Flat Zone Adaptive Control Of A Disturbed Nonlinear System

In the study of control theory,the research of robust adaptive control of linear systems have been unable to meet our need to solve practical problems.In the real life,most model have serious nonlinearity,so the control theory of nonlinear systems has been favored by the majority of researchers.There are many factors affecting the nonlinear system,such as dead zone,external disturbance,uncertain parameters and so on,so it is difficult to study the control problem of the nonlinear system with the approximate linear model.With the development of technology and the rich knowledge of theory,the author puts forward an adaptive algorithm to solve the robust adaptive control of nonlinear output feedback system.In this paper,we consider two cases of robust adaptive control problem for nonlinear output feedback systems with unknown bounded disturbances,i.e.,the known and unknown highfrequency gain symbols.The main sections are listed as follow:(1)For the nonlinear system whose high frequency gain is known,designing a new dead zone function to replace the sign function to make the virtual design of control design is continuous,and the relative order of system is extended to arbitrary order.A simple observer is designed to reduce the order of the filter effectively,and to improve the stable performance of the system in the adaptive design.A new adaptive control algorithm is proposed to estimate the unknown disturbance and unknown parameters and the Lyapunov theorem which based on flat zone is applied to achieve the estimation for unknown bound.The backstepping design method is applied to handle the cross term of different stages in the design process.Finally,it is proved that all system parameters are stable and the tracking error is converged to the origin of a particular neighborhood.(2)For a class of nonlinear systems with unknown high-frequency gain,in order to eliminate the influence of the high-frequency gain,a new Nussbaum function is constructed and the proportional function in the first step control design is introduced.The method of tuning function is used to remove overparameterized problem.The estimated number of unknown parameters and disturbance error are reduced,which improve the stable performance of the system.The new dead zone function designed,observer and the stability theorem based on Nussbaum function are used to estimate the unknown bound.It is proved that all variables of the closed-loop system are bounded and the asymptotic tracking of tracking error can be achieved.