Research On Nonsmooth Control Of Several Classes Of Uncertain Nonlinear Systems

In recent years,non-smooth control system has been an important research topic in the field of nonlinear control,because non-smooth control methods can not only be applied to more general systems but also improve the convergence speed and disturbance rejection performance of the closed-loop system.The contents mainly involve global adaptive finite-time stabilization of uncertain time-varying p-normal nonlinear systems without homogeneous growth nonlinearity restriction,semi-global output feedback control for uncertain nontriangular nonlinear systems with sector-bounded unknown measurement,semi-global active disturbance rejection control of a class of uncertain nonlinear systems,event-triggered state feedback control for p-normal uncertain nonlinear systems,event-triggered tracking control for nonlinear systems subject to time-varying external disturbances.The main findings and contributions of the dissertation are summarized as follows:(1)The problem of global finite-time stabilization for p-normal nonlinear systems subject to uncertain time-varying control coefficients and vanishing nonlinear uncertainties without homogeneous growth restriction is investigated by a new dual-layer adaptive approach.Firstly,by virtue of the tool of adding a power integrator,a non-smooth state feedback controller is designed for the nominal system.Secondly,a new duallayer adaptive mechanism is proposed to deal with the uncertainties of the system.The first layer mainly focuses on handling the nonlinear uncertainties induced by unknown growth rate.The second layer of the adaptive mechanism utilizing an adaptive gain approach is developed to dynamically dominate time-varying control coefficients and complex nonlinear terms without homogeneous growth restriction.Finally,by using the homogeneous domination approach,an adaptive finite-time stabilizer is successfully constructed.Compared with the conventional adaptive finite-time control methods,the proposed control scheme is applicable to nonlinear systems with nonhomogeneous growth condition.(2)The problem of semi-global stabilization for nontriangular nonlinear systems with unknown control coefficients and uncertain output function is investigated by a semi-global output feedback control strategy,and the feasible sector bound of the unknown output function under the proposed control scheme is given.Firstly,a novel non-recursive design combined with the homogeneous systems theory is used to design the global state feedback controller of the nominal system.Meanwhile,the homogeneous domination approach is adopted to counteract the effect of the uncertain nonlinearities.Secondly,a new reduced-order observer based on the output is designed to estimate the unmeasurable states.Thirdly,based on the proposed state feedback controllers and the reduced-order observer,a semi-global output feedback controller is designed,and the sector bound of output function is determined by stability analysis.Compared with the conventional output feedback backstepping control methods,the proposed semi-global output feedback domination control scheme can quantitatively analyze the feasible sector bounded of the unknown output function.(3)The robust control problem of a class of nonlinear systems subject to external disturbances and nonlinear uncertainties is investigated by a semi-global active disturbance rejection control strategy.Firstly,the lumped uncertainties including uncertain nonlinear functions and external disturbances are observed by designing a nonlinear estimator.Secondly,a continuous saturation-based controller is designed based on the uncertainty estimation information and system states.Finally,according to the semi-global stability theory,several sets depending on the initial values of both system and observer states are constructed,and the strict qualitative robust performance analysis of the closed-loop system is given by using the above sets.Compared with the related existing results,based on the semi-global stability theory,the proposed control strategy relaxes the constraint that both the lumped uncertainty and its derivative with respect to time are bounded by some constants.(4)The problem of event-triggered control for a class of p-normal uncertain nonlinear systems is investigated by fixed and relative threshold strategies.Firstly,due to the fact that the traditional backstepping method can only solve the global control problem of strictly feedback nonlinear systems,the adding a power integrator technology is used to design a continuous virtual control signal for p-normal nonlinear systems with higher-order powers.Secondly,an event-triggered mechanism is proposed based on the fixed/relative threshold strategy by the designed continuous virtual controller.Finally,a rigorous Lyapunov stability analysis method is put forward to verify that all the signals of the closed-loop system are globally uniformly bounded and converge to an arbitrarily small set around origin.Compared with the conventional event-triggered control methods,the proposed control scheme can successfully solve the event-triggered control for p-normal nonlinear systems.(5)The problem of event-triggered tracking control for a class of nonlinear systems with disturbances is investigated.Firstly,the estimation of the steady states is achieved by using finite-time disturbance observers.Secondly,by the adding a power integrator technology,a continuous virtual controller is designed for the error system,which is obtained based on the original system and the steady-state estimation system.Finally,with the help of the continuous virtual controller,the event-triggered mechanism based on the relative threshold strategy is designed to ensure that the tracking error is ensured to converge to a set around origin,which can be made as small as desired by adjusting control parameters.Compared with the conventional event-triggered control methods,the proposed control scheme reduces the complexity of traditional event-triggered tracking control design.