Research On Finite-time Adaptive Control For Some Uncertain Nonlinear Systems

Under the framework of adaptive backstepping control,this thesis presents some adaptive finite-time tracking control schemes for several classes of uncertain nonlinear control systems.Fuzzy logic systems and radial basis function(RBF)neural networks are adopted to approximate the unknown nonlinear functions.A new finite-time stability criterion is developed,making the adaptive tracking control scheme more suitable in the practice than traditional methods.The detail contents of this thesis are stated as follows:Chapter 2 considers an adaptive finite-time tracking control issue for a class of nonlinear systems with unmodeled dynamics.By proposing a new finite-time stability criterion,a novel adaptive neural control strategy is developed by backstepping technique.Compared with the existing researches,the unknown nonlinear functions in the considered system do not satisfy the linear growth conditions assumption.Under the presented controller,the desired system performance is realized in finite time.Finally,a numerical example is presented to demonstrate the effectiveness of the proposed control method.Chapter 3 presents a novel adaptive finite-time tracking control scheme for nonlinear systems with time-varying delays.The radial basis function neural networks(RBFNNs)are adopted to approximate the unknown nonlinear functions.A state observer is constructed to estimate the unmeasurable state variables.Based on the finite-time stability criterion proposed in chapter 2,a novel adaptive controller for the uncertain systems with time-varying delays is developed by constructing exponential Lyapunov-Krasovskii functionals.Under the presented controller,the desired system performance is realized in finite time.Finally,a numerical example is presented to demonstrate the effectiveness of the proposed control method.In chapter 4 to chapter 6,the finite time adaptive control for uncertain nonlinear systems with input nonlinear is considered.Chapter 4 considers adaptive finite-time tracking control issue for two classes of nonlinear systems with unknown hysteresis.First,a fuzzy adaptive controller is proposed for the nonlinear systems with non-strict-feedback structure on foundation of the backstepping technology.We proved that the states of the closed-loop system are bounded in a finite time under the designed controller,even though unknown hysteresis in the actuator is considered.The validity of the proposed control scheme is demonstrated by an example.Then,Chapter 4 investigates the adaptive finite-time tracking control issue for a class of multi-input and multi-output(MIMO)nonlinear systems with unknown hysteresis via backstepping technique.A constructive adaptive backstepping control scheme is presented,realizing the finite-time stability of the closed-loop system,when the system states are unmeasurable.Chapter 5 improves the finite time stability criterion proposed in chapter 2.The improved finite time stability criterion reduces design difficulty of the adaptive fuzzy controllers.Based on this stability criterion,an adaptive fuzzy control scheme for uncertain nonlinear systems with dead-zone input is proposed,realizing the finite time stability of the closed-loop system.Chapter 6 considers the asymmetric backlash nonlinearity in the actuator.A new smooth inverse model is developed to approximate the asymmetric actuator backlash arbitrarily.The adaptive fuzzy control scheme is proposed based on the finite time stability criterion proposed in the chapter 5,and the finite time stability of the closed loop system is realized.Finally,a simulation example verifies the effectiveness of the proposed control method.