Prescribed Finite-time Control Design For A Class Of Nonlinear Systems

With the increasing complexity of the controlled objects in many high-tech fields such as intelligent manufacturing and aerospace,the control system exhibits highly complex nonlinear characteristics.On the other hand,with the continuous improvement of the control quality requirements of the system,the traditional control methods are difficult to satisfy the requirements.Therefore,the study of control problems of nonlinear systems with performance constraints has become one of the frontier research issues in the international control field.In some practical applications,the asymptotic stability is sometimes difficult to satisfy the needs of practical problems,and the finite-time stability is a desirable property.Therefore,this paper studies the problem of the prescribed finite-time control design for a class of nonlinear systems by considering the singularity of the control gain,the constraint of the output,and the non-overshoot of the tracking,is studied.A recursive design algorithm with prescribed finite-time stabilization based on the structural characteristics of nonlinear systems is proposed.Provide effective tools for controller design of nonlinear systems with prescribed performance.Further develop and improve the control theory and design method of nonlinear systems.The main research contents are as follows:In Chapter 1,a review of nonlinear systems,finite-time stability,and several system properties is presented.In Chapter 2,the prescribed finite-time stabilization of nonlinear systems with control singularities is studied.Firstly,the error variable is introduced by using backstepping method,and the control Lyapunov function and the corresponding controller are constructed at the same time,so that the state of the closed-loop nonlinear system can converge to the equilibrium point in any finite-time.Second,since the constructed Lyapunov function grows unbounded on the set where the controller becomes unbounded,and its level set always remains within the feasibility region,which makes the feasibility region have positive invariance,ensuring that all trajectories do not cross the control singular set.It realizes that the feasibility region of the system is consistent with the attraction region,thereby maximizing the attraction region.Finally,a simulation example verifies the effectiveness of the proposed method.In Chapter 3,the prescribed finite-time tracking of nonlinear systems with time-varying output constraints is studied.First,for the problem of the prescribed finite-time tracking of nonlinear systems with time-varying output constraints,a sufficient condition for its solvability is proposed.In order to satisfy the time-varying output constraint,by applying the asymmetric time-varying barrier Lyapunov function method,the tracking error transformation is used to eliminate the the dependence of the barrier Lyapunov function on time.Second,a novel virtual stabilizing function is constructed by proposing a method of adding a additional fractional term,which is capable of decreasing the asymmetric time-varying barrier Lyapunov function to the origin within prescribed settling time.Then,based on the backstepping method,a recursive design algorithm is proposed to construct the controller,to ensure that the output trajectory always remains between the asymmetric time-varying output constraints and converges to the desired trajectory within the settling time.Finally,two examples are given to illustrate the effectiveness of the proposed method.In Chapter 4,the prescribed finite-time tracking control for nonlinear systems with guaranteed performance is studied.The prescribed performance in this chapter includes two aspects:time-varying output constraints and non-overshooting response.First,the time-varying barrier Lyapunov function method is applied,and the tracking error transformation is used to eliminate the dependence of the proposed barrier Lyapunov function on time.Second,by using the L_GV-backstepping method,a recursive algorithm is proposed to construct the controller and barrier Lyapunov functions such that the output trajectory converges to the desired trajectory within the settling time.Then,in order to achieve the prescribed performance,appropriate design parameters are selected according to the initial conditions and the initial value of the desired trajectory derivative to ensure that all initial conditions of the closed-loop system are negative.Finally,two examples are used to illustrate the effectiveness of the method proposed in this chapter.In Chapter 5,the main research work of the paper is summarized,and looks forward to the next research work and direction.