使用神经网络的非线性随机系统双效适应控制毕业论文文献翻译.doc

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1、自动化专业英语论文学号： 姓名： 班级：自动化09-02Dual Adaptive Control of Nonlinear Stochastic Systems Using Neural NetworksIntroductionThe use of neural networks for adaptive control of the affined class of nonlinear systems in discrete time has been recently investigated. The neural networks are included for modeling

2、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 equivalence procedure. This implies that the network a

3、pproximations 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 uncertainty of unknowns into consideration, a stochasti

4、c adaptive approach can be taken. This leads to the so-called dual control principle introduced by Feldbaum in the 1960s. Dual adaptive control has been analyzed mainly for adaptive control of linear systems with unknown parameters or for nonlinear systems having known functions but whose state must

5、 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 we investigate the use of adaptive control for the

6、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 brief overview of dual control is given. Section 3 dev

7、elops a conclusion. Dual ControlThe 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 uncertainty of the parameter estimates and (ii) eliciting further

8、 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 they are true. Effect (ii) is called probing because the c

9、ontroller 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 initial parameter uncertainty is large or the parameters are

10、 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 minimizes the N-stage criterion: J=E (44.1)Where y(t) is the

11、 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)y(0)u(t-1)u(0).In principle, this control input can be found by solution of the so-called B

12、ellman 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 reason, most practical adaptive controllers disregard completely the dual features proposed by Fe

13、ldbaum 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 the neural network control schemes proposed in literature, being of the HCE type, avoid the serious

14、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 parameters. Then a control and identification phase is started, with the neural network parameters s

15、et 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 influenced by a control law derived from dual adaptive principles. This is more efficient and economical in p

16、ractical applications because the off-line training scheme can be time consuming and hence expensive.The approach to solve the problem of complexity associated with Bellmans equation is to derive control laws that are practically implementable but which, to a certain extent, retain the desirable pro

17、perties of the ideal dual controller, i.e. caution and probing. This approach does not lead an exact solution of Bellmans equation and so, such controllers are called suboptimal dual. They can be broadly into the implicit and explicit type.This investigation will use an explicit type suboptimal dual

18、 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 radial basis function and sigmoidal multilayer perception neural networks are both considered for modelin

19、g the unknown nonlinear system functions.ConclusionsThe main contribution of the paper is to show how dual control concepts can be applied to neural adaptive control of unknown nonlinear systems that are subjected to stochastic disturbances. This method has the advantage of improving the transient r

20、esponse 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 proposed by Milito et al. for linear systems. It was shown that the advantages of this design, namely superior

21、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 suboptimal dual controller takes into consideration parameter uncertainty by introducing caution-like effects. Hen

22、ce 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 is typically the case with indirect-adaptive HCE neural network control schemes. At the same time, the level of

23、 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 train algorithms were based on Kalman filters for the RBF case and extended Kalman filter theory for the MLP case. S

24、imulation 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 of the conditions under which the assumptions taken in the derivation of the MLP control law are justified and an

25、alysis of the stability properties of the closed loop system.Translation使用神经网络的非线性随机系统双效适应控制引言待添加的隐藏文字内容1关于一类离散时间的非线性系统自适应控制中神经网络应用问题，近来已有了很多研究。神经网络用在对系统的建模工作中，而该模型的系统函数假定是未知的。自适应规律用来调整网络参数以便获得良好的控制性能。至今以来，用于神经自适应控制中具有代表性的方法都用到了启发性的可靠性等效过程。这就意味着，完全忽略了网络的不确定性，而将网络近似值当作真实系统用在控制规律中。当不确定性很大时，例如在启动过程中，这种

26、做法会导致不恰当地暂态响应。为了考虑未知当中的不确定性，可以采用随即自适应的方法。这就导致了20世纪60年代由Feldbaum引入的所谓双效控制原理。至今已经研究过的双效自适应控制主要用于含有未知参数的线性系统和含有已知函数但其状态必须被估计的非线性系统的自适应控制中。由于其相关的优越性，双效控制的研究近来已经有了复苏。然而，没有人致力于解决系统为非线性及系统函数为未知的问题。因此，本文我们将研究双效自适应控制在一类非线性、离散时间系统中的应用，并且系统的非线性函数是未知的以及在系统输出上加上随机干扰。第二节给出双效控制的简短概述。第三节是结论。双效控制双效控制系统的优越性来源于最终系统具有双

