非线性多输入多输出连续时间系统基于历史采样数据的不确定性因素补偿控制  

Sampled-data-based uncertainty compensation control for a class of continuous-time nonlinear MIMO systems

作　　者：姚慧颖 赵志良 陈森 柴天佑 Huiying YAO;Zhiliang ZHAO;Sen CHEN;Tianyou CHAI(School of Mathematics and Statistics,Shaanxi Normal University,Xi'an 710119,China;State Key Laboratory of Synthetical Automation for Process Industries,Northeastern University,Shenyang 110819,China)

机构地区：[1]陕西师范大学数学与统计学院,西安710119 [2]东北大学流程工业综合自动化国家重点实验室,沈阳110819

出　　处：《中国科学：信息科学》2022年第3期483-505,共23页Scientia Sinica(Informationis)

基　　金：国家自然科学基金项目(批准号:61973202,62003202);流程工业综合自动化国家重点实验室联合项目(批准号:2019-KF-23-09)资助。

摘　　要：本文针对一类具有强耦合不确定性因素的连续时间多输入多输出非线性系统,提出了基于历史采样数据的不确定性因素补偿控制策略(sampled-data-based compensation control,SDBCC).与基于观测器的不确定性因素补偿控制不同,本文首先利用当前以及历史采样数据计算出由系统非线性耦合未建模动态和外部扰动构成的总扰动在前一采样周期内某时刻的精确值,然后利用该精确值在反馈环节对总扰动进行补偿以消除它的不利影响.连续时间系统在数据驱动的反馈控制作用下构成了一个混杂闭环控制系统,这连同系统的强耦合非线性不确定性因素为控制闭环系统的稳定性收敛性分析带来了挑战.为克服这一难题,本文发展了基于特征值和迭代序列的分析方法,证明了当系统跟踪目标为有界函数时,跟踪误差可随采样周期的减小而任意小,进而当跟踪目标为常数,并且系统的非线性项为时不变连续可微函数时,跟踪误差随时间趋于无穷大而趋近于零.二自由度无人机姿态控制的仿真结果验证了本文所提出方法的有效性和优越性.This paper proposes a sampled-data-based uncertainty compensation control strategy for a class of continuous-time multi-input multi-output nonlinear systems with strong coupling uncertainties.Unlike observerbased uncertainty compensation control methods,this paper utilizes the true value of the total disturbance at an instant in the previous sampling interval rather than its observed value in the last sampling time to compensate for the total disturbance.The total disturbance considered in this paper is composed of the unmodeled nonlinear coupling dynamics and external disturbance.The continuous-time systems and the sampled-data feedback control make up a hybrid closed-loop control system,which,together with the strongly coupled nonlinear uncertainties of the system,brings a significant hurdle to verifying the stability and convergence of the closed-loop control system.A new eigenvalue-and-series-based analysis method is proposed to overcome this hurdle.It is proved that when the tracking target is a bounded function,the tracking error can be arbitrarily small when the sampling period is small enough.Furthermore,when the tracking target is a constant and the nonlinear term is time-invariant,the tracking error converges to zero as time tends to infinity.Numerical results on the attitude control for a 2-DOF UAV validate the effectiveness and merits of the proposed method.

关 键 词：不确定性 非线性 MIMO 系统 PID 控制 数据驱动控制 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]