Study Of Fixed-Time Control For A Class Of Uncertain Nonlinear Affine Systems

With the continuous development of nonlinear system control theory,in recent years,more and more scholars have pointed out the limitations of the traditional limited time control in theory and practice.Main reason is that convergence time of the finite time control associated with the initial state of the system,the system of the initial condition increases with the increase of the convergence time also,and the theoretical system of the initial condition tends to infinity the convergence time will also go to infinity,finite time control in some of these adverse factors make convergence time has strict requirements of the system is no longer applicable,such as the consistency of multi-agent tracking,multiple autonomous underwater vehicles(AUVS)cooperative formation control,etc.In order to solve this problem,theories and concepts related to fixed time control have been put forward and widely used in recent years.Compared with the finite time control,the fixed time control has stronger robustness and stability,and the upper bound of its convergence time is independent of the initial conditions of the system and only related to the parameters of the controller.However,the design of fixed time controller is more complex and difficult.In addition,there are many input and output constraints in many practical systems,such as saturation,dead zone and output constraints,which bring great challenges to the realization of fixed time convergence of the system.However,at present,there is little information about how to solve the input-output constraint problem of nonlinear system under the fixed time control framework.Therefore,the main research contents of this paper are as follows:1.A new adaptive neural network state feedback controller is designed for fixed time control of uncertain nonlinear affine systems with external disturbances and unknown input dead zone.In the controller design,a virtual feedback controller is designed based on the classical inverse design method and the fixed time stability lemma.Then,two radial basis neural networks are used to compensate the adverse effects of unknown input dead zone,and another nonlinear system function is approximately unknown.Finally,by analyzing the stability of the system,it is proved that the signals in the closed-loop system are bounded.Finally,the control method is applied to a simulation example and a lithography machine motion platform.Thesimulation and experimental results show the effectiveness of the control algorithm.2.A new adaptive neural network state feedback controller is designed for fixed time control of uncertain nonlinear affine systems with external disturbances,unknown input dead zone and output constraints.In the controller design,a new virtual feedback controller is designed by combining a logarithmic barrier lyapunov function with a reverse step design method.At the same time,radial basis neural network is used to compensate unknown input dead zone and approximate unknown nonlinear system function.By analyzing the stability of the system,it is proved that the output of the closed-loop system satisfies the preset constraints and the signals of the closed-loop system are bounded.Finally,the control method is applied to a simulation example and a lithography machine motion platform.The simulation and experimental results show the effectiveness of the control algorithm.