Research On Several Problems Based On Finite-Time Control Theory

The analysis and synthesis of finite-time control is an important research issue in the field of nonlinear control. Compared with conventional smooth control methods, finite-time control method can not only provide faster convergence rate for closed-loop systems, but also improve the anti-disturbance ability of the closed-loop systems. This dissertation will study the position tracking control of pneumatic servo system, the stabilization problem of second-order system with mismatched disturbances and the output consensus of second-order multi-agent systems with mismatched disturbances based on finite-time control theory. The main contents of this dissertation include state observer design of the pneumatic servo system, output feedback controller design for position tracking problem of pneumatic servo system, active anti-disturbance control design of the stabilization problem of second-order systems with mismatched disturbances, output consensus protocol design of second-order multi-agent systems with mismatched disturbances.Firstly, for the position tracking control problem of the pneumatic servo system, finite-time output feedback control algorithm is designed. First, in the case of without velocity sensors, a finite-time state observer is designed to estimate the piston velocity. Then, for the tracking error system, a global finite-time state feedback control algorithm is developed based on the adding a power integrator method. Finally, based on the state feedback controller and the estimates of the piston velocity, a local finite-time output feedback controller is given. While there is no external disturbances in the system, the stability analysis of the closed-loop system is presented. While the system is affected by external disturbances, steady-state error convergence domain of the closed-loop system is given exhibitively. Compared with backstepping based output feedback control method, the proposed finite-time output feedback control method provides a faster convergence velocity and a higher tracking accuracy.Secondly, for the stabilization problem of second-order systems with mismatched disturbances, a composite control algorithm is designed based on disturbance feedforward compensation and finite-time control. To estimate the system disturbances and the unknown state information, a finite-time extended state observer is constructed firstly. Then, based on the disturbance feedforward compensation and output feedback control, by utilizing homogeneity theory, a composite controller is developed, which globally stabilizes the disturbed system.Thirdly, for the output consensus problem of second-order multi-agent systems with mismatched disturbances, finite-time composite consensus protocols with disturbances feed-forward compensation are designed. For each agent, a finite-time extended state observer is constructed to estimate the disturbances and the unknown state. Then, based on the disturbance feedforward compensation and output feedback control, a finite-time composite consensus protocol is developed with homogeneity theory. The finite-time output consensus of multi-agent systems is realized under the proposed consensus protocols.