn)生加快參數(shù)收斂的信號(hào)。這就是積極自適應(yīng)控制器。雙效控制能夠提供對(duì)

28、其他自適應(yīng)方案的改進(jìn)作用，特別當(dāng)控制范圍很短、初始參數(shù)的不確定性很大或參數(shù)變化很快的時(shí)候更是如此。在一些特殊的應(yīng)用場(chǎng)合，例如在經(jīng)濟(jì)系統(tǒng)的最優(yōu)化以及紙漿工業(yè)的碎屑均料機(jī)控制中，雙效控制都展示了改善系統(tǒng)性能的作用。 典型情況而言，一個(gè)雙效控制器的目的就是要找出一個(gè)控制作用輸入u（t）使得如下N階準(zhǔn)則達(dá)到最?。? J=E{} 　　(44.1) 其中y是系統(tǒng)參考輸入，y（t）是受控的輸出，E{ }表示所有隨機(jī)變量（其中包括參數(shù)）的數(shù)學(xué)期望，而Y是時(shí)刻t的信息狀態(tài)，定義為：Y={y(t)…y(0)u(t-1)…u(0)}。 理論上講，這一控制輸入能夠通過(guò)

29、求解所謂貝爾曼方程，由動(dòng)態(tài)規(guī)劃而獲得。然而在大多數(shù)實(shí)際應(yīng)用場(chǎng)合，卻不可能做到這一點(diǎn)，這是因?yàn)閷?duì)計(jì)算量和存儲(chǔ)量的要求都過(guò)于龐大。由于這個(gè)原因，大多數(shù)實(shí)際自適應(yīng)控制器完全不管Fel’dbaum的雙效特征，僅僅涉及到非雙效的控制器。這種情況的兩個(gè)例子是推斷確定性等價(jià)（HCE）和警戒控制器。這些控制器經(jīng)常導(dǎo)致不恰當(dāng)?shù)臅簯B(tài)響應(yīng)，前者的超調(diào)量大而后者響應(yīng)太慢。 文獻(xiàn)中提到的有些HCE類(lèi)型神經(jīng)網(wǎng)絡(luò)控制方案，避免了嚴(yán)重的超調(diào)量以及穩(wěn)定性問(wèn)題。該問(wèn)題之所以可能產(chǎn)生，其原因是忽視了對(duì)這樣一種情況的警戒：為了將受控對(duì)象辨識(shí)出來(lái)，并且為了降低先期參數(shù)的不確定性而首先進(jìn)行了徹底的開(kāi)環(huán)、離線訓(xùn)練。隨后才將神經(jīng)網(wǎng)絡(luò)的參數(shù)

30、設(shè)置到這些預(yù)先訓(xùn)練好的數(shù)值（基本上接近真實(shí)值），接著開(kāi)始一個(gè)控制和辨識(shí)階段。在我們的工作中，避免了這一預(yù)先訓(xùn)練階段，對(duì)參數(shù)的不確定性就可以予以考慮了。通過(guò)一個(gè)由雙效自適應(yīng)原理導(dǎo)出的控制規(guī)律還可以影響這種不確定性。這樣的做法在實(shí)際應(yīng)用中更為有效和經(jīng)濟(jì)，原因是離線訓(xùn)練法可能耗時(shí)，因而耗資。 為了解決其復(fù)雜性與貝爾曼方程緊密相關(guān)的問(wèn)題，一種方法是要推導(dǎo)出特殊的控制規(guī)律。此控制規(guī)律應(yīng)該是可以實(shí)現(xiàn)的，但在一定程度上要保持理想雙效控制的期望特性，即警戒和試探。這一方法并不直接導(dǎo)致貝爾曼方程精確解的獲得，因此這樣的控制器被稱(chēng)之為次優(yōu)雙效的。他們大致可以分為隱式和顯式兩種類(lèi)型。 本研究將使用一種顯式類(lèi)型的

31、次優(yōu)雙效方法。該方法基于Milito等人為線性隨機(jī)系統(tǒng)的次雙優(yōu)控制而提出的內(nèi)容，但將其推廣到一類(lèi)隨機(jī)離散時(shí)間非線性系統(tǒng)的情況。高斯徑向基函數(shù)和S型多層感知器神經(jīng)網(wǎng)絡(luò)都用來(lái)對(duì)未知非線性系統(tǒng)建摸。 結(jié)論 本文的貢獻(xiàn)是表明了對(duì)于受到隨機(jī)干擾的未知非線性系統(tǒng)如何將雙效控制的概念應(yīng)用到神經(jīng)自適應(yīng)控制中。這一方法具有改善系統(tǒng)暫態(tài)響應(yīng)的優(yōu)點(diǎn)，特別是在系統(tǒng)啟動(dòng)時(shí)，參數(shù)估計(jì)的不確定性很高的情況下，更為顯著。所建的系統(tǒng)基于一種對(duì)最初由Milito等人為線性系統(tǒng)而提出的雙效控制器的改進(jìn)形式。本文能夠說(shuō)明：這一設(shè)計(jì)的優(yōu)點(diǎn)，即優(yōu)于非雙效控制器并具有較為簡(jiǎn)單的控制規(guī)律，更復(fù)雜情況下在一類(lèi)非線性系統(tǒng)的神經(jīng)自適應(yīng)控制中仍

32、然能夠保持。特別是，次優(yōu)雙效控制器考慮到了由類(lèi)似警戒效應(yīng)引入的參數(shù)不確定性問(wèn)題。因此，能夠同時(shí)從最初開(kāi)始執(zhí)行控制和估計(jì)這兩項(xiàng)工作，而不必像應(yīng)用間接自適應(yīng)HCE神經(jīng)網(wǎng)絡(luò)控制方案的典型情況那樣，非要先用一個(gè)離線、開(kāi)環(huán)系統(tǒng)辨識(shí)階段來(lái)處理控制階段的工作。同時(shí)，境界的水也可以根據(jù)情況調(diào)整以便減弱響應(yīng)的現(xiàn)象。 高斯RBF和S形MLP兩種神經(jīng)網(wǎng)絡(luò)都用于對(duì)未知非線性的學(xué)習(xí)。網(wǎng)絡(luò)運(yùn)算算法的基礎(chǔ)在RBF的情況下是卡爾曼濾波器，而在MLP情況下是擴(kuò)展的卡爾曼濾波器。仿真結(jié)果在文中已經(jīng)給出，而使用次優(yōu)雙效方法的優(yōu)越性已經(jīng)被蒙特卡洛法所證實(shí)。進(jìn)一步的研究工作包括對(duì)于在推導(dǎo)MLP控制規(guī)律時(shí)所采用假設(shè)條件的評(píng)價(jià)以及對(duì)閉環(huán)系統(tǒng)穩(wěn)定性的分析。