27、重特征：（i）使系统沿最优的轨迹变化，并对参数估计的不确定性予以考虑，以及（ii）得出进一步的信息而降低以后参数的不确定性，因此改善了估计过程。效应（i）被称之为警戒效应，这是因为在提供跟踪功能时，控制器并不会盲目地将估计的参数当作真实值来加以利用。效应（ii）称为试探效应，原因是控制器能产生加快参数收敛的信号。这就是积极自适应控制器。双效控制能够提供对其他自适应方案的改进作用，特别当控制范围很短、初始参数的不确定性很大或参数变化很快的时候更是如此。在一些特殊的应用场合，例如在经济系统的最优化以及纸浆工业的碎屑均料机控制中，双效控制都展示了改善系统性能的作用。典型情况而言，一个双效控制器的目的

28、就是要找出一个控制作用输入u（t）使得如下N阶准则达到最小： J=E (44.1)其中y是系统参考输入，y（t）是受控的输出，E 表示所有随机变量（其中包括参数）的数学期望，而Y是时刻t的信息状态，定义为：Y=y(t)y(0)u(t-1)u(0)。理论上讲，这一控制输入能够通过求解所谓贝尔曼方程，由动态规划而获得。然而在大多数实际应用场合，却不可能做到这一点，这是因为对计算量和存储量的要求都过于庞大。由于这个原因，大多数实际自适应控制器完全不管Feldbaum的双效特征，仅仅涉及到非双效的控制器。这种情况的两个例子是推断确定性等价（HCE）和警戒控制器。这些控制器经常导致不恰当的暂态响应，前者

29、的超调量大而后者响应太慢。文献中提到的有些HCE类型神经网络控制方案，避免了严重的超调量以及稳定性问题。该问题之所以可能产生，其原因是忽视了对这样一种情况的警戒：为了将受控对象辨识出来，并且为了降低先期参数的不确定性而首先进行了彻底的开环、离线训练。随后才将神经网络的参数设置到这些预先训练好的数值（基本上接近真实值），接着开始一个控制和辨识阶段。在我们的工作中，避免了这一预先训练阶段，对参数的不确定性就可以予以考虑了。通过一个由双效自适应原理导出的控制规律还可以影响这种不确定性。这样的做法在实际应用中更为有效和经济，原因是离线训练法可能耗时，因而耗资。为了解决其复杂性与贝尔曼方程紧密相关的问题

30、，一种方法是要推导出特殊的控制规律。此控制规律应该是可以实现的，但在一定程度上要保持理想双效控制的期望特性，即警戒和试探。这一方法并不直接导致贝尔曼方程精确解的获得，因此这样的控制器被称之为次优双效的。他们大致可以分为隐式和显式两种类型。本研究将使用一种显式类型的次优双效方法。该方法基于Milito等人为线性随机系统的次双优控制而提出的内容，但将其推广到一类随机离散时间非线性系统的情况。高斯径向基函数和S型多层感知器神经网络都用来对未知非线性系统建摸。结论本文的贡献是表明了对于受到随机干扰的未知非线性系统如何将双效控制的概念应用到神经自适应控制中。这一方法具有改善系统暂态响应的优点，特别是在系

31、统启动时，参数估计的不确定性很高的情况下，更为显著。所建的系统基于一种对最初由Milito等人为线性系统而提出的双效控制器的改进形式。本文能够说明：这一设计的优点，即优于非双效控制器并具有较为简单的控制规律，更复杂情况下在一类非线性系统的神经自适应控制中仍然能够保持。特别是，次优双效控制器考虑到了由类似警戒效应引入的参数不确定性问题。因此，能够同时从最初开始执行控制和估计这两项工作，而不必像应用间接自适应HCE神经网络控制方案的典型情况那样，非要先用一个离线、开环系统辨识阶段来处理控制阶段的工作。同时，境界的水也可以根据情况调整以便减弱响应的现象。高斯RBF和S形MLP两种神经网络都用于对未知非线性的学习。网络运算算法的基础在RBF的情况下是卡尔曼滤波器，而在MLP情况下是扩展的卡尔曼滤波器。仿真结果在文中已经给出，而使用次优双效方法的优越性已经被蒙特卡洛法所证实。进一步的研究工作包括对于在推导MLP控制规律时所采用假设条件的评价以及对闭环系统稳定性的分析。