Adaptive Fast Finite-Time Control For Nonlinear Systems With Unknown Control Directions

Due to the fact that there are many unknown control directions in practical systems,the control problem of nonlinear systems with unknown control directions has attracted many scholars' attention.Considering that the fast finite-time control method makes the system have faster convergence speed and higher control accuracy,so this paper studies the global switching adaptive fast finite-time control problem for two kinds of nonlinear systems with unknown control directions based on the global fast finite-time control method and the logic switching adaptive control technology.The main contents of this paper are summarized as follows:1.The global switching adaptive fast finite-time stabilization problem was addressed for a class of nonlinear systems with multiple unknown control directions.Aiming at this class of nonlinear systems,a new global switching adaptive fast finite-time control strategy was proposed by combining backstepping method,fast finite-time control method with switching adaptive control technology.And the design method of the global switching adaptive fast finite-time controller was provided.By designing the fast finite-time logic switching law and adaptively adjusting the switching parameters online,the control direction of the controller can be changed according to the proposed switching logic,and the correct control direction of the system can be found quickly.The designed controller can guarantee the closed-loop system being globally fast finite-time stable,namely,all the system states can be converged to equilibrium point within a finite-time.The result can not be achieved by the Nussbaum gain technology.The simulation results show that the proposed control strategy was effective.2.The global switching adaptive fast finite-time stabilization control problem was addressed for a class of p-normal form nonlinear systems with multiple unknown control directions.We consider that the sign of the virtual control coefficient representing the control direction in p-normal form nonlinear systems was unknown,and the power p of the system was considered as a ratio of two odd integers.The design method of global switching adaptive fast finite-time controller for p-normal form nonlinear systems with unknown control direction was given by combining backstepping method,adding power integrator technique,fast finite-time control method,logic switching adaptive control technology and a new coordinate transformation.The designed controller can guarantee the closed-loop systems being globally fast finite-time stable,namely,all the system states can be converged to equilibrium point within a finite-time.The simulation results show that the proposed control strategy was effective.