Based On The Non-adaptive Neural Network Control Problems

This paper mainly deals with the problem of nonlinear adaptive control with neural networks(NN) that can not be solved by conventional adaptive control. This paper is composed of three parts.--Introduction of the problemThere are several kinds of control designs for nonlinear adaptive system. For two concrete examples of nonlinear continuous systems and nonlinear discrete systems, this thesis obliterate the key obstacle that is encountered when solving the problem of adaptive control by NN.One of the important prerequisites for NN to approximate the nonlinear function f(x) is the states x of the system should be in a compact set. Therefore, the unkown unlinear systems can be expressed by NN and a model error e(x), and there exists a positive constant 6 such that e(x) < 8. So the problem can be incorporated into robust adaptive control. But if the key prerequisite in the above conclusion that the states of system x lie in a compact set can not be satisfied, the conclusion can not be used. For continuous systems and discrete systems, we uses two diffrent designs respectively in this thesis to prove that the states of systems lie in a compact set, thus obtain a series of good conclusions by using NN approximating nonlinear functions.HI. An continuous exampleMagnetic levitation systems are widely used in various fields shch as highspeed maglev passenger trains, levitation of wind tunnel models, vibration isolation of sensitive machinery, levitation of molten metal in induction furnaces. Since a magnetic levitation system is usually strongly nonlinear and open-loop unstable, it is an important task to construct a hign performance feedback controller to control the position of the levitated object. High performance control of a magnetic levitation system of attractive type in the presence of papameter uncertainties isof particular interest.For an example of ralative degree one:where supposed that xi is in a compact U first, then it proved that the state of system is bounded by using NN approximating nonlinear function. It is an unstrict conclusion. Under a relatively relaxed assumption, based on RBF NN and using backstepping design, this article obtains a robust adaptive controller.where is the adaptive feedback linearization control term, us is a robust control term.By using Lyapunov function, we get the adaptive lawwhere n = 1,2, ---N, r\ > 0, r2 > 0 are adaptive gain,Z1 = xi - yr,^2 = ? -ai, is the output of the RBF neural network designed by this paper to approxmite .The above design satisfies the following objectives: At first, the state of system should be proved bounded, then nonlinear function can be expressed by NN model and a model error. In terms of feedback control and adaptive law, we get conclusions as follows:(1). All the signals of the system are all bounded and the concrete bounds are found.where e and / are constants.(3). If is squarely integrable, that is ,thenandwhere----An discrete exampleThis part of the paper deals with the adaptive control problem of nonlinear discrete systems based on RBF NN. When the nonlinear function of the system is bounded or satisfies some kind of linear increasing assumption,we prove the states of system being in a compact set, and can be expressed by RBF NN and a model error. Then we can find a feedback control and an adaptive law , which assure that the following conclusions hold:(1). All signals are all globally stable. That is for all are constants.(2). The tracking error should be as small as possible. is a given reference signal, , m is a constant.