Adaptive Neural Network Control Of Nonlinear Systems Within Predetermined Approximation Sets

Neural network are often used to deal with unknown dynamics in complex nonlinear systems due to its powerful learning and reasoning capabilities.The neural network control design of uncertain nonlinear systems has received widespread attention and research,and a large number of fruitful results have emerged.It is worth pointing out that the existing research results all depend on the neural network universal approximation theorem.For the purpose of ensuring that the neural network can effectively approximate/fit the unknown dynamics of the nonlinear system,the neural network universal approximation theorem requires that the input signal of the neural network is always stay within a certain approximation set.However,the approximation set cannot be predetermined accurately,which will lead to the inability of the neural network to effectively compensate the unknown dynamics of the system.This deficiency severely limits the reliability of the neural network control method and becomes an important bottleneck restricting the further development of the neural network control field.In order to solve this predetermined approximation set problem,this thesis mainly conducts the following researches on uncertain nonlinear systems with unknown dynamics:(1)An adaptive neural network tracking control problem within a predetermined approximation set is explored for a class of strictly feedback uncertain nonlinear systems with unknown dynamics.First,the unknown dynamic state variables of the system are replaced by a vector consisting of the system state error,the desired expected tracking signal and its higherorder derivative,and the optimal weight estimator of the neural network through the signal replacement technique,which is used as the input signal of the neural network.Seccond,the state error is restricted by the barrier function,and the estimated value range of the optimal weight of the neural network is solved by combining the differential equation theory.The neural network approximation set is quantitatively predetermined,so that the neural network can dispose of the unknown dynamics of the system.The tracking control is achieved without the system model information,and the validity of the developed algorithm is illustrated by a simulation example.(2)An adaptive neural network tracking control problem within a predetermined approximation set is explored for a class of uncertain high-order nonlinear systems with unknown powers.By using signal replacement technology,barrier function,differential equation theory,and using related inequality scaling,an adaptive neural network controller is designed that does not depend on the unknown power and power upper and lower bounds of high-order nonlinear systems,and the neural network approximation set is predetermined.The designed controller can not only achieve that all signals of the closed-loop system are consistent bounded,but also realize the tracking control within a predetermined neural network approximation set.The simulation results illustrate that the designed controller can effectively deal with the situation of unknown model information and unknown power information.(3)An adaptive neural network asymptotic tracking control problem within a predetermined approximation set is explored for a class of uncertain nonlinear systems with unknown control gains.Based on the signal permutation technology and the barrier function,the input signal of the neural network is always kept within a certain known approximation set,which ensure the effective and reliable approximation ability of the neural network.The proposed algorithm ensures asymptotic tracking control performance without involving any prior knowledge of the system model.Simulation results demonstrate the effectiveness and correctness of the proposed algorithm.