This study investigates the trajectory tracking problem for stochastic systems and proposes a novel adaptive gain design to enhance the transient convergence performance of the learning control scheme. Differing from the existing results that mainly focused on gain’s transition from constant to decreasing ones to suppress noise influence, this study leverages the adaptive mechanisms based on noisy signals to achieve an acceleration capability by addressing diverse performance at different time instants throughout the operation interval. Specifically, an additional gain matrix is introduced into the adaptive gain design to further enhance transient convergence performance. An iterative learning control approach with such a gain design is proposed to realize high precision tracking and it is proven that the input error generated by the newly proposed learning control scheme converges almost surely to zero. The effectiveness of the proposed scheme and its improvement on the transient performance of the learning process are numerically validated.

中文翻译：

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随机学习控制中的加速自适应增益设计


本研究研究了随机系统的轨迹跟踪问题，并提出了一种新颖的自适应增益设计，以增强学习控制方案的瞬态收敛性能。与现有的主要关注增益从恒定到递减的转变以抑制噪声影响的结果不同，本研究利用基于噪声信号的自适应机制，通过解决整个操作间隔中不同时刻的不同性能来实现加速能力。具体来说，在自适应增益设计中引入了额外的增益矩阵，以进一步增强瞬态收敛性能。提出了一种采用这种增益设计的迭代学习控制方法来实现高精度跟踪，并证明新提出的学习控制方案产生的输入误差几乎肯定会收敛到零。该方案的有效性及其对学习过程瞬态性能的改进得到了数值验证。