Pulse compensated iterative learning control to nonlinear systems with initial state uncertainty
具有初始状态不确定性的非线性系统脉冲补偿迭代学习控制

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.