Finite-Time Stability Analysis And Control Design For Nonlinear Systems With Lower-Triangular Structures

Finite-time control for nonlinear systems with lower-triangular structures is a research hotspot in control theory,and it has received extensive attention from many scholars.On the one hand,almost all actual systems are nonlinear.Many nonlinear systems,such as electromechanical systems,circuit systems,and mobile robots,etc.,can be modeled or transformed into nonlinear systems with lower-triangular structures.On the other hand,the finite-time control systems have the advantages of fast convergence,strong robustness and wide application range.With ever-growing demands of control system performances in modern industries and the rapid development of precision machinery manufacturing,aerospace and other industries,the existing finite-time control theory is facing more challenges.Therefore,the research on the finite-time control has both theoretical and practical significance for nonlinear systems with lower-triangular structures.This dissertation mainly contains three parts.The first part focuses on nonlinear systems with lower-triangular structures subject to external disturbances.In detail,the finite-time bounded control is studied for planar lower-triangular nonlinear systems subject to mismatched disturbances,and the finite-time regulation control is investigated for lower-triangular nonholonomic systems subject to matched disturbances.The second part concentrates on the fixed-time stability analysis and stabilization control for lower-triangular nonlinear systems with monotone degrees.The third part aims at the prescribed finite-time stabilization and regulation for several classes of nonlinear systems with lower-triangular structures.Specifically,the main contents of this dissertation can be summarized as below:1.Finite-time bounded and regulating controllers will be constructed for nonlinear systems with lower-triangular structures subject to external disturbances.First,planar lower-triangular nonlinear systems are considered subject to mismatched disturbances.By introducing a new state transformation,the systems with mismatched disturbances are transformed into that without disturbances.A controller with a new structure is constructed by improving the adding a power integrator technique,which realizes the finite-time bounded control for the considered systems.Then,for lower-triangular nonholonomic systems with matched disturbances,a new state transformation is used to transform the systems into that without disturbances.Based on a new inequality and the adding a power integrator technique,a class of"semi-linear" integral controllers are proposed,under which the finite-time regulation is achieved for the considered systems.(Chapter 2 in the dissertation)2.Fixed-time stabilizing controllers will be designed for lower-triangular nonlinear systems with monotone degrees.First,an extended fixed-time stability criterion is presented,which can explicitly give the Lyapunov function and ensure its continuous differentiability in the whole definition domain.Then,by the adding a power integrator technique and the proposed extended fixed-time stability criterion,the fixed-time state feedback stabilizing controllers are put forward for lowertriangular nonlinear systems with monotone degrees,and partial state constraints of the considered systems are not violated.(Chapter 3 in the dissertation)3.Prescribed finite-time controllers will be proposed for several classes of nonlinear systems with lower-triangular structures.First,the lower-triangular nonlinear systems with essential time-varying characteristics are studied.By a new state transformation based on time-varying high-gain parameters,the construction of prescribed finite-time stabilizing controllers is transformed into the selection of dynamic parameters.The dynamic parameters are further selected,which achieves the prescribed finite-time stabilization for the studied systems.Then,the lower-triangular nonholonomic systems are considered,where the growth rate is an unknown constant or essential time-varying function.With the help of the input-sate-scaling technique,a new state transformation is employed with time-varying high-gain parameters.The controllers are then constructed based on the prescribed finite-time observers,which guarantees the prescribed finite-time output feedback regulation and stabilization for the considered systems.Finally,the lower-triangular nonlinear multi-agent systems are investigated with an unknown essential time-varying growth rate.An error system consisting of the leader and followers is defined,and the prescribed finite-time regulation problem of the multi-agent systems is thus transformed into that of the error system.Together a new state transformation with the time-varying high-gain parameters,the consensus protocols are designed to achieve the prescribed finite-time distributed regulation for the multi-agent systems.(Chapter 4 in the dissertation)4.A bounded gain-based prescribed finite-time stabilizing control strategy is proposed for a class of lower-triangular nonlinear systems with a constant growth rate.First,a state transformation based on two dynamic parameters is employed to convert designing the prescribed finite-time stabilizing controller into designing the two dynamic parameters.Then,by virtue of the temporal scale transformation,the design problem of the dynamic parameters in t domain is transformed into the design problem of the dynamic parameters in ? domain.Finally,based on the traditional finite-time Lyapunov stability theorem,the two bounded dynamic parameters are determined,which ensures the prescribed finite-time stabilization for the considered systems.(Chapter 5 in the dissertation)In summary,this dissertation designs a series of finite-time,fixed-time and prescribed finite-time control strategies for nonlinear systems with lower-triangular structures.The main contributions are summarized as follows:1.A class of controllers with new structure are presented,which effectively deals with external disturbances and guarantees the finite-time convergence of system states;2.The extended fixed-time stability criterion is introduced and the fixed-time stabilizing control strategy is proposed;3.The prescribed finite-time stabilizing and regulating control strategies are proposed,which provides a new research idea for the prescribed finitetime control of nonlinear systems with lower-triangular structures.