Barrier Function-based Adaptive Neural Networks Control For Uncertain High-order Nonlinear Systems

For the past few years,the control design of high-order nonlinear systems has attracted extensive attention from researchers in the domestic and overseas.In addition,with the advancement of modern information technology,the model of the control system becomes more and more complicated,such as the system nonlinear or system parameters are unknown,but the traditional design method of nonlinear control often requires the accurate dynamic model,gives the system control design difficulties and challenges.The adaptive control method combined with neural network(NN)can well deal with the control design problems of these kind of uncontrollable modal nonlinear systems.Therefore,the high-order nonlinear systems with completely unknown nonlinear adaptive neural network control research has attracted wide attention of research workers,and achieved some results,but there are still many difficult to solve,such as: how to design a controller for a class of high-order nonlinear systems with unknown power? How to extend the power range to the set of unknown positive odd rational numbers? This paper will study this kind of problem.In this paper,several different uncertain high-order nonlinear systems are analyzed and studied.The main research contents are as follows:1.For a class of uncertain high-order nonlinear systems,a novel adaptive NN control algorithm is proposed by fusing barrier function,NN and backstepping design without knowing the prior information of the system model.By using the barrier function and the qualitative theory of differential equation,it is proved that the input signal of neural network is always kept in a certain approximation set under the action of the proposed control strategy.Then,an adaptive controller is constructed by the backstepping recursive design method.The controller not only ensures that all closed-loop signals are bounded,but also ensures that the output tracking error converges to an arbitrarily small residual set.2.The problem of adaptive neural network output tracking control for a class of uncertain high-order nonlinear systems with unknown powers.Compared with the existing research results,the high-order nonlinear system considered in this chapter does not need to know not only the system nonlinear function,but also the power information of the system.A novel adaptive neural network control algorithm is proposed by combining neural network,barrier Lyapunov function and backstepping method.The main characteristic of this algorithm is that the designed adaptive neural network(NN)controller does not depend on the unknown power of the high-order nonlinear system,and can ensure that all the closed-loop signals are bounded.3.The problem of adaptive neural network(NN)tracking control for a class of uncertain high-order nonlinear systems with unknown positive odd rational powers.Without incorporating a priori information of system model,a novel adaptive neural network control algorithm is proposed by combining neural network,barrier Lyapunov function and backstepping method.By using the barrier function and the qualitative theory of differential equation,it is proved that the input signal of neural network is always kept in a certain approximation set under the action of the proposed control strategy.Then,an adaptive controller is constructed by the backstepping recursive design method.Worth pointing out that the controller designed by this algorithm can not only ensure in each of the highorder subsystem,the power of high-order nonlinear system for the unknown and odd rational numbers,and ensures that all closed-loop signals are bounded.