Adaptive Switching Control For Uncertain Nonlinear Systems And Its Applications

Based on the adaptive Backstepping method and Lyapunov stability theory,the stability problem of uncertain nonlinear switched systems under arbitrary switching is studied.This thesis is divided into two parts: The first part mainly discusses how to design a desirable adaptive controller to make sure that the tracking error could eventually fall into the predefined neighborhood;the second part mainly considers how to realize that the state of the nonlinearly parameterized switched system converge to equilibrium point in finite-tine.That is,how to realize that the considered closed-loop system is the finite-time stable.This thesis are summarized as follows:The first part considers the tracking control problem of uncertain nonlinear switched systems with known tracking accuracy.Firstly,the tracking control problem of linear parameterized systems is discussed.By introducing two bilaterally smooth functions,combined the Backstepping method and Lyapunov stability theory,a common Lyapunov function for all subsystems and an adaptive controller are designed.Secondly,the above algorithm is extended to a more general system,and the tracking control problem of nonlinear parametric switched systems is studied.The variable separation method is adopted to separate the unknown parameters from the nonlinearly parameterized functions.Based on the existing algorithm,a common Lyapunov function is redesigned,and an adaptive controller is developed.Finally,the experimental results show that the above two proposed control methods are effective.It is proved that all signals of the closed-loop control system keep bounded and the tracking accuracy satisfies the performance index given in advance.Then,the asymptotic stability of the close-loop system is proved by Barbalat lemma.In the second part,we will further discuss the finite-time control issue for the aforementioned nonlinearly parameterized switched system.First,based on the adding a power integrator technique and the Lyapunov stability theory,a common Lyapunov function with power function terms is designed.Then,the variable separation method is borrowed to deal with nonlinear parameter terms,which simplifies the difficulty of the controller design.Subsequently,based on the Backstepping method,an adaptive finite-time control scheme is proposed.Finally,a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.It is proved that the closed-loop system is globally finite-time stable,and guaranteed that all signals of the closed-loop system converge to the small neighborhood of zero point in finite time.