CAJ | 학술논문

针对于具有初始状态不确定性的非线性时不变系统,采用矩形脉冲信号补偿传统的比例微分型一阶和二阶迭代学习控制律.在Lebesgue-p范数度量跟踪误差意义下,利用卷积的推广的Young不等式分析学习控制律的跟踪性能.分析表明,在适当选取比例学习增益,微分学习增益和非线性状态函数的Lipschitz常数以保证收敛因子小于1的前提下,渐近跟踪误差是由初始状态不确定性引起的,而且可通过调节补偿因子予以消减.数值仿真验证了补偿策略的有效性和理论分析的正确性.
침대우구유초시상태불학정성적비선성시불변계통,채용구형맥충신호보상전통적비례미분형일계화이계질대학습공제률.재Lebesgue-p범수도량근종오차의의하,이용권적적추엄적Young불등식분석학습공제률적근종성능.분석표명,재괄당선취비례학습증익,미분학습증익화비선성상태함수적Lipschitz상수이보증수렴인자소우1적전제하,점근근종오차시유초시상태불학정성인기적,이차가통과조절보상인자여이소감.수치방진험증료보상책략적유효성화이론분석적정학성.
A type of rectangular pulse is adopted to compensate for conventional proportional-derivative-type firstorder and second-order iterative learning controllers of nonlinear time-invariant systems with initial state uncertainty,The tracking error is measured in the form of Lebesgue-p norm and the tracking performance is analyzed by the technique of generalized Young inequality of convolution integral.The analysis shows that the asymptotical tracking error is incurred by the initial state uncertainty and can be eliminated by tuning the compensation gain in the presuppose that the proportional and derivative learning gains together with the Lipschitz constant of the nonlinear state function are properly chosen to guarantee that convergence factor is less than one.Numerical simulations exhibit the validity of the theoretical derivation and the effectiveness of the compensation strategy.