Research On Strict Feedback Nonlinear System With Unknown Control Direction

In practical applications,system nonlinearity and uncertainty cannot be ignored,and the presence of these issues poses an impediment to the design of system controllers.The problem of unknown control directions(UCD)as a class of uncertainty problem means that the sign of the gain coefficient of system is uncertain.The gain coefficient is the term in front of control input of the system,also known as the control direction of the system.Therefore,it is necessary to consider the effect of UCD problem in the system modeling and analysis when designing a feedback control strategy.In this paper,based on Lyapunov stability theory,backstepping control method,Nussbaum gain functions and radial basis neural network,the adaptive control problem of a class of nonlinear systems with UCD is investigated.The work of this paper is divided into three sections as follows.1.The control problem of strict-feedback systems with unmodeled dynamics and UCD is solved.The sign of the control input is monitored by Nussbaum gain functions,and a dynamic signal is added to solve the problem of unmodeled dynamics.For the uncertain terms in the system,a radial basis neural network is used,and dynamic surface control is applied to eliminate complexity explosion problem in the backstepping method.The boundedness of the system can be proved.2.The control problem of strict-feedback systems with input time-delay and UCD is studied.The Pade approximation and Laplace transform are used in the algorithm to eliminate the effect of input time lag on the system,and a symmetric barrier Lyapunov function is applied to deal with the static restraints present in the system.The above method is combined with the backstepping method and neural network to propose a new adaptive control law that can ensure all states in the closed-loop system can reach semi-globally uniformly ultimately bounded.3.The control problem of strict-feedback nonlinear systems with UCD and asymmetric timevarying restraints is studied,and the output constraints of the system are asymmetric and time-varying.The controller design process is simplified by transforming the output restraints so as to obtain simpler controllers,which results in a significant reduction in computational effort.The proposed controller can ensure the stability of the closed-loop system,and by selecting the proper control parameters,the tracking error can be ideal.