Finite Time Control Algorithms Design And Implementation For Nonlinear Systems Without Initial State Constraints

Due to the complexity and uncertainty of practical nonlinear systems,the research on nonlinear systems has become one of the hot spots and difficulties in the control field for a long time.Scholars are committed to designing control algorithms that can be more suitable for the actual industrial environment to improve the control performance.Finite time control theory is more suitable for practical needs because it avoids the limitations of traditional control law design methods.In recent years,fruitful research results have been achieved in relevant fields.However,most of them are aimed at low-order nonlinear systems and are easily disturbed by the initial state of the system,or there are a lot of differential and derivative operations in the controller design,which can easily lead to the failure of the actual system.This thesis takes two kinds of complex nonlinear systems as the research object.Based on the finite-time stability theory,combined with backstepping technology and the sliding mode control method,two finitetime control strategies without the initial state constraints of the systems are proposed,which can achieve the finite-time convergence of the systems while reducing the amount of computation.The main research work of this thesis are as follows:(1)Research of finite time control algorithm without initial state constraintsIn this thesis,a class of simple low-order nonlinear systems is taken as an example,and the basic model of finite-time controller which can make the system converge to the given boundary in a finite time is proposed,and the convergence time is not affected by the initial states of the system.The basic model of the controller is simulated by Matlab,and its effectiveness and generalization are proved.Then the low-order finite-time control algorithm is extended to the more universal high-order strict feedback control system based on backstepping method,and the stability and convergence of the system are analyzed and proved by designing appropriate Lyapunov functions,and the feasibility and applicability of the algorithm are proved by simulation.(2)Research of finite time guidance algorithm without initial launch constraintsConsidering the scene of a missile attacking a stationary target in threedimensional space,the three-dimensional nonlinear missile-target relative motion model is derived,the finite time guidance law without initial launch condition constraints is designed based on the sliding mode control theory in this thesis,and the designed sliding mode dynamic surface can converge to zero in finite time,which can be proved by constructing the appropriate Lyapunov function.The effectiveness and feasibility of the algorithm are verified by Matlab.The simulation results indicate that this guidance strategy effectively avoids the limitations of traditional guidance methods,and can not only meet the dual requirements of miss distance and attack angle but also be applicable to missiles of different types of structures and different initial launch conditions.(3)Simulation implementation of two finite time control algorithmsTwo finite time control algorithms proposed in this thesis can be simulated and validated by Matlab software.The simulation results show that the two finite time control algorithms can make the nonlinear systems meet the expected performance,and are effective and feasible.The finite time control algorithm designed for the strict feedback nonlinear system can make the system converge to the given boundary in a finite time,and the convergence time does not depend on the initial state;The finite time guidance algorithm designed based on a threedimensional nonlinear missile target relative motion model can enable missiles to accurately strike targets without being affected by initial launch conditions.