Finite-time Bounded-H_∞ Control For Nonlinear Systems With Prescribed Performance

Nonlinear systems are widely used in practical production systems,such as machinery,metallurgy,aerospace and other engineering systems.The control problems of nonlinear systems have attracted the attention of many scholars in recent years.The prescribed performance control method can guarantee both the steady-state performance and the dynamic performance of the system,but the classical prescribed performance control design method relies on the initial conditions of the controlled variable excessively,and this method will be limited to the control design of the controlled system with unknown initial conditions.Therefore,a new method of prescribed performance control independent of the initial tracking condition is adopted in this thesis.The problem of prescribed performance finite-time bounded-H∞tracking control under unknown initial tracking condition is studied for a class of nonlinear systems with external disturbance.The main research contents of this thesis are as follows:1.Combined backstepping method,prescribed performance control method with finite time control theory,a prescribed performance finite-time tracking control method independent of initial tracking conditions is studied for a class of nonlinear systems with external disturbances.In order to realize the design of the prescribed performance control,a nonlinear mapping and a new error conversion idea are used to design the prescribed performance function,so as to ensure that the initial condition of the constrained variable is independent of the design of the prescribed performance function.The problem that the prescribed performance control depends on the initial condition of the system constrained quantity is solved.In addition,the time when the constrained variables of the system enter the specified constrained area can be set arbitrarily.Based on this method,a finite time tracking controller of prescribed performance is designed.This controller can not only guarantee the steady-state performance of the system,but also ensure the good dynamic performance of the system under the condition of bounded stability.Moreover,the constrained variables of the system are constrained by the prescribed performance function in the prescribed region within the given settling time,and all the signals in the system are bounded stable.Finally,a simulation example is given to verify the effectiveness of the proposed control strategy.2.The adaptive prescribed performance finite-time bounded-H∞ tracking control problem for a class of nonlinear systems with external disturbances is studied.However,the general H∞ control method requires that the system must be asymptotically stable.Therefore,combined with the prescribed finite-time control,an adaptive prescribed bounded-H∞ control method is proposed for the nonlinear system with external disturbances in this thesis,and the design of H∞ controller only requires the system to achieve bounded stability conditions.In the control design,the radial basis neural network is used to deal with the packaged unknown nonlinear function.Through the mathematical processing method,the singularity problem is solved when designing the finite-time controller,and the rationality of the finite-time control design is guaranteed.At the same time,a new error conversion function is proposed to simplify the design process of bounded-H∞ control.The proposed control method ensures that the system has good suppression performance against external disturbances,so that the system can obtain good tracking performance,and all the signals in the system are bounded stable.The effectiveness and superiority of the proposed control method are verified by simulation.