Two Nonlinear Dynamic Surface Control System

Time-delay systems and stochastic systems are very important systems in practical engi-neering application and of great research value. Compared with general systems, time-delaysystems and stochastic systems have more complex structures. In recent years, researchmethod such as backstepping control is widely used in the control feld, but the “diferentialexplosion” problem appears in its design process, which make the calculation of the controllerquite large. To overcome this defect, the dynamic surface control method is proposed. How-ever, the dynamic surface control method for nonlinear systems still has some disadvantagesin adjustment of too much parameters online. Therefore, in this paper we will make a com-bination of dynamic surface technique and neural network control scheme, and propose anew adaptive control method which is based on dynamic neural network. This new adaptivecontrol method not only overcomes the defects in the backstepping design procedure, butalso solves the problem of adjusting too much parameters online, which greatly reduces theamount of calculation. In this paper, a class of time-delay system and stochastic systemwith dead zone are studied based on dynamic neural network control method. The mainresults include the following two parts:1) Adaptive dynamic surface control of a class of non afne nonlinear systems with timedelay.For a class of time-delay systems with unknown state delay and uncertain disturbances,the design of the controller and the stability analysis is studied. In order to make theunknown non-afne function has explicit control input, we use the mean value theorem fordecomposition, after which we give out the dynamic surface control design based on neuralnetworks. Firstly, the unknown functions are packaged and approximated by neural network.Then, we use Lyapunov-Kraoskii functional to compensate for the time-delay uncertainties.Finally, we make stability analysis and give out a simulation example to show the efectivenessof the controller design.2) Output feedback adaptive dynamic surface nerve network control of a class of uncer-tain stochastic systems with dead zone.The design of the controller for a class of uncertain stochastic systems with dead zonebased on output feedback adaptive dynamic surface nerve network control is studied. Firstof all, we design the observer for the system. Then, the design of the controller and stabilityanalysis based on the dynamic surface control are proposed. We approximate all the unknown function with only one neural network, RBF neural network is used to compensate fora a suitable unknown constants. Finally, a simulation example is proposed to prove thecorrectness of the result and the efectiveness of the control method.