| In recent years,the control theory based on intelligence and automation has been widely used in military,aerospace,education,industry and other fields,which has attracted more and more scholars’ attention.However,the traditional linear control theory has been difficult to meet the requirements of the development of the times for the control performance of the system,mainly because most of the actual systems are nonlinear in nature,such as mechanical arms,inverted pendulum and chaotic systems.In addition,some industrial control processes need to achieve high-performance time response to match certain quality or safety standards.For example,the shorter the time required for voltage and frequency to converge to the nominal value,the smaller the chance of accident propagation,and the smaller the economic loss.In addition,some missions are time critical,such as rescue,reconnaissance and attack.If these tasks cannot be completed within the specified time,they will face failure.Therefore,the predefined time(PT)control of nonlinear systems has become a research hotspot of scholars at home and abroad,and has made significant progress,but there are still many problems to be solved.Based on the above discussion,the adaptive PT control algorithm for nonlinear systems is studied.The specific research contents are as follows:(1)An adaptive fuzzy PT and precision control algorithm is proposed for a class of strict feedback nonlinear systems with functional uncertainties.First,based on the definition of PT stability,a sufficient condition is given to determine whether the tracking error converges to a given region in a PT.Then,based on the proposed stability criterion,an adaptive fuzzy controller is proposed using the backstepping recursive technique,and the stability time and convergence accuracy of the tracking error can be preset,which promotes the engineering application requiring convergence accuracy and time.In particular,in order to minimize chattering and energy consumption while ensuring stability,an inequality is introduced to construct a continuous term to replace the sign function.Finally,a practical example is used to verify the effectiveness of the main results.(2)An adaptive controller is designed to solve the PT synchronization problem of neural networks with different dimensions affected by time-varying delays and unknown parameters.A sufficient condition is given,which can judge whether the synchronization error can converge to sufficiently small region in a user-defined time.Based on Lyapunov-Krasovskii function,the proposed controller combined with parameter update laws can complete the synchronization task.In addition,the proposed control method avoids the singular problem in the existing results.Apart from theoretical analysis,a numerical simulation is given to verify the effectiveness of the proposed method,and comparative experiments are made to show its advantages. |
