不确定混沌系统有限时间自适应终端滑模控制  

Finite-Time Adaptive Terminal Sliding Mode Control of Chaotic Systems with Uncertain Parameters

作　　者：江道根[1] 江维 吕龙进 李均恒[1] JIANG Dao-gen;JIANG Wei;LV Long-jin;LI Jun-heng(School of Information and Intelligent Engineering,Ningbo City College of Vocational Technology,Ningbo 315100,China;School of Mechanical Engineering and Automation,Wuhan Textile University Wuhan 430200,China;College of Finance Information,Ningbo University of Finance Economics,Ningbo 315302,China)

机构地区：[1]宁波城市职业技术学院信息与智能工程学院,浙江宁波315100 [2]武汉纺织大学机电工程与自动化学院,湖北武汉430200 [3]宁波财经学院金融与信息学院,浙江宁波315302

出　　处：《数学的实践与认识》2021年第20期93-106,共14页Mathematics in Practice and Theory

基　　金：国家自然科学基金优秀青年科学基金(11801288);宁波城市职业技术学院重点科技课题(ZZX20105)。

摘　　要：运用一种新型积分终端自适应滑模控制理论,并结合有限时间控制方法,解决了不确定性和参数未知且带干扰的主从混沌系统的同步问题.首先,设计出新型积分终端滑模面,确保不确定性主从混沌误差系统在有限时间内收敛至平衡点;其次,针对系统未知参数和界已知的外部干扰,设计出自适应控制律,在线估计出参数项和干扰项,以此消除其对系统的同步影响;再次,为抑制滑模控制所固有抖振的缺陷,在控制律中将一种高增益开关函数(s/|s|+ξ)代替传统的开关函数(sign (s))从而实现控制量的光滑弱抖振并达到主从混沌系统高品质同步控制目标;最后,通过Lorenz系统和Liu系统的数值仿真,结果表明不确定性主从混沌同步误差在有限时间内收敛到零并且控制具备一定鲁棒性,从而验证出所运用控制方法的有效可行性.Based on finite time control theory,a new type of integral terminal adaptive sliding mode control method is adopted to solve the uncertainty synchronization problem of master-slave chaotic system with unknown parameters and disturbance.Firstly,a new integral terminal sliding surface is designed to ensure the uncertain master-slave chaotic error system converges to the equilibrium point in finite time;Secondly,a self-adaptive control law is designed for the known bounds external disturbances and unknown parameters,the parameters and disturbances are estimated on-line to eliminate their synchronization effects on the system;Thirdly,in order to suppress the inherent chattering defect of sliding mode control,a high gain switching function is used to replace the traditional switching function in the control law,so as to attenuate chattering of sliding mode control variables and achieve the goal of high quality synchronization control of master-slave chaotic system;Finally,the numerical simulation of Lorenz system and Liu system is carried out,the results show that the uncertainty master-slave chaos synchronization error converges to zero in finite time and the control has a certain robustness,which verifies the effectiveness and feasibility of the control method.

关 键 词：不确定混沌系统同步 参数辨识 有限时间 自适应终端滑模控制 

分 类 号：O415.5[理学—理论物理] O231[理学—物理]