This paper considers control protocol design for a class of discrete-time uncertain nonlinear systems with random iteration-varying trial length (RIVTL), where the input–output coupling parameter (IOCP) and the gain matrix of the system input are assumed to be unknown. Firstly, we prove that the control system either has complete learning ability or has no learning ability. And the learning ability is merely dependent on the IOCP. Secondly, by using the repetitiveness of the control system, a data-based observer is proposed to overcome the obstacle arising from the unknown IOCP and the unknown input matrix. Thirdly, a discrete-type random step function is utilised to model the RIVTL. Then, we develop a joint control protocol that is composed of a successive iterative learning scheme and a current state feedback, where iterative learning part is used to guarantee the convergence and state feedback part is used to improve the transient tracking performance. Finally, an example is delivered to validate the effectiveness of the findings.

中文翻译：

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一类具有迭代变化试验长度的不确定非线性系统的联合控制协议

本文考虑了一类具有随机迭代变化试验长度 (RIVTL) 的离散时间不确定非线性系统的控制协议设计，其中输入输出耦合参数 (IOCP) 和系统输入的增益矩阵被假定为未知. 首先，我们证明控制系统要么具有完全学习能力，要么没有学习能力。而学习能力仅仅依赖于IOCP。其次，利用控制系统的重复性，提出了一种基于数据的观测器来克服未知IOCP和未知输入矩阵带来的障碍。第三，利用离散型随机阶跃函数对 RIVTL 进行建模。然后，我们开发了一个由连续迭代学习方案和当前状态反馈组成的联合控制协议，其中迭代学习部分用于保证收敛，状态反馈部分用于提高瞬态跟踪性能。最后，提供了一个例子来验证结果的有效性。