基于迭代扩张状态观测器的数据驱动最优迭代学习控制

针对一类带扰动有限时间内重复运行的离散时间非线性非仿射不确定系统,本文提出了一种基于迭代扩张状态观测器的数据驱动最优迭代学习控制方法.首先,提出了改进的迭代动态线性化方法,将被控系统线性化为与控制输入有关的仿射形式,并将不确定性合并到一个非线性项中;然后,设计了迭代扩张状态观测器对非线性不确定项进行估计,作为对扰动的补偿;最后,设计了性能指标函数,通过最优技术,提出了参数迭代更新律和最优学习控制律.本文通过数学分析,证明了跟踪误差的有界收敛性.仿真结果验证了方法的有效性.所提出的新型迭代动态线性化方法可很大程度上降低线性化后的控制增益的动态复杂性,使其易于估计.所提出的迭代扩张状态观测器可以在重复中学习,对非重复扰动可进行有效的估计.此外,本文控制器的设计与分析是数据驱动的控制方法,除了被控系统的输入输出数据以外,不需要任何其他模型信息.

Iterative extended state observer based data driven optimal iterative learning control

In this work, an iterative extended state observer based data-driven optimal iterative learning control is proposed for a class of nonlinear non-affine discrete-time system with exogenous disturbances and operated repetitively over a finite time interval. First, a modified iterative dynamic linearization method is proposed to linearize the controlled system into an affine form related to control input, where the uncertainties are incorporated into a nonlinear term; second, an iterative extended state observer is developed to estimate the nonlinear uncertainty term as a compensation for the disturbances; finally, both a parameter iterative updating law and an optimal learning control law are proposed via the optimization technique by designing two objective functions. The bounded convergence of tracking error is proved rigorously through mathematical analysis. Simulation results have been provided to verify the effectiveness of the proposed method. The proposed new iterative dynamic linearization method can reduce the dynamic complexity of the linearized control gain greatly such that it easy to be estimated. The proposed iterative extended state observer can learn from repetitions, and thus estimate the non-repetitive disturbances effectively. Moreover, the controller design and analysis in this work are data driven, depending on the input-and-output data only without using other explicit model information.